Glossary

The standard symbol (B) used to represent the magnetic field.

an electrical circuit containing a resistor (R), an inductor (L), and a capacitor (C)

The component of orbital angular momentum measured along the selected z-axis, given by [latex]L_z=m_l\frac{h}{2\pi}[/latex].

The component of an electron's intrinsic spin measured along the z-axis, given by [latex]S_z=m_s\frac{h}{2\pi}[/latex].

An optical imperfection that prevents all light rays from converging at a single focus, resulting in image blur, distortion, or other departures from ideal image formation.

The amount of energy deposited by ionizing radiation per unit mass of material. The SI unit is the gray (Gy).

a current that varies sinusoidally with time, commonly described by
[latex]I=I_0\sin(2\pi ft),[/latex]
where [latex]I_0[/latex] is the peak current and [latex]f[/latex] is the frequency

a voltage that varies sinusoidally with time, commonly described by
[latex]V=V_0\sin(2\pi ft),[/latex]
where [latex]V_0[/latex] is the peak voltage and [latex]f[/latex] is the frequency

the process by which the eye changes the shape of its lens to adjust its focal length and keep objects at different distances in sharp focus on the retina

A rotating disk of gas, dust, or other matter that spirals inward toward a massive object such as a black hole, often becoming hot enough to emit X-rays.

The rate at which radioactive nuclei decay, usually measured in becquerels (Bq) or curies (Ci).

A collection of health effects caused by exposure to a high dose of ionizing radiation over a short period of time. Symptoms may include nausea, vomiting, fatigue, decreased blood cell counts, infections, and organ damage.

A technology that uses computer-controlled mirrors or lenses to compensate for distortions caused by Earth's atmosphere or other optical imperfections, producing sharper images.

An acronym for As Low As Reasonably Achievable, the guiding principle of radiation protection that seeks to minimize unnecessary radiation exposure while achieving the intended medical or scientific objective.

A type of radioactive decay in which a nucleus emits an alpha particle ([latex]{}^{4}\mathrm{He}[/latex] nucleus).

A positively charged particle consisting of two protons and two neutrons emitted during certain types of radioactive decay. Alpha particles have high ionizing power but very limited penetration.

One of the three principal types of nuclear radiation. Alpha radiation consists of helium nuclei emitted from unstable atomic nuclei.

electric current that periodically reverses direction, typically varying sinusoidally with time

an instrument that measures current

The SI unit of electric current. One ampere is equal to one coulomb of charge passing a point each second ([latex]1\ \text{A}=1\ \text{C/s}[/latex]).

Historically defined as the current that, when flowing through each of two infinitely long parallel conductors separated by 1 m in vacuum, produces a magnetic force of exactly
[latex]2.0\times10^{-7}\ \text{N/m}[/latex]
between the conductors.

A law that relates electric current to the magnetic field it produces. It states that the total magnetic field generated by a current-carrying conductor is the combined contribution of all current segments.

The maximum magnitude of a wave's oscillation relative to its equilibrium value.

a method of transmitting information by varying the amplitude of a carrier wave while keeping its frequency constant

a measuring instrument that gives a readout in the form of a needle movement over a marked gauge

A medical imaging device, also called a gamma camera, that detects gamma rays emitted by radiopharmaceuticals and converts them into images.

the angle between an incoming light ray and the normal (perpendicular) to the surface at the point of incidence

the angle between a reflected light ray and the normal to the surface, equal to the angle of incidence

The factor by which a telescope increases the apparent angular size of a distant object. For a simple telescope,

[latex]M=-\frac{f_{\mathrm{o}}}{f_{\mathrm{e}}}[/latex]

where [latex]f_{\mathrm{o}}[/latex] is the focal length of the objective and [latex]f_{\mathrm{e}}[/latex] is the focal length of the eyepiece.

The quantum number [latex]l[/latex] that determines the magnitude of an electron's orbital angular momentum and is related to the shape of an atomic orbital. For a given principal quantum number, the allowed values are [latex]l=0,1,\ldots,n-1[/latex].

A process in which a particle and its antiparticle interact and convert their energy into other particles, often photons.

Another name for a positron, the antimatter counterpart of the electron.

Matter composed of antiparticles, which have the same mass as ordinary particles but opposite electric charge and certain other quantum properties.

A particle with the same mass and intrinsic spin as another particle but opposite electric charge and other opposite quantum numbers.

A refractive error caused by unequal focusing of light in different directions, usually due to an irregularly shaped cornea or, less commonly, an irregular crystalline lens.

The basic unit of an element that retains that element's chemical properties. An atom consists of a small, positively charged nucleus surrounded by negatively charged electrons.

The process by which an excited atom returns to a lower-energy state, often accompanied by the emission of one or more photons.

The process by which an atom or ion absorbs energy, promoting one or more electrons from the ground state to higher-energy electronic states.

The total mass of an atom, including its protons, neutrons, and electrons.

The number of protons in an atomic nucleus, represented by the symbol [latex]Z[/latex]. The atomic number uniquely identifies an element.

The number of protons in the nucleus of an atom. For a neutral atom, this is also equal to the number of electrons.

A region around the nucleus where there is a high probability of finding an electron. In modern quantum mechanics, electrons are described by probability distributions rather than fixed circular paths.

The characteristic pattern of electromagnetic radiation emitted or absorbed by atoms as electrons transition between allowed energy levels.

The magnetic force that occurs between two parallel conductors when the currents flow in the same direction, causing the wires to pull toward one another.

A hypothetical elementary particle proposed as one possible candidate for dark matter.

The transmission direction of a polarizing filter. Only the component of the electric field parallel to this axis passes through the filter.

the emf generated by a rotating motor as its coils move through a magnetic field. According to Lenz's law, this induced emf opposes the applied voltage that powers the motor, reducing the current drawn as the motor speeds up.

Ionizing radiation naturally present in the environment from cosmic rays, naturally occurring radioactive materials in the Earth, radon gas, and radioactive isotopes within the human body.

A quantum mechanical process in which a particle has a finite probability of passing through a potential energy barrier despite having less energy than the barrier height. Also called quantum tunneling.

A hadron composed of three quarks. Protons and neutrons are baryons.

A conserved quantum number represented by [latex]B[/latex]. Baryons have [latex]B=+1[/latex], antibaryons have [latex]B=-1[/latex], and leptons and mesons have [latex]B=0[/latex].

The microscopic theory that explains conventional superconductivity through the formation of Cooper pairs.

The SI unit of radioactivity, equal to one radioactive decay per second.

A class of radioactive decays in which a nucleus emits an electron, a positron, or captures an orbital electron.

One of the three principal types of nuclear radiation. Beta radiation consists of high-speed electrons emitted during certain types of radioactive decay.

The scientific model stating that the observable universe began approximately 13.8 billion years ago in an extremely hot, dense state and has been expanding and cooling ever since.

The energy required to completely separate a nucleus into its individual protons and neutrons. It is equal to the mass defect multiplied by [latex]c^2[/latex].

The minimum energy required to remove an electron from the surface of a material.

The total binding energy of a nucleus divided by its number of nucleons, [latex]\mathrm{BE}/A[/latex]. It indicates how tightly the average proton or neutron is bound within the nucleus and provides a useful measure of nuclear stability.

the study of electrical phenomena produced by or occurring within living organisms

A mathematical law that describes the magnetic field produced by a small segment of electric current. It forms the basis for calculating magnetic fields generated by conductors of any shape.

The optical property of certain materials that causes an incoming beam of light to split into two rays with perpendicular polarizations that travel at different speeds within the material.

An object whose gravitational field is so strong that nothing, including light, can escape from within its event horizon.

An ideal radiator that absorbs all incident electromagnetic radiation and emits the maximum possible radiation at every wavelength.

The electromagnetic radiation emitted by a blackbody. Its spectrum depends only on the object's temperature.

A rapidly moving region of extremely high pressure produced by an explosion that can damage structures and cause traumatic injuries.

A decrease in the observed wavelength and a corresponding increase in frequency when a source of electromagnetic radiation moves toward an observer.

An early model of the atom in which electrons occupy specific circular orbits with quantized energies and angular momentum.

The radius of the lowest-energy (ground-state) electron orbit in a hydrogen atom, equal to [latex]0.529\times10^{-10}\ \text{m}[/latex].

A specialized form of radiation therapy in which a boron-containing drug accumulates in tumor cells before irradiation with low-energy neutrons. The neutron capture reaction produces high-energy particles that destroy cancer cells while minimizing damage to surrounding healthy tissue.

A particle with integer intrinsic spin. Bosons do not obey the Pauli exclusion principle.

a quark flavor

A form of radiation therapy in which sealed radioactive sources are placed inside or near a tumor to deliver a high radiation dose directly to the treatment area.

The condition for constructive interference when waves scatter from regularly spaced planes in a crystal:
[latex]n\lambda=2d\sin\theta.[/latex]

The constructive interference of waves scattered from parallel atomic planes in a crystal. It occurs only at angles that satisfy the Bragg equation.

The condition in which a fusion plasma produces as much fusion power as the external heating power supplied to it.

A nuclear reactor designed to convert fertile isotopes, such as [latex]{}^{238}\mathrm{U}[/latex], into fissile fuel such as [latex]{}^{239}\mathrm{Pu}[/latex] through neutron capture and subsequent radioactive decay.

The process of producing a new fissile isotope by nuclear transformation. An important example is the conversion of uranium-238 into plutonium-239 inside a nuclear reactor.

German for braking radiation; the continuous spectrum of X-rays produced when energetic electrons are rapidly decelerated in matter.

The angle of incidence at which the reflected light is completely linearly polarized. It is given by

[latex]\theta_b=\tan^{-1}\left(\frac{n_2}{n_1}\right).[/latex]

The relationship that determines Brewster's angle:

[latex]\tan\theta_b=\frac{n_2}{n_1},[/latex]

where [latex]n_1[/latex] is the refractive index of the incident medium and [latex]n_2[/latex] is the refractive index of the transmitting medium.

A circuit configuration that compares two branches of a network. Bridge circuits are commonly used for high-precision electrical measurements, including many null measurement techniques.

The continuous random motion of microscopic particles suspended in a liquid or gas, caused by countless collisions with surrounding atoms or molecules.

Stationary electrical contacts that transfer current between the external circuit and the rotating commutator of a motor.

The amount of electric charge stored per unit potential difference; mathematically, [latex]C=Q/V[/latex].

The opposition that a capacitor presents to alternating current. It is measured in ohms and is calculated using
[latex]X_C=\frac{1}{2\pi fC}[/latex].
Capacitive reactance decreases as either the frequency or the capacitance increases.

A device that stores electrical energy by separating equal amounts of positive and negative charge on two conductors.

A set of capacitors connected across the same two nodes of a circuit so that each has the same voltage while the total charge is shared among them.

A set of capacitors connected end-to-end so that each stores the same magnitude of charge while the total voltage is divided among them.

A radiometric dating technique that estimates the age of once-living materials by measuring the remaining amount of carbon-14.

A particle associated with the transmission or mediation of one of the fundamental interactions.

an electromagnetic wave whose amplitude or frequency is modulated to carry information

A vacuum tube that produces a beam of electrons. Cathode-ray tubes were used to investigate the properties of electrons and were later widely used in televisions, computer monitors, and scientific instruments.

The brightest and widest region of a single-slit diffraction pattern, located at [latex]\theta=0[/latex], where all portions of the wavefront interfere constructively.

The inward force required to keep an object moving in a circular path. For a charged particle in a magnetic field, the magnetic force provides the centripetal force.

A self-sustaining sequence of nuclear reactions in which neutrons released by one fission event trigger additional fission reactions.

The behavior of a deterministic system that is extremely sensitive to its initial conditions, making long-term prediction difficult.

The characteristic time, denoted by [latex]\tau[/latex], that describes how quickly current increases or decreases in an RL circuit. It is given by
[latex]\tau=\frac{L}{R}[/latex],
where [latex]L[/latex] is the inductance and [latex]R[/latex] is the resistance. After one time constant, the current has reached about 63.2% of its final value when increasing, or decreased to about 36.8% of its initial value when decreasing.

X-rays emitted when electrons in an atom transition between inner electron shells; their energies are characteristic of the target material.

the process of charging an object without direct contact by using charge separation and, when necessary, grounding

a quark flavor, which is the counterpart of the strange quark

A graphical arrangement of stable and unstable nuclei according to their numbers of protons and neutrons.

an optical distortion in which different wavelengths are focused at different positions, producing colored fringes or a blurred image

the outer layer of an optical fiber, which has a lower index of refraction than the core and keeps light confined by total internal reflection

The method used to combine velocities when all speeds are much smaller than the speed of light. For one-dimensional motion,

[latex]u=v+u',[/latex]

where [latex]v[/latex] is the relative velocity between two observers, [latex]u'[/latex] is the velocity of an object measured by one observer, and [latex]u[/latex] is the velocity measured by the other observer.

Describes waves that have the same frequency and maintain a constant phase relationship with one another.

The simultaneous detection of two gamma rays emitted during positron-electron annihilation, allowing PET scanners to determine the line along which the annihilation occurred.

Two beams of particles traveling in opposite directions that collide head-on, allowing much more of the beam energy to be converted into the creation of new particles.

A thick lead plate containing many small holes that allows only gamma rays traveling in selected directions to reach the detector, improving image resolution.

a quark flavor

The property of quarks and gluons that produces the strong interaction. It is unrelated to visible color.

The ability of the visual system to perceive the true color of an object even when the color of the illuminating light changes.

A split-ring electrical switch that reverses the direction of current in a rotating coil every half revolution, allowing a DC motor to continue rotating in the same direction.

A system composed of many interacting components whose collective behavior cannot be understood simply by studying the individual parts.

An optical microscope that uses two or more lens systems—typically an objective lens and an eyepiece—to produce a highly magnified image.

The increase in wavelength and corresponding decrease in energy of a photon when it scatters from a particle such as an electron.

An imaging technique that uses x-rays acquired from multiple angles to produce detailed cross-sectional images of the body. CT typically delivers higher radiation doses than conventional radiography but provides substantially more diagnostic information.

a curved mirror whose reflecting surface bends inward and that can converge parallel rays of light toward a focal point

a material that allows electric charge to move easily through it

Photoreceptor cells in the retina that function best in bright light and provide high-resolution color vision. Humans normally have three types of cones, each sensitive to a different range of visible wavelengths.

A microscope that uses laser illumination, pinholes, and computer image reconstruction to collect light only from the focal plane, producing high-resolution optical sections and three-dimensional images.

Fundamental physical principles stating that certain quantities, such as electric charge and energy, cannot be created or destroyed. Kirchhoff's rules are direct applications of these conservation laws to electrical circuits.

The principle that the total momentum of an isolated system remains constant if no net external force acts on the system.

The reinforcement of two or more waves when their crests and troughs align, producing a wave with greater amplitude. Allowed electron states occur when electron matter waves interfere constructively.

The reinforcement of light from many equally spaced openings or reflecting structures. A principal maximum occurs when [latex]d\sin\theta=m\lambda[/latex], where [latex]d[/latex] is the grating-line spacing, [latex]\theta[/latex] is the diffraction angle, [latex]\lambda[/latex] is the wavelength, and [latex]m[/latex] is an integer representing the interference order.

Interference that produces a bright fringe because the path difference between waves from the two slits is an integer multiple of the wavelength.

The difference in brightness or intensity between an object and its background. High contrast makes structures easier to distinguish in an image.

The direction in which positive charge would move. In metallic conductors, this direction is opposite the motion of electrons.

A convex lens that causes light rays traveling parallel to its principal axis to converge at a focal point on the opposite side of the lens.

a concave mirror that reflects rays traveling parallel to its principal axis so that they converge near a focal point in front of the mirror

a curved mirror whose reflecting surface bulges outward and that produces virtual, upright, reduced images

A weakly bound pair of electrons that moves collectively through a superconductor without electrical resistance.

an optical device consisting of two mutually perpendicular reflecting surfaces that returns light parallel to its original direction

The principle stating that quantum mechanics approaches the predictions of classical physics in the limit of large objects or large quantum numbers.

The faint microwave radiation that fills the universe, originating about 380,000 years after the Big Bang when neutral atoms first formed and light was able to travel freely through space.

A term in Einstein's equations of general relativity that represents a uniform energy density filling space and is the simplest explanation for dark energy.

The increase in the wavelength of light caused by the expansion of space as light travels through the universe.

The branch of physics and astronomy that studies the origin, evolution, structure, and large-scale properties of the universe.

another name for the electrostatic force between charged objects

the attractive or repulsive interaction between charged particles caused by the electrostatic, or Coulomb, force

the physical law that describes the magnitude of the electrostatic force between two point charges

the angle of incidence that produces an angle of refraction of [latex]90^\circ[/latex]; for larger incident angles, total internal reflection occurs

The average density of matter and energy required for a spatially flat universe.

The minimum amount of fissile material required to sustain a nuclear chain reaction under specified conditions.

The temperature below which a material becomes superconducting.

The operating condition in which a nuclear chain reaction is self-sustaining because each fission event produces, on average, one additional fission.

A traditional unit of radioactivity equal to [latex]3.70\times10^{10}[/latex] decays per second, or [latex]3.70\times10^{10}[/latex] Bq.

The temperature above which a ferromagnetic material loses its strong magnetic properties because thermal motion disrupts the alignment of its magnetic domains.

the rate at which electric charge flows through a circuit, measured in amperes (A)

the maximum current that a galvanometer can read

A circular particle accelerator that uses a constant magnetic field and an alternating electric field to accelerate charged particles along an outward spiral path.

An unknown form of energy that appears to be responsible for the accelerating expansion of the universe.

A form of matter that does not emit, absorb, or reflect light but whose presence is inferred from its gravitational effects on visible matter and the large-scale structure of the universe.

The nucleus produced when a radioactive parent nucleus undergoes nuclear decay.

The wavelength associated with any particle that has momentum, given by
[latex]\lambda=\frac{h}{p}[/latex],
where [latex]h[/latex] is Planck's constant and [latex]p[/latex] is the particle's momentum. The de Broglie wavelength describes the wave-like behavior of matter and becomes significant for microscopic particles such as electrons, neutrons, and atoms.

The spontaneous transformation of an unstable atomic nucleus into a more stable configuration through the emission of particles or electromagnetic radiation.

A constant that characterizes the probability of radioactive decay and is related to the half-life by [latex]\lambda=0.693/t_{1/2}[/latex].

A nuclear equation showing the parent nucleus, the emitted particles, and the daughter nucleus produced during radioactive decay.

A sequence of radioactive decays in which one unstable daughter nucleus decays into another until a stable nucleus is produced.

A medical device that stores electrical energy in a capacitor and delivers a controlled electrical shock to help restore a normal heart rhythm during certain cardiac emergencies.

The cancellation of waves when the crest of one wave overlaps the trough of another. Electron states that produce destructive interference are not allowed.

Interference that produces a dark fringe because the path difference between waves from the two slits is an odd half-integer multiple of the wavelength.

The condition in which light from different parts of a single slit completely cancels because the path difference equals an integer multiple of the wavelength. Diffraction minima occur when [latex]D\sin\theta=m\lambda[/latex], where [latex]D[/latex] is the slit width, [latex]\theta[/latex] is the diffraction angle, [latex]\lambda[/latex] is the wavelength, and [latex]m=\pm1,\pm2,\pm3,\ldots[/latex].

A biological effect of radiation that occurs only after a threshold dose has been exceeded and becomes more severe as dose increases. Examples include skin burns and cataracts.

A material that absorbs one polarization of light more strongly than the perpendicular polarization. Modern polarizing filters operate using this principle.

An insulating material placed between the plates of a capacitor that increases its capacitance and helps prevent electrical breakdown.

The maximum electric field a material can withstand before it begins to break down and conduct electricity.

The bending and spreading of a wave as it passes around the edge of an obstacle or through an opening whose size is comparable to the wavelength.

An optical element containing a large number of equally spaced parallel openings, grooves, or reflecting structures that separate light into different wavelengths through diffraction and interference.

A dark region in a diffraction pattern where destructive interference causes the light intensity to fall essentially to zero.

reflection from a rough surface that scatters light in many directions, allowing an object to be seen from many viewing angles

a measuring instrument that gives a readout in a digital form

a separation of positive and negative charge within a neutral atom or molecule

electric current that flows in only one direction

The direction a north-seeking compass needle points when placed in the magnetic field.

The direction of the electric field oscillation in a linearly polarized electromagnetic wave.

the separation of light into its component wavelengths because different wavelengths travel or refract differently in a material

A concave lens that causes parallel light rays to spread apart, appearing to originate from a focal point on the same side of the lens as the incoming light.

a convex mirror that reflects parallel rays so that they spread apart and appear to originate from a focal point behind the mirror

A device worn by radiation workers to measure and record accumulated occupational radiation exposure.

An interference phenomenon produced when waves or particles passing through two closely spaced openings combine to form alternating bright and dark regions due to constructive and destructive interference.

the second-lightest of all quarks

The average velocity of charge carriers as they move through a material in response to an electric field.

a circulating current induced within a conductor when the magnetic flux through the conductor changes, such as when the conductor moves through a magnetic field or the magnetic field changes over time

A measure of radiation exposure that accounts for both the type of radiation and the varying sensitivities of different tissues. The SI unit is the sievert (Sv).

A nearly circular image of a distant object produced when the source, a massive gravitational lens, and the observer are closely aligned.

a fundamental property of matter that causes objects to experience electric forces of attraction or repulsion

The rate at which electric charge flows through a conductor, defined by [latex]I=\Delta Q/\Delta t[/latex].

a vector field that gives the electric force per unit positive test charge at each point in space

imaginary lines used to represent the direction and relative strength of an electric field; the field is tangent to the lines at every point

The magnitude of the electric field vector, represented by [latex]E[/latex] and commonly measured in volts per meter (V/m) or newtons per coulomb (N/C).

a device that converts mechanical energy into electrical energy by inducing an emf as a coil rotates in a magnetic field

The electric potential energy per unit charge at a given point in an electric field. It is commonly called voltage and is measured in volts (V).

The electric potential produced by an isolated point charge, given by V = kQ/r, where the potential is defined to be zero at infinity.

The rate at which electrical energy is transferred, supplied by a source, or converted by an electrical device. It is measured in watts (W) and is given by the product of current and voltage, [latex]P=IV[/latex].

a recording of the voltage changes produced by the depolarization and repolarization of the heart, used to evaluate cardiac electrical activity

A magnet whose magnetic field is produced by an electric current and can be controlled by changing or switching off the current.

one of the four fundamental forces of nature, responsible for electric and magnetic interactions, chemical bonding, and many of the forces encountered in biology, chemistry, and everyday life

The process by which a changing magnetic field produces an electromotive force (emf) and, if a conducting path is present, an electric current.

the complete range of wavelengths or frequencies of electromagnetic radiation

a self-propagating wave consisting of oscillating electric and magnetic fields that can travel through a vacuum or through matter

The branch of physics that studies the relationship between electric charges, electric currents, and magnetic fields.

the maximum potential difference provided by a voltage source when no current is flowing; measured in volts

a negatively charged subatomic particle that occupies the region surrounding an atomic nucleus

The antimatter counterpart of the electron neutrino, emitted during beta-minus decay.

A stream of high-energy electrons produced by a particle accelerator and used for food irradiation and sterilization.

A form of beta decay in which a proton-rich nucleus captures an inner-shell electron, converting a proton into a neutron while emitting an electron neutrino.

The nuclear equation representing an electron-capture reaction.

A probability distribution that describes where an electron is most likely to be found around an atomic nucleus.

The arrangement of electrons among an atom's shells and subshells, usually written using spectroscopic notation.

The interference pattern produced when electrons scatter from structures whose spacing is comparable to the electrons' de Broglie wavelength. Electron diffraction provides evidence for the wave nature of matter.

An imaging instrument that uses a beam of electrons rather than visible light. The short wavelengths of electrons allow electron microscopes to resolve much smaller structures than optical microscopes.

An electrically neutral elementary particle emitted during beta-plus decay and electron capture.

A unit of energy equal to the energy gained by a particle carrying one elementary charge when it moves through a potential difference of 1 V. One electron volt equals [latex]1.60\times10^{-19}\ \text{J}[/latex].

the state of a conductor in which free charges have finished redistributing and no longer move

the attractive or repulsive force between electrically charged objects

An air-cleaning device that electrically charges airborne particles and then removes them by attracting them to oppositely charged collecting plates.

the force that causes objects with like electric charges to push away from one another

The study of electric charges at rest, the electric fields they produce, and the forces between them.

The theory that unifies the electromagnetic and weak interactions, showing that they are different manifestations of a single fundamental force at sufficiently high energies.

A large-scale property or pattern that arises from interactions among many components of a system.

the instantaneous emf produced by a rotating coil in a magnetic field, given by
[latex]\text{emf}=\text{NAB}\omega \,\text{sin}(\omega t)[/latex],
where [latex]N[/latex] is the number of turns, [latex]A[/latex] is the area of the coil, [latex]B[/latex] is the magnetic field strength, [latex]\omega[/latex] is the angular velocity, and [latex]t[/latex] is time

The quantized electron energies predicted by Bohr's model, given by [latex]E_n=-\frac{Z^2}{n^2}E_0[/latex], where [latex]E_0=13.6\ \text{eV}[/latex] and [latex]Z[/latex] is the atomic number.

The electrical potential energy stored by separated charges on the plates of a capacitor.

The magnetic energy stored by an inductor carrying current, given by
[latex]E_{\text{ind}}=\frac{1}{2}LI^2.[/latex]

A graphical representation of the allowed energy states of a system, showing the energies of electrons and the transitions responsible for emission and absorption spectra.

A line connecting points that all have the same electric potential. Moving a charge along an equipotential line requires no work because the potential difference is zero.

A three-dimensional surface on which every point has the same electric potential. Electric field lines always intersect an equipotential surface at right angles.

The principle stating that the effects of gravity are locally indistinguishable from the effects of acceleration, forming the foundation of general relativity.

The capacitance of a single capacitor that stores the same amount of charge at the same applied voltage as an entire combination of capacitors.

A measure of radiation dose that accounts for the biological effectiveness of different types of radiation by applying a radiation weighting factor. The SI unit is the sievert (Sv).

The boundary surrounding a black hole beyond which nothing, including light, can escape.

A method of cancer treatment in which radiation is delivered from a machine outside the body and directed toward the tumor.

The second ray produced in a birefringent material. It experiences a different refractive index and does not follow Snell's law in the usual way.

electromagnetic radiation at frequencies of roughly 3 Hz to 3 kHz, commonly used for applications such as communication with submerged submarines

The lens or combination of lenses closest to the observer's eye. It magnifies the intermediate image formed by the objective lens.

Radioactive particles produced during a nuclear explosion that settle from the atmosphere onto Earth's surface, potentially contaminating air, water, soil, and food.

The farthest point from the eye that can be seen clearly when the eye is completely relaxed and not accommodating.

a conducting enclosure that shields its interior from external electric fields

The relationship that gives the induced emf produced by a changing magnetic flux:
[latex]\mathrm{emf}=-N\frac{\Delta\Phi}{\Delta t}.[/latex]

Another term for hyperopia, a refractive error in which nearby objects appear blurred because the eye does not have enough optical power to focus their images on the retina.

A process in which the output of a system influences its future behavior, either amplifying or reducing changes.

A particle with half-integer intrinsic spin. Fermions obey the Pauli exclusion principle.

Describes materials, such as iron, cobalt, nickel, gadolinium, and some rare-earth alloys, that can become strongly magnetized.

A visual and mathematical representation of a particle interaction showing incoming particles, outgoing particles, interaction vertices, and exchanged particles.

A periodic variation in the refractive index of an optical fiber that reflects a narrow range of wavelengths while transmitting other wavelengths.

the use of thin glass or plastic fibers to guide light by total internal reflection for imaging and communication applications

a physical quantity that describes how an object influences the space around it, allowing it to exert forces on other objects at a distance

The splitting of atomic spectral lines into closely spaced components that becomes visible at high spectral resolution.

The extremely hot, expanding region of plasma formed immediately after a nuclear explosion.

The principle stating that the laws of physics are the same and take their simplest form in every inertial frame of reference.

The two smaller daughter nuclei produced when a heavy nucleus undergoes nuclear fission.

A nuclear weapon that releases energy primarily through the uncontrolled fission of heavy atomic nuclei.

a plane reflecting surface that forms a virtual, upright image of the same size as the object and at an equal distance behind the mirror

quark type

The process in which an atom or molecule absorbs a photon of one energy and subsequently emits one or more photons of lower energy.

A microscopy technique in which fluorescent molecules emit light after being excited by a laser or another light source, allowing specific structures within a specimen to be visualized.

A glucose analog labeled with fluorine-18 that is widely used in PET imaging to identify tissues with high metabolic activity.

The distance from the center of a lens to its focal point.

The point where parallel rays converge after passing through a converging lens, or the point from which rays appear to diverge after passing through a diverging lens.

The controlled exposure of food to ionizing radiation to reduce microorganisms, control insects, delay spoilage, or sterilize food products.

The magnetic force per unit length between two long, parallel current-carrying wires separated by a distance
[latex]r[/latex], given by
[latex]\frac{F}{l}=\frac{\mu_0 I_1 I_2}{2\pi r}[/latex].

the small central region of the retina with the highest density of cone photoreceptors, providing the sharpest color vision and greatest visual acuity

The delivery of a prescribed radiation dose over multiple treatment sessions rather than in a single exposure, allowing healthy tissues time to repair between treatments.

an electric charge that can move freely through a material, such as the conduction electrons in a metal

an electron that is not tightly bound to an individual atom and can move freely through a conductor

A highly reactive atom or molecule produced by ionizing radiation that can damage cellular structures, including DNA.

The number of complete wave cycles passing a point each second; measured in hertz (Hz).

a method of transmitting information by varying the frequency of a carrier wave while keeping its amplitude constant

the maximum deflection of a galvanometer needle, also known as current sensitivity; a galvanometer with a full-scale deflection of [latex]\text{50 μA}[/latex] has a maximum deflection of its needle when [latex]\text{50 μA}[/latex] flows through it

particle with no substructure

A nuclear reaction in which light atomic nuclei combine to form heavier nuclei, releasing energy.

A nuclear weapon that uses a fission reaction to initiate nuclear fusion, allowing much larger amounts of energy to be released.

A sensitive analog instrument that measures small electric currents using the torque on a current-carrying coil in a magnetic field.

Another name for an Anger camera.

A nuclear transition in which an excited nucleus emits one or more high-energy gamma-ray photons without changing its atomic or mass number.

([latex]\gamma[/latex] ray) extremely high-frequency electromagnetic radiation emitted by atomic nuclei during radioactive decay or nuclear reactions; gamma rays occupy the highest-energy region of the electromagnetic spectrum

High-energy electromagnetic radiation emitted from an excited atomic nucleus during radioactive decay.

A boson that carries one of the fundamental interactions, such as the photon or the [latex]W[/latex] and [latex]Z[/latex] bosons.

A non-SI unit of magnetic field strength commonly used in some scientific fields. One gauss is equal to [latex]10^{-4}\,\text{T}[/latex].

A gas-filled radiation detector that detects ionizing radiation by collecting the charged particles produced when radiation ionizes the gas inside the tube.

Einstein's theory describing gravity as the curvature of spacetime. It extends special relativity to include accelerated motion and gravitational effects.

the branch of optics that describes light as traveling along straight-line rays

A massless fundamental particle that carries the strong interaction between quarks. Gluons also carry color charge and therefore interact with one another.

A class of theoretical models proposing that the strong, weak, and electromagnetic interactions become a single unified force at extremely high energies.

The bending of light caused by the curvature of spacetime around a massive object, producing distorted, magnified, or multiple images of distant objects.

A ripple in spacetime produced by accelerating massive objects, such as merging black holes or neutron stars, that travels at the speed of light.

A hypothetical elementary particle that would carry the gravitational interaction in a quantum theory of gravity.

The SI unit of absorbed dose, equal to one joule of radiation energy absorbed per kilogram of material.

connected to the Earth through a conductor, allowing excess charge to flow to or from the Earth

The process of connecting a conductor to the Earth (ground) so that its electric potential is maintained at approximately zero volts and excess charge can flow safely to or from the Earth.

A composite particle made of quarks that participates in the strong nuclear interaction.

The time required for approximately one-half of the radioactive nuclei in a large sample to decay.

The production of a voltage across a current-carrying conductor when it is placed in a magnetic field.

The voltage (electromotive force) generated across a current-carrying conductor by the Hall effect. When the magnetic field, charge velocity, and conductor width are mutually perpendicular, its magnitude is given by [latex]\epsilon = Blv[/latex].

The theoretical emission of particles from a black hole caused by quantum effects near its event horizon, leading to a gradual loss of mass over extremely long times.

A type of particle therapy that uses accelerated ions, such as carbon ions, to deliver highly localized radiation with increased biological effectiveness for selected cancers.

A fundamental principle of quantum mechanics stating that the uncertainties in certain pairs of physical quantities, such as energy and time, cannot both be made arbitrarily small simultaneously.

A fundamental principle of quantum mechanics stating that certain pairs of physical quantities—most notably position and momentum, or energy and time—cannot both be known simultaneously with arbitrary precision. Their uncertainties satisfy the relationships [latex]\Delta x\,\Delta p\ge\frac{h}{4\pi}[/latex] and [latex]\Delta E\,\Delta t\ge\frac{h}{4\pi}[/latex].

a fundamental limit to the precision with which pairs of quantities (momentum and position, and energy and time) can be measured

The SI unit of inductance, defined as [latex]1\,\text{H}=1\,\Omega\cdot\text{s}[/latex].

the SI unit of frequency, equal to one cycle per second

An elementary particle discovered in 2012 that is associated with the Higgs field, which gives mass to many elementary particles in the Standard Model.

Food irradiation using doses greater than 10 kGy for sterilization and specialized medical or commercial applications.

A three-dimensional image created by recording and reconstructing the interference pattern of coherent light.

The process of recording and reconstructing three-dimensional images using the interference of coherent light.

Light whose electric field oscillates in a horizontal direction.

The proportionality constant in Hubble's Law that describes the present-day rate at which the universe is expanding.

The current discrepancy between different methods used to measure the value of the Hubble constant, representing one of the major open questions in modern cosmology.

The relationship stating that the recession speed of a distant galaxy is proportional to its distance from Earth, expressed as [latex]v=H_0d[/latex].

A specific perceived color that is primarily determined by the wavelength or combination of wavelengths of visible light.

The principle stating that every point on a wavefront acts as a source of secondary wavelets that propagate at the speed of the wave, with the new wavefront formed by the surface tangent to those wavelets.

The wavelengths of light emitted or absorbed by hydrogen atoms. They are described by the Rydberg equation, which relates each wavelength to transitions between quantized electron energy levels.

An atom or ion containing only a single electron, such as hydrogen, [latex]\mathrm{He}^{+}[/latex], or [latex]\mathrm{Li}^{2+}[/latex].

A refractive error in which light from nearby objects would come to a focus behind the retina, making close vision difficult without accommodation.

The condition in which a fusion reaction produces enough energy to sustain itself without continued external heating.

A radiation therapy technique that uses medical imaging immediately before or during treatment to verify the tumor position and improve treatment accuracy.

The total opposition that an AC circuit offers to the flow of current. Impedance combines resistance, inductive reactance, and capacitive reactance, and is calculated using
[latex]Z=\sqrt{R^2+(X_L-X_C)^2}.[/latex]

Describes waves whose phase relationship changes randomly with time, preventing the formation of a stable interference pattern.

the ratio of the speed of light in a vacuum to the speed of light in a material, expressed as [latex]n=c/v[/latex]

A property of an electrical device that describes how effectively it produces an induced emf when the current through it changes.

The opposition that an inductor presents to alternating current. It is measured in ohms and is calculated using
[latex]X_L=2\pi fL[/latex].
Inductive reactance increases as either the frequency or the inductance increases.

An electrical component designed to have significant self-inductance and to store energy in a magnetic field.

A fusion approach that uses powerful laser or particle beams to rapidly compress and heat a tiny fuel pellet to the temperatures and densities required for nuclear fusion.

A reference frame in which an object at rest remains at rest, and an object in motion continues moving at constant velocity in a straight line unless acted upon by a net external force.

A frame of reference that is not accelerating or rotating. Special relativity applies directly to observers in inertial reference frames.

A hypothesized period of extremely rapid expansion that occurred during the earliest moments of the universe, helping explain its large-scale uniformity and geometry.

Electromagnetic radiation with photon energies lower than visible light, commonly associated with molecular vibrations and thermal radiation.

electromagnetic radiation with wavelengths from approximately [latex]0.74\,\mu\text{m}[/latex] to [latex]300\,\mu\text{m}[/latex], lying between visible light and microwaves in the electromagnetic spectrum

A printer that forms tiny electrically charged ink droplets and uses electric fields to accurately direct them onto paper.

a material that strongly resists the movement of electric charge

the average electromagnetic power transmitted per unit area, measured in watts per square meter ([latex]\text{W/m}^2[/latex])

An advanced form of external beam radiation therapy that varies the intensity of radiation beams to better match the shape of the tumor while reducing radiation exposure to nearby healthy tissues.

One of the alternating bright or dark bands produced when coherent light waves overlap.

A microscope that improves image contrast by combining an object beam with a reference beam so that differences in phase produce constructive and destructive interference.

the effective resistance inside a voltage source that reduces the terminal voltage when current flows

The magnetic field associated with the intrinsic spin of an electron.

An intrinsic form of angular momentum possessed by elementary particles such as electrons. Spin is a fundamental quantum property and is not due to the particle physically rotating.

The principle stating that radiation intensity from a point source decreases in proportion to the square of the distance from the source.

Electromagnetic radiation whose individual photons carry enough energy to remove electrons from atoms or molecules.

a region of Earth's upper atmosphere containing many charged particles that helps produce Earth's natural electric field

An angle-dependent change in color produced when microscopic structures selectively reinforce different wavelengths through interference.

Exposure of a person or object to ionizing radiation without necessarily becoming contaminated by radioactive material.

Nuclides of the same element that contain the same number of protons but different numbers of neutrons.

the relationship describing the electrical power dissipated in a circuit, commonly expressed as
[latex]P = IV[/latex], [latex]P = I^2R[/latex], or [latex]P = \frac{V^2}{R}[/latex]

Kirchhoff's first rule, which states that the total current entering any junction must equal the total current leaving the junction. This rule follows directly from the conservation of electric charge:

[latex]I_1=I_2+I_3[/latex]

A unit used to express explosive energy equivalent to the energy released by 1,000 tons of TNT.

A set of two fundamental rules for analyzing electrical circuits, based on the conservation of charge and conservation of energy. Together, they can be used to analyze any circuit, regardless of its complexity.

An acronym for Light Amplification by Stimulated Emission of Radiation, a device that produces coherent, nearly monochromatic electromagnetic radiation.

A printer that uses a laser to create an electrostatic image on a photoconducting drum, which attracts toner that is then transferred and fused onto paper.

A medical procedure that permanently changes the eye's focusing power by reshaping the cornea with a laser to correct refractive errors such as myopia, hyperopia, and astigmatism.

the principle stating that the total electric charge of an isolated system remains constant; charge can be transferred between objects but cannot be created or destroyed

the principle stating that the angle of reflection is equal to the angle of incidence, with both angles measured relative to the normal to the surface

The reduction in the measured length of an object along the direction of its motion when the object moves relative to an observer. It is described by

[latex]L=L_0\sqrt{1-\frac{v^2}{c^2}} =\frac{L_0}{\gamma}.[/latex]

The principle stating that the induced current always produces a magnetic field that opposes the change in magnetic flux that created it. This behavior is represented by the negative sign in Faraday's law of induction.

A fundamental particle that does not participate in the strong nuclear interaction. Electrons, muons, tau particles, and neutrinos are leptons.

A quantum number associated with the electron, muon, or tau family and represented by [latex]L_e[/latex], [latex]L_\mu[/latex], or [latex]L_\tau[/latex].

A unit of distance equal to the distance light travels through a vacuum in one year.

The number of parallel lines or grooves per unit length on a diffraction grating. Line density is the reciprocal of the line spacing.

A machine that accelerates electrons to produce high-energy x-rays or electron beams for external beam radiation therapy.

A material that flows like a liquid but whose molecules maintain an ordered arrangement, allowing it to rotate the polarization of light. Liquid crystals are used in LCD displays.

A simplified model of the atomic nucleus that treats it as a liquid droplet, helping explain phenomena such as nuclear deformation and fission.

Kirchhoff's second rule, which states that the algebraic sum of all potential changes around any closed loop is zero. Equivalently, the energy supplied by voltage sources equals the total energy lost across circuit elements:

[latex]\text{emf}=\text{Ir}+IR_1+IR_2+\cdots[/latex]

The dimensionless quantity that determines the magnitude of relativistic effects:
[latex]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}.[/latex]

The magnetic force experienced by a charged particle moving through a magnetic field.

Food irradiation using doses generally below 1 kGy to delay ripening, inhibit sprouting, and control insects.

A compact astronomical object, such as a faint star, brown dwarf, or black hole, that was once proposed as a possible explanation for dark matter.

Specific numbers of protons or neutrons that correspond to closed nuclear shells and produce unusually stable nuclei.

A fusion approach that uses strong magnetic fields to confine hot, electrically charged plasma and keep it away from the walls of the reactor.

the resistive force produced by eddy currents that opposes the motion of a conductor through a magnetic field, slowing the object without physical contact

Microscopic regions within a ferromagnetic material in which many atomic magnetic moments are aligned in the same direction.

A region of space surrounding a magnet or moving electric charge in which magnetic forces can act on other magnets or moving charges.

The magnetic field produced at the center of a circular current loop, given by
[latex]B=\frac{\mu_0 I}{2R},[/latex]
where [latex]R[/latex] is the radius of the loop.

The nearly uniform magnetic field inside a long solenoid, given by
[latex]B=\mu_0 nI,[/latex]
where [latex]n=N/l[/latex] is the number of turns per unit length.

Imaginary lines used to represent the direction and relative strength of a magnetic field. The closer the lines are together, the stronger the field.

The magnetic field surrounding a long straight current-carrying wire, given by
[latex]B=\frac{\mu_0 I}{2\pi r},[/latex]
where [latex]I[/latex] is the current, [latex]r[/latex] is the perpendicular distance from the wire, and [latex]\mu_0[/latex] is the permeability of free space.

The magnitude of the magnetic field vector, represented by [latex]B[/latex] and measured in teslas (T).

A measure of the magnetic field passing through a surface. For a uniform magnetic field, the magnetic flux is given by
[latex]\Phi=BA\cos\theta[/latex],
where [latex]B[/latex] is the magnetic field strength,
[latex]A[/latex] is the area of the surface, and
[latex]\theta[/latex] is the angle between the magnetic field and the line perpendicular (normal) to the surface.

The force exerted on a moving electric charge by a magnetic field. The force is always perpendicular to both the particle's velocity and the magnetic field.

A region where an increasing magnetic field causes charged particles spiraling along field lines to slow, reverse direction, and become trapped.

A hypothetical isolated magnetic north or south pole. Although predicted by some theories, no magnetic monopole has ever been experimentally observed.

The quantum number [latex]m_l[/latex] that specifies the orientation of an orbital's angular momentum relative to an external magnetic field. Its allowed values range from [latex]-l[/latex] to [latex]+l[/latex].

A noninvasive medical imaging technique that uses strong magnetic fields and radio waves to produce detailed images of internal organs and soft tissues without using ionizing radiation.

The process by which a material becomes magnetic through the alignment of its magnetic domains.

A recording of the extremely weak magnetic fields produced by the electrical activity of the heart during each heartbeat.

A recording of the extremely weak magnetic fields generated by electrical activity in the brain, used to study brain function and diagnose certain neurological disorders.

The use of magnetic fields and electric currents to control or move electrically conducting fluids without moving mechanical parts.

The ratio of image height to object height, indicating how much larger or smaller the image is compared with the object.

The relationship describing the intensity of polarized light after passing through a polarizing filter:

[latex]I=I_0\cos^2\theta,[/latex]

where [latex]I_0[/latex] is the incident intensity and [latex]\theta[/latex] is the angle between the light's polarization direction and the transmission axis of the filter.

The difference between the combined masses of the separate protons and neutrons in a nucleus and the actual mass of the bound nucleus.

The total number of nucleons in a nucleus, equal to the sum of its protons and neutrons ([latex]A=N+Z[/latex]).

An instrument that measures the mass-to-charge ratio of ions by analyzing the curvature of their paths in electric and magnetic fields.

The wave-like behavior associated with a material particle. The wavelength of the matter wave is determined by the particle's momentum.

The observed imbalance in which the universe contains much more matter than antimatter, despite theories suggesting they should have been produced in nearly equal amounts during the Big Bang.

the largest magnitude reached by the electric or magnetic field of an electromagnetic wave; represented by [latex]E_0[/latex] or [latex]B_0[/latex]

A set of four fundamental equations that describe the behavior of electric and magnetic fields and unify electricity, magnetism, and electromagnetic waves.

The total energy of a system due to its motion and position. It is the sum of the kinetic energy and potential energy:

[latex]\text{KE}+\text{PE}[/latex]

For a system acted on only by conservative forces, the total mechanical energy remains constant.

Food irradiation using doses of approximately 1–10 kGy to reduce harmful microorganisms and extend shelf life.

A unit of astronomical distance equal to one million parsecs, or approximately 3.26 million light-years.

A unit used to express explosive energy equivalent to the energy released by 1 million tons of TNT.

The expulsion of magnetic fields from the interior of a material as it enters the superconducting state.

A composite particle made of one quark and one antiquark. Pions are the lightest mesons and play an important role in describing the residual strong nuclear force between nucleons.

An excited atomic or molecular state whose lifetime is much longer than that of typical excited states because transitions to lower-energy states are quantum mechanically inhibited.

An excited nuclear state with a measurable lifetime before it decays to a lower-energy state by emitting gamma radiation.

An instrument that measures electrical quantities by balancing the magnetic torque on a current-carrying coil against a restoring spring, producing a pointer deflection proportional to the current.

An 1887 experiment that demonstrated that the measured speed of light in a vacuum is independent of Earth's motion, providing key experimental evidence supporting special relativity.

A form of gravitational lensing in which a compact object briefly magnifies the light from a distant star as it passes between the star and the observer.

A condition in which the skin's protective resistance is bypassed, often by a medical procedure or device, making very small currents potentially dangerous to the heart.

electromagnetic waves with wavelengths ranging from about 1 mm to 1 m; they can be produced by currents in macroscopic circuits and electronic devices

a smooth surface that reflects light in a predictable direction, allowing clear images to be formed

A measure of an object's motion that depends on both its mass and its velocity. Momentum is conserved whenever the net external force on a system is zero.

An optical instrument that separates light by wavelength and selects a narrow range of wavelengths for transmission.

the voltage (emf) induced when a conductor moves through a magnetic field; when the magnetic field, conductor length, and velocity are mutually perpendicular, it is given by [latex]\text{emf}=B\ell v[/latex]

A device that converts electrical energy into mechanical energy by using the torque produced on a current-carrying loop in a magnetic field.

The ability of one electrical device or circuit to induce an emf in another nearby device or circuit.

A refractive error in which distant objects appear blurred because light is focused in front of the retina rather than directly on it.

The closest point to the eye at which an object can be focused sharply on the retina when the eye is fully accommodated.

Another term for myopia, the inability to see distant objects clearly because their images are focused in front of the retina.

the propagation of electrical signals along neurons through the generation and transmission of action potentials

An electrically neutral elementary particle that interacts only through the weak nuclear force (and gravity) and has an extremely small mass.

The transformation of a neutrino from one family type into another as it travels.

An electrically neutral nucleon found in the atomic nucleus.

A fission reaction initiated when a nucleus absorbs an incoming neutron.

an imaginary line drawn perpendicular to a surface at the point where a light ray strikes

The end of a magnet that, when freely suspended, points approximately toward Earth's geographic North Pole (also called the north-seeking pole).

A nuclear reaction in which a heavy atomic nucleus splits into two or more smaller nuclei, releasing energy and usually several neutrons.

A nuclear reaction in which two light atomic nuclei combine to form a heavier nucleus, releasing energy when the products have a greater binding energy per nucleon than the reactants.

A physical phenomenon in which atomic nuclei interact with an external magnetic field and absorb and reemit radio-frequency energy at specific resonant frequencies. MRI is based on this principle.

Radiation emitted directly from the nucleus of an atom during radioactive decay.

The energy released or absorbed during a nuclear reaction as a result of a change in mass.

The collective name for the protons and neutrons that make up atomic nuclei.

The dense central region of an atom that contains its protons and neutrons and nearly all of its mass.

A specific atomic nucleus characterized by a particular number of protons and neutrons.

A measurement technique in which a circuit is adjusted until no current flows through the measuring instrument, minimizing the instrument's effect on the circuit and improving measurement accuracy.

A measure of the light-gathering ability and resolving power of an objective lens, defined by

[latex]\mathrm{NA}=n\sin\alpha[/latex]

where [latex]n[/latex] is the refractive index of the medium between the specimen and the objective, and [latex]\alpha[/latex] is half of the acceptance angle of the objective.

The lens closest to the specimen. It forms the first real, magnified image and largely determines the microscope's resolution.

The portion of the universe from which light has had enough time to reach Earth since the Big Bang.

The wavelength measured by an observer who may be moving relative to the source, represented by [latex]\lambda_{\text{obs}}[/latex].

The SI unit of electrical resistance, equal to one volt per ampere: [latex]1~\Omega=1~\frac{\text{V}}{\text{A}}[/latex].

An empirical relationship stating that, for an ohmic material, the current is directly proportional to the applied voltage; commonly written as [latex]I=\frac{V}{R}[/latex].

A material whose current is directly proportional to the applied voltage, so that it obeys Ohm's law over its operating range.

An instrument that determines electrical resistance by applying a known voltage, measuring the resulting current, and calculating the resistance using Ohm's law.

The apparent contradiction that if the universe were infinitely old, static, and uniformly filled with stars, the night sky should be bright rather than dark.

The ability of certain materials to rotate the plane of polarization of linearly polarized light. The amount of rotation depends on the material, its concentration, the path length, and the wavelength of light.

A three-dimensional region around the nucleus where there is a high probability of finding an electron. An orbital is described by a unique set of quantum numbers rather than by a classical trajectory.

The angular momentum associated with an electron's motion around an atomic nucleus.

The magnetic field generated by the orbital motion of an electron, which behaves like a tiny current loop.

The integer [latex]m[/latex] used to identify a constructive interference maximum relative to the central maximum.

One of the two rays produced in a birefringent material. It obeys Snell's law and experiences the ordinary refractive index.

To vary repeatedly back and forth about an equilibrium value.

Two or more current-carrying wires that run alongside one another. Their magnetic fields interact, producing attractive or repulsive forces depending on the directions of the currents.

a circuit configuration in which components are connected across the same two points, so each component experiences the same voltage while the current divides among the branches

A capacitor consisting of two parallel conducting plates separated by a small distance and an insulating material (or vacuum).

The original unstable nucleus that undergoes radioactive decay.

A form of radiation therapy that uses charged particles, such as protons or carbon ions, instead of x-rays to treat cancer.

The fundamental quantum property that light and matter exhibit both wave-like and particle-like behavior, with the observed behavior depending on the type of measurement or experiment being performed.

The difference between the distances traveled by two waves from their sources to the same observation point.

The principle stating that no two electrons in the same atom can have the same set of four quantum numbers.

the maximum value of the alternating emf produced by a generator, given by
[latex]{\text{emf}}_{0}=\text{NAB}\omega[/latex]

The physical constant
[latex]\mu_0=4\pi\times10^{-7}\ \text{T}\cdot\text{m/A},[/latex]
which determines how magnetic fields are produced in a vacuum.

Protective equipment, such as lead aprons, thyroid shields, and protective barriers, used to reduce occupational radiation exposure when appropriate.

A hybrid imaging technique that combines the functional information obtained from PET with the detailed anatomical images produced by computed tomography (CT).

The angle, denoted by [latex]\phi[/latex], that describes the difference in phase between the voltage and the current in an AC circuit.

An optical element used in a phase-contrast microscope to shift the phase of selected light rays, creating interference that enhances image contrast.

A microscope that converts small phase differences in light passing through a transparent specimen into differences in brightness, allowing unstained living cells to be observed.

The delayed emission of light that occurs when electrons return from a metastable excited state to a lower-energy state.

A material that behaves as an electrical insulator in the dark but becomes conducting when exposed to light.

The phenomenon in which mechanical stress changes the optical properties of a transparent material, allowing stress patterns to be observed using polarized light.

The phenomenon in which electrons are emitted from a material after it absorbs electromagnetic radiation.

A device that converts very small flashes of light into amplified electrical signals using the photoelectric effect and successive stages of electron multiplication.

An electronic device that detects tiny flashes of light produced in a scintillation crystal and amplifies them into measurable electrical signals.

A quantum, or discrete particle, of electromagnetic radiation.

The energy carried by a photon, given by

[latex]E=hf.[/latex]

The linear momentum carried by a photon, calculated using [latex]p=h/\lambda=E/c[/latex].

The tendency of parallel electric currents in a plasma or electric arc to attract one another, compressing the current into a narrower region due to magnetic forces.

The lightest meson, exchanged between neighboring protons and neutrons in Yukawa's model of the nuclear force. Three types exist: positively charged, negatively charged, and neutral.

The characteristic length scale of quantum gravity, approximately [latex]1.6\times10^{-35}\ \text{m}[/latex].

A fundamental constant of quantum mechanics with the value

[latex]h=6.626\times10^{-34}\ \text{J}\cdot\text{s}.[/latex]

Rutherford's model of the atom in which lightweight electrons orbit a small, massive, positively charged nucleus. Although later superseded by quantum mechanics, it correctly recognized the existence of the atomic nucleus and that atoms are mostly empty space.

an idealized charged object whose size is negligible compared with the distances involved, allowing it to be treated as a single point

a molecule with a permanent separation of positive and negative charge

the separation or slight redistribution of positive and negative charge within an otherwise neutral object

A microscope that uses polarized light to reveal structures that are optically active or birefringent by analyzing changes in the polarization of light passing through a specimen.

a state in which positive and negative charges become separated within an object while the object remains electrically neutral overall

Light whose electric field oscillates in a specific direction rather than in random directions.

An optical device that produces polarized light by transmitting one orientation of the electric field while absorbing or blocking the perpendicular orientation.

The condition in which more atoms or molecules occupy a metastable excited state than the ground state, making laser action possible.

The positively charged antimatter counterpart of the electron, emitted during beta-plus decay.

Another name for beta-plus decay, in which a proton is converted into a neutron while a positron and an electron neutrino are emitted.

A nuclear imaging technique that detects pairs of gamma rays produced by positron-electron annihilation to create detailed three-dimensional images of physiological activity.

A fundamental assumption accepted without proof that serves as the starting point for developing a scientific theory.

The difference in electric potential between two points. It is equal to the change in electric potential energy per unit charge:

[latex]\Delta V=\frac{\Delta\text{PE}}{q}[/latex]

A null measurement instrument used to determine an unknown voltage or electromotive force (emf) by comparing it with a precisely known reference voltage.

The reciprocal of the focal length (measured in meters), expressed in diopters (D).

A measure of how efficiently electrical power is delivered to an AC circuit. The power factor is equal to
[latex]\cos\phi[/latex]
and ranges from 0 to 1. A power factor of 1 indicates that the voltage and current are in phase and power transfer is maximized.

the age-related loss of the eye's ability to accommodate, making it increasingly difficult to focus on nearby objects

The quantum number [latex]n[/latex] that specifies an electron's principal energy level. The allowed values are [latex]n=1,2,3,\ldots[/latex].

the principle that the total electric field from multiple charges is the vector sum of the electric fields produced by each individual charge

A graphical representation of the probability of finding an electron at different locations around the nucleus. Darker regions indicate a higher probability.

The statistical distribution that describes the likelihood of finding a particle at different locations or in different states. Individual measurements produce definite outcomes, but repeated measurements follow the probability distribution predicted by quantum mechanics.

Gamma rays and neutrons emitted during the first moments of a nuclear explosion.

The distance between two points measured in the reference frame in which both points are at rest. It is represented by [latex]L_0[/latex] and is the greatest measured distance between those points.

The time interval, denoted by [latex]\Delta t_0[/latex], measured by an observer who is at rest relative to the event or process being observed. It is related to the time measured in another inertial frame by
[latex]\Delta t=\gamma\Delta t_0.[/latex]

a positively charged subatomic particle found in the nucleus of an atom; it carries a charge equal in magnitude and opposite in sign to that of an electron

A type of particle therapy that uses accelerated protons to deliver most of their radiation dose at a specific depth within the body, reducing radiation exposure beyond the tumor.

The sequence of fusion reactions that powers the Sun and other Sun-like stars by converting hydrogen into helium while releasing energy, gamma rays, and neutrinos.

Positively charged nucleons found within the atomic nucleus.

An older term, now largely replaced by the radiation weighting factor, used to account for differences in the biological effectiveness of various types of ionizing radiation.

The restriction that certain physical quantities, such as energy or angular momentum, can take only specific discrete values.

The property of certain physical quantities that can exist only in specific discrete values rather than a continuous range of values.

The property that the orbital angular momentum of an electron can take only discrete values given by

[latex]L=n\frac{h}{2\pi},\qquad n=1,2,3,\ldots[/latex]

The quantum field theory describing the strong interaction between quarks and gluons; commonly abbreviated QCD.

The theory describing the strong interaction between quarks and gluons through the exchange of color charge.

A computer that uses quantum mechanical properties, such as superposition and entanglement, to perform certain calculations more efficiently than classical computers.

The quantum field theory describing electromagnetic interactions between charged particles and photons; commonly abbreviated QED.

A proposed theory that would unify general relativity and quantum mechanics into a single description of gravity.

The quantum mechanical phenomenon in which a particle crosses a potential energy barrier that it cannot overcome according to classical mechanics because its wave function extends through the barrier. Also called barrier penetration.

The branch of physics that describes the behavior of matter and energy at atomic and subatomic scales, where many physical quantities are quantized.

A set of numerical values that uniquely specifies the quantum state of an electron or other quantum particle.

A quantum mechanical phenomenon that allows particles to pass through an energy barrier even when they do not have enough energy to overcome it classically. Tunneling enables nuclear fusion to occur in the Sun at temperatures lower than would otherwise be required.

an elementary particle and a fundamental constituent of matter

a technology that uses microwaves to determine the distance, position, or speed of objects by analyzing reflected electromagnetic waves

An instrument that detects and measures ionizing radiation by converting its interactions with matter into measurable electrical or optical signals.

A physician who specializes in treating cancer and other diseases using radiation therapy.

The pressure exerted when electromagnetic radiation transfers momentum to a surface through absorption or reflection. Although extremely small for ordinary light, radiation pressure can produce measurable forces in space and in high-intensity laser applications.

The science and practice of minimizing unnecessary exposure to ionizing radiation through appropriate use of time, distance, shielding, and safe work practices.

A numerical factor used to convert absorbed dose into equivalent dose by accounting for the relative biological effectiveness of different types of radiation.

electromagnetic waves with wavelengths ranging from about 1 mm to 100 km; they are produced by currents in wires and circuits as well as by many astronomical phenomena

Describes a substance or object containing unstable nuclei that spontaneously emit nuclear radiation.

The presence of radioactive material on or inside a person, object, or environment.

A family of techniques that determine the age of materials by measuring the decay of radioactive isotopes.

The spontaneous emission of particles or electromagnetic radiation from unstable atomic nuclei.

Chemical compounds formed when ionizing radiation interacts with molecules in food. Similar compounds are also produced during other food processing methods such as cooking and pasteurization.

An unstable isotope that undergoes radioactive decay while emitting ionizing radiation.

A biologically active compound that contains a radioactive isotope and is used for diagnostic imaging or targeted radiation therapy.

Tissue that is relatively less sensitive to damage from ionizing radiation, such as muscle or mature nerve tissue.

Tissue whose rapidly dividing cells are especially susceptible to radiation damage, including bone marrow and the lining of the digestive tract.

A radioactive isotope incorporated into a molecule that allows its distribution within the body to be monitored using radiation detectors.

The approximate nuclear radius, given by [latex]r=r_0A^{1/3}[/latex], where [latex]r_0\approx1.2\ \text{fm}[/latex].

The radius of the circular path followed by a charged particle moving perpendicular to a uniform magnetic field, given by [latex]r=\frac{mv}{qB}[/latex].

A naturally occurring radioactive gas produced during the decay of uranium in rocks and soil. Long-term exposure to elevated indoor radon concentrations increases the risk of lung cancer.

An internationally recognized symbol used on qualifying irradiated foods to indicate that the product has been treated with ionizing radiation.

a continuous spectrum of colors produced when sunlight is refracted, internally reflected, and dispersed by water droplets in the atmosphere

The distance that ionizing radiation can travel through a material before losing essentially all of its energy.

The number of radioactive decay events that occur per unit time.

a straight line used to represent the direction in which light travels

A condition for determining whether two nearby point sources can be distinguished. Two images are just resolved when the center of the diffraction pattern produced by one source lies at the first minimum of the diffraction pattern produced by the other.

A circuit that contains both a resistor (R) and a capacitor (C), producing characteristic charging and discharging behavior described by the RC time constant.

An image formed where light rays actually converge and that can be projected onto a screen.

The apparent speed at which a distant galaxy moves away from an observer because of the expansion of the universe.

An increase in the observed wavelength and a corresponding decrease in frequency when a source of electromagnetic radiation moves away from an observer.

A coordinate system or viewpoint used to measure the positions, motions, and physical properties of objects.

the change in direction of light when it strikes a surface and returns to the original medium

the change in direction of light as it passes from one material into another because its speed changes

A measure of how effective a particular type of radiation is at producing biological damage compared with a reference radiation for the same absorbed dose.

The change in the observed wavelength or frequency of electromagnetic radiation caused by relative motion between the source and the observer. The observed wavelength is

[latex]\lambda_{\text{obs}} = \lambda_s \sqrt{\frac{1+\frac{u}{c}} {1-\frac{u}{c}}},[/latex]

where [latex]\lambda_{\text{obs}}[/latex] is the observed wavelength, [latex]\lambda_s[/latex] is the emitted wavelength, and [latex]u[/latex] is the relative velocity between source and observer.

The kinetic energy of an object moving at relativistic speeds. It is given by

[latex]KE_{\rm rel}=(\gamma-1)mc^2,[/latex]

where

[latex]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}.[/latex]

The momentum of an object moving at relativistic speeds, given by

[latex]p=\gamma mu.[/latex]

A speed that is a significant fraction of the speed of light, at which effects such as time dilation and length contraction can no longer be neglected.

The method used to combine velocities when one or more speeds are a significant fraction of the speed of light. For one-dimensional motion,

[latex]u=\frac{v+u'}{1+\frac{vu'}{c^2}}.[/latex]

This equation ensures that the resulting speed does not exceed [latex]c[/latex].

The branch of physics that studies how different observers measure the same physical events. Modern relativity includes both special and general relativity.

The principle that two events occurring simultaneously for one observer may not be simultaneous for another observer moving relative to the first.

A traditional unit of equivalent or effective dose. One sievert equals 100 rem.

The magnetic force that occurs between two parallel conductors when the currents flow in opposite directions, causing the wires to push away from one another.

The remaining strong interaction between color-neutral protons and neutrons. It can be modeled effectively through the exchange of mesons such as pions.

The electrical property of a material that opposes the flow of electric current; for an ohmic material, [latex]R=\frac{V}{I}[/latex].

An intrinsic property of a material that measures how strongly it opposes the flow of electric current. It is independent of the object's size and shape and is denoted by [latex]\rho[/latex].

an electrical component designed to oppose the flow of electric current by providing a specific resistance

The ability of an imaging system to distinguish two closely spaced objects as separate.

The enhanced response of a system when it is driven at or near its natural frequency.

The frequency at which the inductive and capacitive reactances are equal, producing the minimum impedance and the maximum current in a series RLC circuit. It is given by
[latex]f_0=\frac{1}{2\pi\sqrt{LC}}.[/latex]

The energy associated with an object's mass when it is at rest. It is given by

[latex]E_0=mc^2.[/latex]

The mass of an object measured in a reference frame where the object is at rest. In modern physics, this is simply called the object's mass.

the light-sensitive layer at the back of the eye where a real image is formed and converted into nerve signals that are sent to the brain

A proposed visual processing system that combines information from the retina and the brain to explain color constancy and brightness perception.

A theory proposed by Edwin Land stating that the brain compares information from the three cone systems across an entire visual scene to determine the perceived colors of objects.

A rule used to determine the direction of the magnetic force on a positive moving charge. Point your right thumb in the direction of the particle's velocity and your fingers in the direction of the magnetic field; your palm points in the direction of the magnetic force. For a negative charge, the force is in the opposite direction.

A rule used to determine the direction of the magnetic force on a positive moving charge: point your right thumb in the direction of the particle's velocity and your fingers in the direction of the magnetic field. Your palm points in the direction of the magnetic force. For a negative charge, the force is in the opposite direction.

A rule used to determine the direction of the magnetic field around a current-carrying conductor. Point your right thumb in the direction of the conventional current; your curled fingers indicate the direction of the magnetic field lines.

the root mean square (rms) current, given by
[latex]I_{\text{rms}}=\frac{I_0}{\sqrt{2}},[/latex]
which is the effective current that produces the same average power as an equivalent DC current

the root mean square (rms) voltage, given by
[latex]V_{\text{rms}}=\frac{V_0}{\sqrt{2}},[/latex]
which is the effective voltage that produces the same average power as an equivalent DC voltage

Photoreceptor cells that are highly sensitive to light and provide night vision, peripheral vision, and motion detection but do not distinguish colors.

A fundamental physical constant used to calculate the wavelengths of spectral lines in hydrogen and hydrogen-like atoms, with the value [latex]1.097\times10^7\ \text{m}^{-1}[/latex].

A physical quantity that has magnitude but no direction. Electric potential (voltage), electric potential energy, mass, and temperature are all scalar quantities.

A physical quantity that has magnitude but no direction. Electric potential, electric potential energy, mass, and temperature are scalar quantities.

An electron microscope that scans a focused electron beam across the surface of a specimen and detects emitted secondary electrons to produce a detailed image of surface structure.

Polarization produced when light is scattered by small particles or molecules, such as the molecules in Earth's atmosphere.

The radius of the event horizon of a non-rotating black hole, given by the equation

[latex]R_\mathrm{S}=2GM/c^2[/latex]

The emission of visible light by certain materials after they absorb ionizing radiation.

Materials that emit brief flashes of visible light when ionizing radiation deposits energy within them. These flashes are used to detect and measure radiation.

the reduction of an electric field or electrostatic interaction by nearby charges or polar molecules

The principle stating that the speed of light in a vacuum is the same constant, c, for every inertial observer, regardless of the motion of the light source or the observer.

The property of a device by which a changing current through it induces an emf in the same device.

The spontaneous formation of organized structures or patterns without centralized control.

describes a membrane that allows some ions or molecules to pass while restricting others

a circuit configuration in which components are connected one after another so that the same current flows through each component

A group of electron states that share the same principal quantum number, \(n\).

The use of absorbing materials between a radiation source and a person to reduce radiation exposure.

A hazard that occurs when electric current passes through a person, potentially causing physiological injury.

A high-pressure wave that travels faster than the speed of sound and is responsible for much of the physical damage caused by explosions.

A low-resistance path between the terminals of a voltage source, often producing dangerously large currents and rapid heating.

a small resistance [latex]R[/latex] placed in parallel with a galvanometer G to produce an ammeter; the larger the current to be measured, the smaller [latex]R[/latex] must be; most of the current flowing through the meter is shunted through [latex]R[/latex] to protect the galvanometer

The SI unit of equivalent dose and effective dose that reflects the biological effects of ionizing radiation.

A circuit consisting of a single voltage source connected to a single resistor (load).

The theory that human color vision results from the combined responses of three types of cone cells, each sensitive to a different range of visible wavelengths.

Events that an observer measures as occurring at the same time.

A three-dimensional nuclear imaging technique that reconstructs images from gamma rays emitted directly by a radiopharmaceutical.

The spreading and self-interference of light after it passes through a narrow opening, producing a broad central maximum and weaker secondary maxima separated by dark minima.

A long, tightly wound coil of wire that produces a strong, nearly uniform magnetic field inside it when an electric current flows through the coil.

Semiconductor-based detectors that directly convert ionization produced by incident radiation into electrical signals, providing high detection efficiency and excellent energy resolution.

The wavelength of electromagnetic radiation measured in the reference frame in which the source is at rest, represented by [latex]\lambda_s[/latex].

The end of a magnet that, when freely suspended, points approximately toward Earth's geographic South Pole (also called the south-seeking pole).

The quantum mechanical restriction that angular momentum vectors may assume only certain discrete orientations relative to an external magnetic field.

The four-dimensional framework that combines the three dimensions of space with time into a single geometric structure.

Einstein's theory describing the relationships between space, time, energy, and motion for observers moving at constant velocity. It is based on two fundamental postulates and applies only to inertial reference frames.

The ability of an optical instrument to distinguish between two closely spaced wavelengths.

An instrument that separates light into wavelengths and measures the intensity associated with each wavelength.

A family of microscopy techniques that combine imaging with wavelength analysis to identify the chemical composition of microscopic regions within a specimen.

A notation that identifies an electron's shell, subshell, and the number of electrons occupying that subshell, such as \(2p^4\).

reflection from a smooth surface in which parallel incident rays remain parallel after reflection, producing a clear image

the constant speed at which electromagnetic waves travel through a vacuum, equal to approximately [latex]3.00\times10^8\ \text{m/s}[/latex]

an optical imperfection in which rays striking different regions of a spherical mirror do not all converge at exactly the same point

The second allowed orientation of an electron's intrinsic spin relative to an external magnetic field.

The quantum number [latex]m_s[/latex] that specifies the orientation of an electron's spin relative to an external magnetic field. For electrons, the allowed values are [latex]+\frac12[/latex] and [latex]-\frac12[/latex].

The quantum number [latex]s[/latex] that specifies the intrinsic angular momentum of a particle. For electrons, [latex]s=\frac12[/latex].

One of the two allowed orientations of an electron's intrinsic spin relative to an external magnetic field.

The current theory of particle physics that describes all known elementary particles and three of the four fundamental interactions: the electromagnetic, weak, and strong interactions.

A wave pattern that appears to remain in place and contains fixed nodes, where the amplitude is always zero, and antinodes, where the amplitude is greatest.

a buildup of electric charge on the surface of an object

A transformer that reduces the output voltage compared with the input voltage while increasing the output current.

A transformer that increases the output voltage compared with the input voltage while decreasing the output current.

The emission of a photon triggered by an incoming photon of the same energy, producing a second photon with identical wavelength, phase, polarization, and direction.

A radiation-induced effect whose probability increases with dose but whose severity does not depend on dose. Cancer is the primary example.

the third lightest of all quarks

A quantum number represented by [latex]S[/latex] and associated with the presence of strange quarks in a hadron. Strangeness is conserved in strong interactions but may change in weak interactions.

A proposed framework in which elementary particles are modeled as tiny vibrating strings rather than point-like particles. It is one of several approaches being explored in the search for a unified theory that includes gravity.

Color produced by the interaction of light with microscopic physical structures rather than primarily by pigments.

A subdivision of an electron shell whose electrons share the same angular momentum quantum number, \(l\).

A material that exhibits essentially zero electrical resistance below its critical temperature.

A condition in which more than one neutron from each fission event causes another fission, leading to an increasing rate of nuclear reactions.

A circular accelerator in which both the magnetic field and the radio-frequency accelerating field are synchronized with the increasing energy of the particles so they remain on a nearly constant-radius orbit.

Electromagnetic radiation emitted by charged particles when they are accelerated perpendicular to their direction of motion, such as when they travel around curved paths in a magnetic field.

The process of attaching a radioactive isotope to a biologically active molecule to create a radiopharmaceutical.

A treatment that uses radioactive isotopes attached to molecules that selectively accumulate in cancer cells, delivering radiation from within the body.

A device containing molybdenum-99 that continuously produces fresh technetium-99m for use in nuclear medicine.

A metastable radioactive isotope that emits a 140-keV gamma ray and is the most widely used radioisotope in diagnostic nuclear medicine.

a system that transmits video and audio information using electromagnetic waves

A material constant, denoted by [latex]\alpha[/latex], that describes how a material's resistivity (and therefore its resistance) changes with temperature.

the actual voltage measured across the terminals of a voltage source while it is supplying or receiving current

The SI unit of magnetic field strength, defined as [latex]1\,\text{T}=\frac{1\,\text{N}}{1\,\text{A}\cdot\text{m}}[/latex].

a very small positive charge used to measure an electric field without significantly disturbing it

A proposed theory that would unify all four fundamental interactions into a single mathematical framework.

explains how quarks can exist and yet never be isolated or directly observed

The balance between delivering a sufficient radiation dose to control or eliminate a tumor while minimizing radiation damage to surrounding healthy tissues.

the random thermal motion of atoms and molecules in matter above absolute zero, causing them to emit and absorb electromagnetic radiation

A hazard caused by excessive electrical heating that can damage equipment, burn tissue, or ignite surrounding materials.

Electromagnetic radiation, including visible, infrared, and ultraviolet light, emitted by the intensely hot fireball of a nuclear explosion.

interference between light reflected from different surfaces of a thin film

a modern electrical wiring system that uses live (hot), neutral, and ground (earth) conductors to reduce the risk of electric shock and overheating

The characteristic time of an RC circuit, given by [latex]\tau = RC[/latex]. After one time constant, a charging capacitor reaches about 63.2% of its final voltage, while a discharging capacitor falls to about 36.8% of its initial voltage.

The phenomenon in which an observer measures a clock moving relative to them as running more slowly than a clock at rest in their own frame.

The three fundamental principles of radiation protection: minimizing exposure time, maximizing distance from the source, and using appropriate shielding.

a quark flavor

The turning effect produced when a current-carrying loop is placed in a magnetic field, given by [latex]\tau = NIAB\sin\theta[/latex].

The total energy of an object moving at any speed, including both its rest energy and its kinetic energy. It is given by

[latex]E=\gamma mc^2,[/latex]

where

[latex]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}.[/latex]

the complete reflection of light back into a medium when it strikes a boundary with a lower-index material at an angle greater than the critical angle

An electrical device that uses electromagnetic induction to increase or decrease alternating voltage between two circuits while transferring electrical energy.

The relationship between the voltages and number of turns in the primary and secondary coils of an ideal transformer:
[latex]\frac{V_s}{V_p}=\frac{N_s}{N_p}.[/latex]

An electron microscope that forms an image from electrons transmitted through an extremely thin specimen. TEMs can reveal internal structures at very high resolution.

A wave in which the oscillation is perpendicular to the direction of propagation. In an electromagnetic wave, the electric and magnetic fields are both perpendicular to the direction in which the wave travels.

The process of using medical imaging, computer modeling, and dose calculations to design a radiation treatment that maximizes tumor coverage while protecting healthy organs.

A quantum mechanical process in which the wave nature of matter allows particles to penetrate and sometimes pass through potential energy barriers that are classically forbidden.

A thought experiment in which one twin travels at relativistic speed and returns younger than the twin who remained on Earth. It is not a true paradox because the traveling twin accelerates and changes inertial reference frames, so the twins' situations are not symmetric.

the radio-frequency band extending from 300 MHz to 3 GHz; many television broadcasts, mobile communications, and wireless technologies operate in this range

A microscope that uses ultraviolet light, which has shorter wavelengths than visible light, to improve image resolution. Specialized optics and detectors are required because ordinary glass absorbs much of the UV spectrum.

Electromagnetic radiation with photon energies greater than visible light and, at sufficiently short wavelengths, capable of ionizing atoms and molecules.

electromagnetic radiation with wavelengths from about 400 nm down to about 10 nm, extending from the violet end of the visible spectrum into the X-ray region

The unavoidable limitation in how precisely the energy of a quantum system can be known or measured, represented by [latex]\Delta E[/latex]. It is related to the uncertainty in time through Heisenberg's uncertainty principle.

The unavoidable limitation in how precisely a particle's momentum can be known or measured, represented by [latex]\Delta p[/latex]. Increasing the precision of a momentum measurement necessarily increases the uncertainty in the particle's position.

The unavoidable limitation in how precisely a particle's location can be known or measured, represented by [latex]\Delta x[/latex]. Increasing the precision of a position measurement necessarily increases the uncertainty in the particle's momentum.

The uncertainty in the duration over which a quantum system exists in a particular state or the time interval associated with an energy measurement, represented by [latex]\Delta t[/latex]. Short-lived states have correspondingly larger uncertainties in energy.

Light consisting of many waves whose electric fields are randomly oriented in all directions perpendicular to the direction of propagation.

the lightest of all quarks

The electrons in the outermost occupied shell of an atom. They determine most of an element's chemical properties and participate in chemical bonding.

Two regions surrounding the Earth where energetic charged particles are trapped by the Earth's magnetic field.

A machine that uses a moving insulating belt to accumulate a very large electric charge on a conducting sphere, producing extremely high voltages for demonstrations and scientific applications.

a physical quantity that has both magnitude and direction

the process of combining two or more vectors while accounting for both their magnitudes and directions to obtain a single resultant vector

A physical quantity that has both magnitude and direction. Electric field, electric force, velocity, and acceleration are vector quantities.

A point in a Feynman diagram at which particle lines meet, representing an elementary interaction.

Light whose electric field oscillates in a vertical direction.

the radio-frequency band extending from 30 MHz to 300 MHz; traditional VHF television channels occupy portions of this range

an image that appears to come from a location where light rays do not actually converge, such as the image seen behind a plane mirror

A short-lived particle permitted by the Heisenberg uncertainty principle that cannot be detected directly but whose effects can be observed through the forces it mediates.

the narrow region of the electromagnetic spectrum that can be detected by the human eye

the decrease in electric potential (voltage) across a circuit element as electrical energy is transferred or converted

an instrument that measures voltage

An advanced radiation therapy technique in which the linear accelerator rotates around the patient while continuously adjusting the radiation beam shape and intensity to deliver treatment efficiently and precisely.

The quantum principle that objects such as photons, electrons, and other particles can exhibit both wave-like and particle-like behavior, depending on how they are observed.

The distance between equivalent points on successive wave cycles, such as from one crest to the next; represented by [latex]\lambda[/latex].

A bridge circuit that determines an unknown resistance by balancing two branches of the circuit until no current flows through a galvanometer or other sensitive detector.

A hypothetical particle that interacts primarily through gravity and the weak nuclear force and is one of the leading proposed candidates for dark matter.

A hypothetical tunnel connecting two distant regions of spacetime. Although permitted by some mathematical solutions of general relativity, no observational evidence for wormholes currently exists.

high-frequency electromagnetic radiation capable of penetrating many materials; X-rays overlap the ultraviolet and gamma-ray regions of the electromagnetic spectrum

A technique that analyzes the diffraction and interference of x rays scattered by a material to determine its atomic or molecular structure. X-ray diffraction is the foundation of x-ray crystallography.

High-energy electromagnetic radiation generated electrically and used as an alternative to gamma rays for commercial food irradiation.

A dry copying process that uses electrostatic charges to attract toner and transfer images to paper.

The hypothetical force-carrying particle proposed by Hideki Yukawa in 1935 to explain the strong nuclear force. It was later identified as the pion.

The splitting of atomic or molecular spectral lines into multiple components when an external magnetic field is applied.

a natural gemstone with a high index of refraction that is often used as a diamond substitute