Atomic Physics
106 Discovery of the Parts of the Atom: Electrons and Nuclei
Learning Objectives
- Describe how electrons were discovered.
- Explain the Millikan oil drop experiment.
- Describe Rutherford's gold foil experiment.
- Describe Rutherford's planetary model of the atom.
Atoms are themselves made of even smaller particles. The discovery of the electron and the atomic nucleus transformed our understanding of matter, revealing that atoms are not indivisible objects but have an internal structure. The experiments described in this section are landmarks in the history of physics because they combined careful observation with the principles of electricity and magnetism to uncover the building blocks of the atom.
Many of the ideas developed in earlier chapters—including electric charge, electric fields, magnetic fields, and the forces acting on charged particles—will now be applied to understand how scientists determined the properties of particles far too small to see directly.
Charges and Electromagnetic Forces
Previous chapters showed that positively charged particles are found in atomic nuclei, while negatively charged electrons surround the nucleus. The experiments described in this section explain how scientists first identified these particles and measured some of their most important properties. They also demonstrate how electric and magnetic forces can be used to investigate matter on microscopic scales.
The Electron
The first evidence that atoms contain smaller particles came from experiments with gas discharge tubes. These devices consist of a sealed glass tube containing two metal electrodes separated by a low-pressure gas. When a large voltage is applied across the electrodes, an electric current passes through the gas, causing it to glow.
During the second half of the nineteenth century, researchers such as Heinrich Geissler and William Crookes used these tubes to investigate the mysterious rays that traveled from the negative electrode, or cathode, toward the positive electrode, or anode. These rays became known as cathode rays.
Today we know that cathode rays are streams of electrons. As the electrons accelerate through the low-pressure gas, they collide with gas atoms and molecules, transferring energy that causes the gas to emit visible light. The glowing path makes the otherwise invisible electron beam observable.
Crookes demonstrated that cathode rays possess momentum by showing they could rotate a lightweight paddle wheel placed inside the tube. He also observed that the beam could be deflected by a magnetic field in exactly the way expected for negatively charged particles. These experiments provided the first strong evidence that cathode rays consisted of particles carrying negative electric charge.
Connection to Medicine and Technology
Cathode-ray tubes were once widely used in television sets and computer monitors, but they also played an important role in science and medicine. Electron beams produced in vacuum tubes laid the foundation for technologies such as electron microscopes, medical imaging displays, particle accelerators, and radiation therapy systems. Understanding how electrons behave in electric and magnetic fields remains essential in many areas of modern healthcare.
The decisive breakthrough came through the work of English physicist J. J. Thomson (1856–1940). Thomson improved cathode-ray tube experiments by applying both electric and magnetic fields to the electron beam (Figures 106.2–106.4). He showed that the beam always behaved as negatively charged particles, regardless of the type of gas inside the tube or the material used for the electrodes. This demonstrated that electrons are universal components of all atoms rather than particles unique to a particular substance.
Thomson also performed the first measurement of the electron's charge-to-mass ratio,
an important milestone because neither the electron's charge nor its mass was known individually. By measuring their ratio, Thomson established that electrons have an extraordinarily large amount of charge compared with their mass, implying that they are far lighter than any atom.
To make this measurement, Thomson passed the electron beam through crossed electric and magnetic fields. By carefully adjusting the strengths of the fields until the electric and magnetic forces exactly balanced, the beam traveled in a straight line instead of being deflected. Under these conditions, the electron's speed is given by
where E is the electric field strength and B is the magnetic field strength. Once the electron velocity was known, Thomson could determine the charge-to-mass ratio by measuring how much the beam was deflected when either the electric or magnetic field acted alone. This experiment marked the first quantitative measurement of a property of the electron and provided compelling evidence that atoms contain much smaller, negatively charged particles.
To understand how Thomson determined the electron's charge-to-mass ratio, consider first the force exerted on an electron by an electric field. The electric force is
This force causes the electron to accelerate. According to Newton's second law, the acceleration is
Substituting the expression for the electric force into Newton's second law gives
Rearranging the equation yields the quantity Thomson wished to measure:
The acceleration of the beam can be determined from its observed deflection, while the electric field is calculated from the applied voltage and the separation of the plates. Together, these measurements provide the electron's charge-to-mass ratio.
Thomson verified his results independently using magnetic fields. The magnetic force on a moving charged particle is
where v is the electron's speed and B is the magnetic field strength. Since this force also produces the observed acceleration,
which can be rearranged to obtain the same ratio:
The agreement between measurements using electric and magnetic fields provided strong evidence that the results were correct.
Thomson found that the electron's charge-to-mass ratio is
This remarkably large value indicated that electrons either carry an unusually large electric charge or, more likely, have an extremely small mass. Comparison with positively charged hydrogen ions (now known to be protons) showed that the electron has a much larger charge-to-mass ratio than any known atom or ion.
For comparison, the charge-to-mass ratio of a proton is
where qp and mp are the proton's charge and mass. Because electrons and protons carry equal amounts of charge but with opposite signs, this comparison shows that the proton is approximately
or 1836 times more massive than the electron.
Why the Charge-to-Mass Ratio Matters
Thomson's experiment did not measure the electron's charge or mass separately. Instead, it measured their ratio. This was a crucial first step because once another experiment determined the electron's charge, its mass could be calculated immediately. Together, Thomson's and Millikan's experiments established two of the most fundamental constants in physics.
Thomson repeated his experiments using different gases and different methods of producing electrons, including the photoelectric effect. Every experiment gave the same value for the charge-to-mass ratio, demonstrating that electrons are identical particles present in every atom. This discovery fundamentally changed the view of matter: atoms were no longer considered indivisible but instead were shown to contain smaller constituents.
For his pioneering work, much of which was published beginning in 1897, Thomson received the 1906 Nobel Prize in Physics. Reflecting on his discovery, he later wrote, "It was only when I was convinced that the experiment left no escape from it that I published my belief in the existence of bodies smaller than atoms."
Although Thomson successfully measured the charge-to-mass ratio, he was unable to determine the charge of an individual electron with high precision. Earlier work by Michael Faraday on electrolysis had suggested that electric charge exists in discrete units, leading to an estimate of approximately
for the charge carried by a single ion. However, a direct and accurate measurement required a different experimental approach.
American physicist Robert Millikan developed that approach in what became one of the most famous experiments in physics. His oil drop experiment provided the first precise measurement of the electron's charge and confirmed that electric charge is quantized—that is, it always occurs in integer multiples of a fundamental unit. The experiment is shown in Figures 106.5 and 106.6.
In the Millikan oil drop experiment, microscopic droplets of oil were sprayed into a chamber between two parallel metal plates. During the spraying process, some droplets acquired extra electrons and became negatively charged. By applying a voltage across the plates, an upward electric force could be produced to oppose the downward force of gravity.
When a droplet was suspended motionless, the electric and gravitational forces were exactly balanced:
This simple balance allowed the electric charge on the droplet to be determined.
The electric field between the plates is related to the applied voltage by
where V is the voltage applied across the plates and d is their separation. By adjusting the voltage until a droplet neither rose nor fell, Millikan precisely determined the electric field acting on that droplet.
The droplets themselves were too small to weigh directly. Instead, Millikan measured how quickly each droplet fell after the electric field was turned off. Because air resistance is significant for such tiny particles, the droplet eventually reaches a constant terminal speed. Using this speed together with the known properties of air and oil, the droplet's mass could be calculated.
Substituting the electric field into the force balance gives the charge carried by the droplet:
By repeating this procedure for many different droplets, Millikan made two remarkable discoveries. First, he measured the magnitude of the electron's charge with unprecedented precision. Second, he found that every measured charge was an integer multiple of the same fundamental value. This demonstrated that electric charge is quantized; it exists only in discrete units rather than varying continuously.
By 1913, Millikan had measured the electron's charge to within about 1% of its true value and later improved the accuracy by nearly an order of magnitude. The accepted value is
For this achievement, together with his studies of the photoelectric effect, Millikan received the 1923 Nobel Prize in Physics.
A Fundamental Constant of Nature
The electron's charge is one of the fundamental constants of physics. Every electron anywhere in the universe carries exactly the same charge, and every proton carries an equal amount of positive charge. This universal property underlies all electrical phenomena, from the flow of current in electronic devices to the electrical activity of nerve cells and the interactions between atoms in biological molecules.
Once both the electron's charge and its charge-to-mass ratio were known, calculating the electron's mass became straightforward:
Substituting the measured values gives
which yields
This extraordinarily small mass has been confirmed by many independent experiments and is now known with extremely high precision. A similar calculation gives the proton's mass:
The proton is therefore approximately 1836 times more massive than the electron, even though the two particles carry electric charges of equal magnitude.
Together, the experiments of Thomson and Millikan established that electrons are fundamental constituents of every atom. They showed not only that atoms possess internal structure, but also that electrons contribute only a tiny fraction of an atom's total mass. The obvious question that remained was: Where is the rest of the mass located? The answer came only a few years later through Ernest Rutherford's famous gold foil experiment.
These discoveries also revealed an important feature of the microscopic world: all electrons are completely identical. Every electron has exactly the same mass and electric charge, regardless of where it is found. The same is true for other fundamental particles such as protons. Unlike macroscopic objects, which vary from one another, elementary particles are indistinguishable copies of one another—a key principle of quantum physics.
The Nucleus
By the beginning of the twentieth century, scientists knew that atoms contained electrons, but they still did not know how those electrons were arranged or where most of an atom's mass was located. The next major breakthrough came from experiments that revealed the existence of an extremely small, dense central nucleus. These experiments completely changed the accepted picture of the atom and laid the foundation for modern atomic and nuclear physics.
Understanding the nucleus is essential because nearly all of an atom's mass resides there. The nucleus also determines the identity of an element and is responsible for the nuclear processes that power stars, produce medical isotopes, and enable technologies such as PET imaging and radiation therapy.
Following the discovery of radioactivity in 1896, scientists began using naturally emitted radiation to probe matter. One of the leading researchers was Ernest Rutherford (1871–1937), often called the father of nuclear physics. Working with his collaborators, Rutherford designed an experiment that used energetic alpha particles to investigate the internal structure of atoms.
In Rutherford's experiment, a radioactive source emitted a narrow beam of alpha particles, which are helium nuclei carrying two positive charges. The beam was directed at an extremely thin sheet of gold foil, and a surrounding phosphorescent screen detected the locations where the alpha particles emerged after passing through the foil.
Figure 106.7. Rutherford's gold foil experiment used a beam of energetic alpha particles to probe the internal structure of atoms. Most particles passed straight through the thin gold foil, while a small fraction were deflected through large angles or even scattered backward. These observations demonstrated that nearly all of an atom's mass and positive charge are concentrated within a tiny central nucleus. Alpha particles typically had energies of about
Alpha particles have kinetic energies of approximately
which is millions of electron volts—far greater than the energies associated with ordinary atomic processes. Because of this high energy, physicists expected the alpha particles to pass almost unaffected through a thin metal foil if the positive charge inside the atom were spread uniformly throughout its volume, as proposed in J. J. Thomson's "plum pudding" model.
The results were surprising. As expected, most alpha particles passed straight through the foil with little or no deflection. However, a very small number were scattered through large angles, and some even rebounded almost directly back toward the source.
These observations could only be explained if nearly all of the atom's positive charge and mass were concentrated into an extremely small central region. When an alpha particle passed close to this region, the strong electrostatic repulsion between two positively charged objects caused its path to bend sharply. A nearly head-on encounter produced a complete reversal of direction.
Detailed analysis of the scattering pattern showed that atomic nuclei are extraordinarily small compared with the atoms themselves while containing almost all of the atom's mass. This conclusion completely overturned previous models of atomic structure.
Rutherford later recalled his astonishment at the result:
"It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."
After carefully analyzing the experimental evidence, Rutherford proposed in 1911 that every atom contains a tiny central nucleus with a diameter of approximately
roughly 100,000 times smaller than the diameter of a typical atom, which is about
Because nearly all of an atom's mass is packed into such a tiny volume, nuclear matter has an extraordinarily high density. The existence of such a dense, positively charged nucleus also implied that previously unknown forces must act within the nucleus to hold its positively charged particles together despite their mutual electrostatic repulsion. These forces, now known as the strong nuclear force, will be explored in later chapters.
Perhaps the most important conclusion from Rutherford's experiment is that atoms are mostly empty space. Since the nucleus occupies only a tiny fraction of the atom's volume, most alpha particles pass through the foil without ever approaching a nucleus closely enough to experience a significant force.
Figure 106.8. Enlarged view of atoms within the gold foil. The circles represent atoms approximately
in diameter, while the dots represent nuclei about
across. (The nuclei are drawn much larger than scale for visibility.) Most alpha particles pass through the empty space surrounding the nuclei, while the rare particles that approach a nucleus closely are strongly deflected.
Based on these findings, Rutherford proposed the planetary model of the atom. In this model, lightweight electrons orbit a massive, positively charged nucleus much as planets orbit the Sun. Although this classical picture was later refined by quantum mechanics, it represented a major advance because it correctly identified the existence of the nucleus and recognized that atoms are mostly empty space.
Figure 106.9. Rutherford's planetary model depicts electrons moving around a tiny, massive nucleus. Although modern quantum mechanics has replaced the idea of fixed electron orbits with electron probability distributions, Rutherford's model correctly identified the central nucleus and the largely empty interior of the atom.
Connection to Nuclear Medicine
Rutherford's work established that radioactive emissions originate in the atomic nucleus. Today, this understanding forms the basis of nuclear medicine. Radioactive nuclei are used to produce diagnostic images in PET and SPECT scanners, while carefully selected radioactive isotopes are used to destroy cancer cells during radiation therapy. These medical applications all rely on the same fundamental nuclear properties first revealed by Rutherford's experiments.
Rutherford's discovery marked the beginning of nuclear physics and fundamentally changed our understanding of matter. It showed that atoms possess an internal structure consisting of tiny electrons surrounding an even smaller nucleus. The next challenge for physicists was to explain why electrons remain around the nucleus instead of simply collapsing into it—a question whose answer required the development of quantum mechanics.
Interactive Exploration: Rutherford Scattering
In 1909, Ernest Rutherford and his collaborators carried out one of the most influential experiments in the history of physics. By directing a beam of alpha particles at a thin sheet of gold foil, they discovered that atoms are composed mostly of empty space surrounding a tiny, dense, positively charged nucleus. This experiment overturned the previously accepted Plum Pudding model of the atom and led to the modern nuclear model.
In the simulation below, you can recreate Rutherford's experiment by firing alpha particles at atoms represented by different atomic models. Compare the behavior of the particles in each model and observe how experimental evidence can be used to test scientific ideas. As you work through the activity, consider how the observed scattering patterns reveal the internal structure of the atom.
Guided Exploration
As you explore the simulation, answer the following questions:
- Select the Plum Pudding model. How do the alpha particles behave as they pass through the atom? Are any particles scattered through large angles?
- Switch to the Rutherford Nuclear model. What differences do you observe in the paths of the alpha particles?
- Approximately what fraction of the alpha particles pass straight through the atom without noticeable deflection? What does this suggest about the amount of empty space inside an atom?
- Observe the few particles that undergo large-angle deflections or are reflected backward. What feature of the atom must exist to produce these rare events?
- Compare the predictions of the Plum Pudding and Rutherford models. Which model better matches the experimental observations? Explain your reasoning.
- Based on your observations, explain why Rutherford concluded that nearly all of an atom's positive charge and mass are concentrated within a tiny central nucleus.
Reflection: Rutherford's experiment showed that although most alpha particles passed through the foil unaffected, a small fraction experienced dramatic deflections. This combination of common and rare events provided convincing evidence that atoms are mostly empty space containing a very small, dense, positively charged nucleus—a model that remains the foundation of modern atomic physics.
Section Summary
- Atoms are composed of two primary components: negatively charged electrons and a small, positively charged nucleus that contains nearly all of the atom's mass.
- J. J. Thomson's cathode-ray tube experiments demonstrated that electrons are fundamental particles found in every atom. He measured the electron's charge-to-mass ratio as
- Robert Millikan's oil drop experiment provided the first precise measurement of the electron's charge and demonstrated that electric charge is quantized, occurring only in integer multiples of a fundamental unit.
- Combining Thomson's and Millikan's results allowed scientists to calculate the electron's mass:
- The positive charge of the nucleus is carried by protons, whose charge-to-mass ratio is
- and whose mass is
- Rutherford's gold foil experiment showed that atoms are mostly empty space with nearly all of their positive charge and mass concentrated in a tiny central nucleus approximately
in diameter, about 100,000 times smaller than the atom itself.
- Rutherford's planetary model placed electrons around a small, massive nucleus. Although later replaced by the quantum mechanical model, it correctly identified the existence of the nucleus and represented a major advance in understanding atomic structure.
Conceptual Questions
- What two pieces of evidence allowed the first calculation of [latex]{m}_{e}[/latex], the mass of the electron? (a) The ratios [latex]{q}_{e}/{m}_{e}[/latex] and [latex]{q}_{p}/{m}_{p}[/latex]. (b) The values of [latex]{q}_{e}[/latex] and [latex]{E}_{B}[/latex]. (c) The ratio [latex]{q}_{e}/{m}_{e}[/latex] and [latex]{q}_{e}[/latex]. Justify your response.
- How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.
Problems & Exercises
- Rutherford found the size of the nucleus to be about [latex]{\text{10}}^{-\text{15}}\phantom{\rule{0.25em}{0ex}}\text{m}[/latex]. This implied a huge density. What would this density be for gold?
- In Millikan's oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2033 V, and the plate separation to be 2.00 cm. The oil drop (of density [latex]0\text{.}{\text{81 g/cm}}^{3}[/latex]) has a diameter of [latex]4\text{.}0\times{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m}[/latex]. Find the charge on the drop, in terms of electron units.
- (a) An aspiring physicist wants to build a scale model of a hydrogen atom for her science fair project. If the atom is 1.00 m in diameter, how big should she try to make the nucleus? (b) How easy will this be to do?
Glossary
- cathode-ray tube (CRT)
- 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.
- planetary model of the atom
- 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.
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.
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.
