Biographies & Memoirs

Part V

The Quantum and the Universe

In this part . . .

Quantum theory began with Einstein’s paper on the photoelectric effect, during his miracle year of 1905. With that paper, Einstein created his second revolution in physics. In this part, I tell you why it was a revolution and how it changed our ideas of reality.

I also describe to you Einstein’s famous letter to President Franklin Delano Roosevelt about the possibility of an atomic bomb and Einstein’s limited involvement with its development. Finally, I show you the relevance of Einstein’s work and the important role that it’s still playing today in the current theories of the universe and in the unification of all of physics. This unification was Einstein’s lifelong dream.

Chapter 15

Atoms Before Einstein

In This Chapter

bullet Considering Einstein’s PhD thesis

bullet Exploring the nature of the atom

bullet Refining our understanding of the atom and its components

bullet Explaining light quanta

bullet Introducing Bohr’s atom

A s I explain in Chapter 4, the idea of the atom didn’t originate in the modern world. The Greek philosopher Democritus, who lived in the fifth century B.C., first penned the idea that all things are made up of small, indivisible particles called atoms, meaning “indivisible.”

But the human race got a little distracted and forgot all about the atom for about two millennia. In the 19th century, English chemist John Dalton reintroduced the idea and backed it up with some experiments.

In his PhD thesis, Einstein showed the world how to determine the real dimensions of atoms. But he didn’t develop his ideas in isolation; as always, he used the existing knowledge of atoms at the time as a springboard. In this chapter, I show you what that existing knowledge was. I give you a quick tour of what Einstein knew about the atom as he was working on his PhD, and I explain some important discoveries during Einstein’s lifetime that changed the way we think about matter.


Greek atomic physics

In the fifth century BC, Democritus thought that everything was made up of indivisible atoms that came in different sizes, masses, and colors. He explained that the different substances we see are combinations of these atoms.

But the ancient Greeks didn’t really do much science in the way we understand it today. Except for Archimedes (whose work I describe in Chapter 4), the Greek thinkers were thinking, not experimenting. Their ideas were much further ahead than their technology. You need delicate instruments to show that atoms exist, and the Greeks didn’t have them.

It’s no wonder that the idea of atoms didn’t catch on. Aristotle came along with the much simpler idea that everything is made up of only four elements — earth, water, air, and fire. He explained that these four elements have their own natural place, and that motion is an attempt to reach these natural places. His idea, which was easier to digest, caught on.


Proving the Reality of Atoms

Einstein’s PhD thesis was entitled “A new determination of molecular dimensions.” He wrote it during the incredible output of creativity of his miracle year (see Chapter 3). This thesis was part of his second attempt at getting a PhD. He’d tried before, back in 1901, a year and a half after graduating from the Polytechnic. (At that time, he’d submitted a thesis on molecular forces, but it was rejected. See the sidebar “Einstein’s rejected thesis.”)

In his PhD dissertation, Einstein described a new method to calculate the diameters of individual molecules, as well as a new way to calculate Avogadro’s number. This number had been discovered in 1811 by the Italian physicist Amadeo Avogadro in connection with his suggestion that the same volumes of any gas kept at the same temperature and pressure contain the same number of molecules; the chemical or physical properties of the gas don’t affect the number of molecules. Avogadro’s theory inspired experiments that eventually determined that a specific volume of any gas (22.4 liters, or the volume of a box that holds a basketball) contains what we now call Avogadro’s number of molecules. Avogadro’s number is 600 sextillion (6 followed by 23 zeros) molecules — a mind-boggling number.

With Einstein’s dissertation paper, as well as with a follow-up paper he wrote that explained Brownian motion (the constant motion of tiny particles that had been observed by Scottish botanist Robert Brown), Einstein was concerned with “discovering facts which would guarantee as far as possible the existence of atoms of definite, finite size.”

Today, we can see atoms. Modern scanning tunneling microscopes can map surfaces with atomic resolution. Figure 15-1 shows a scanning tunneling microscope image of graphite atoms. Graphite is a form of carbon, and each hill is a carbon atom. The distance between adjacent carbon atoms is 25 billionths of a centimeter.

Figure 15-1: A scanning tunneling microscope image of graphite atoms.

Figure 15-1: A scanning tunneling microscope image of graphite atoms.

Image by the author

Even back in the 1950s, field ion microscopes allowed scientists to obtain direct images of atoms. Not so at the beginning of the 20th century. Although most physicists and chemists accepted the reality of atoms, there were still some doubters. So Einstein set out to offer irrefutable proof of atoms’ existence.


Einstein’s rejected thesis

Einstein’s first attempt at getting a PhD was unsuccessful because of a combination of politics and a bit of immaturity on Einstein’s part. After graduating from the Polytechnic, he’d been accepted as a doctoral student by Dr. Alfred Kleiner at the University of Zurich and was working on a thesis on molecular forces.

He became interested in physicist Paul Drude’s work on the theory of metals, which indicated that electrons behave as a gas within a metal. Einstein was impressed with this work but found a couple of flaws with Drude’s theory. It appears that Einstein didn’t agree with Drude’s assumption that there were both positive and negative charges within the metal. Einstein’s second objection was related to Drude’s use of Ludwig Boltzmann’s statistical theory on molecular motion, in which he had also found a gap.

Einstein wrote to Drude expressing his concerns. Drude replied to Einstein, dismissing his disagreement and stating that an eminent colleague had agreed with his theory. Einstein became angry. In a letter to his fiancée, Mileva Maric, Einstein promised to attack Drude in the Annalen der Physik (which was going to be a bit difficult because Drude was the editor).

Einstein included his criticisms of Drude’s theories in his thesis, even though they weren’t directly related to his subject matter. Kleiner was not about to approve a thesis that criticized Drude or questioned Boltzmann’s well-established theory. He rejected it.


Understanding Atoms with a Grain of Salt

Atoms are complicated little things. Take your salt shaker and sprinkle a few grains on the table. Each one of those tiny grains has one quintillion (1 followed by 18 zeros) atoms of sodium and the same number of atoms of chlorine. How did we ever discover what these incredibly small things are made of? It wasn’t easy.

Figuring out why balloons pop

The first step on the long road was taken in 1738, when the Swiss mathematician Daniel Bernoulli used the idea that gases are made up of small particles to explain how these gases exert pressure on a container. He explained that the pressure is due to the collisions of these particles with the walls of the container.


According to Bernoulli, if you have a gas in a container, the pressure of the gas comes from the speed of the molecules hitting the walls of the container and how often they hit it. The speed of the molecules is related to temperature. If you keep the same volume, pressure, and temperature, then you always have the same number of molecules.

Eighty years before Bernoulli, Newton’s contemporary Robert Boyle had performed experiments with gases and discovered what we know today as Boyle’s law, which explains how the pressure of a gas increases when its volume decreases (as long as we keep the gas at the same temperature). For example, if you squeeze a balloon, the pressure increases. If you keep squeezing harder and harder, the pressure becomes so large that the balloon pops.

Bernoulli analyzed the increase in particle collisions when the volume of a container (such as a balloon) shrinks. In doing so, he was able to arrive at the same mathematical conclusion stated in Boyle law. Bernoulli’s analysis marks the first time that anyone used the idea of atoms as the building blocks of matter to successfully calculate a property of something.

Explaining elements

The next important step toward the understanding of the atom was the discovery that certain substances can’t be reduced any further by chemical means. These basic substances, or elements, combine in very specific and predictable ways to form all the substances that we know.

In 1808, the great chemist John Dalton showed that you can explain these chemical rules of how the elements combine with each other by assuming three things:


bullet Each element is made of a specific atom.

bullet All the atoms of the same element are identical and different from the atoms of other elements.

bullet These atoms combine in very specific ways to form all the substances we see in the universe.


Another line of work, initially unrelated to the search for the atom, was taking place in the 19th century. Michael Faraday, the self-taught English scientist who invented the idea of fields (see Chapter 6), was studying how electrical currents break up water and other chemical compounds. He proposed that electricity wasn’t a fluid but existed as small particles that carry the electric charge, as Ben Franklin had suggested. Some time later, scientists began to call these particles electrons.

Discovering electrons

In the late 19th century, scientists studying electricity began to use an apparatus made of a sealed glass tube with no air in it that had two small metal discs at each end (see Figure 15-2). The metal discs were connected to a battery, and the idea was to see what would happen with electricity in the vacuum of the tube.

Figure 15-2: A cathode ray tube, the precursor of the television tube and the computer CRT.

Figure 15-2: A cathode ray tube, the precursor of the television tube and the computer CRT.

What happened was that the tube glowed with a strange green light. At the time, this phenomenon had no explanation. Physicists called the metal disk that emitted the glow the cathode and the opposite disk the anode. The cathode was connected to the negative end of the battery and the anode to the positive. The rays were named cathode rays, and the whole device was a cathode ray tube, or CRT. (You probably use CRTs all the time. Television tubes are CRTs, and older computer models use them as well.)


In 1897, at the Cavendish laboratory in Cambridge, England, the physicist J.J. Thomson, the director of the lab, designed experiments in an effort to understand the nature of the mysterious green glow in CRTs. Thomson and his 20 researchers were able to deflect the green light beam and discovered that it had a negative charge. Thomson concluded that the green glow was made by individual particles passing through the vacuum of the tube, and he was able to measure their charge. These negatively charged particles were later called electrons.

Thomson was also able to measure the ratio of the electron’s mass to its charge. That measurement told him that these electrons are about 2,000 times smaller than the smallest atom, hydrogen.

Envisioning plum pudding

Atoms, then, aren’t the smallest bits of matter, like Dalton had said. These electrons are much smaller still. Are atoms made up of electrons? That possibility sounded interesting to Thomson. However, matter is neutral, and these electrons are negatively charged.

Thomson needed some positive body in the atom that would counterbalance the negative electrons and form a neutral atom. He proposed a plum pudding type of arrangement. The electrons would be the raisins, and the pudding was the positive body in the atom (see Figure 15-3).

As soon as Thomson proposed his model, two major discoveries made it obsolete. In Germany, Wilhelm Roentgen discovered a powerful radiation that he called x-rays. In Paris, Henri Becquerel and Marie and Pierre Curie, experimenting with uranium crystals, discovered that certain atoms emit radiation of a type that they hadn’t seen before. The new phenomenon was called radioactivity.

What was causing these new rays? Thomson’s atom, with electrons in a positive “pudding,” wouldn’t account for these rays coming out of certain atoms. Clearly, there were other things inside the atom.

Figure 15-3: The first model of the atom, with the negative electrons like raisins inside a positive pudding.

Figure 15-3: The first model of the atom, with the negative electrons like raisins inside a positive pudding.

One of J.J. Thomson’s former students, a New Zealander by the name of Ernest Rutherford, saw that the radioactivity that the French scientists had discovered was of two different kinds. He placed sheets of aluminum foil in front of the device that was detecting the radiation and noticed that he could easily stop one kind of radiation, which he called alpha rays, while the other, the beta rays, required more sheets of aluminum to stop. (Later, physicists discovered yet another type, gamma rays.) As I explain in the next section, Rutherford later showed that the alpha rays have positive charge. And the Paris group showed that the beta rays are negative.

Probing the Atom

What scientists needed was a way to look inside the atom. Physicists knew that atoms were too small to be seen even with the most powerful microscopes available.

Rutherford and his assistant, Hans Geiger, discovered that when an alpha particle hit a screen painted with a specific type of coating, the coating would flash. The coating gave Rutherford the tool he needed. He couldn’t see the atom, but he might be able to see what the atom does to the alpha particles if he could throw the particles at the atom. Because he now had a way to detect the alpha particles, he could see where they hit and how the atoms changed or didn’t change their path.


Think of Rutherford’s experiment this way: If you are in a pitch-dark room and have a ball painted with a fluorescent paint, you can throw the ball around and see how it bounces off any columns or walls (see Figure 15-4). You can’t see the walls, but you can deduce their presence by looking at how the ball bounces off them.

Figure 15-4: If you throw projectiles at invisible obstacles, you can make them visible.

Figure 15-4: If you throw projectiles at invisible obstacles, you can make them visible.

That’s what Rutherford did: He threw alpha particles at gold atoms to see how the particles would bounce off the invisible atoms. With Geiger’s help, he used the radioactive element radium as his source of alpha particle projectiles, and he aimed the projectiles at the gold atoms in a thin sheet of gold foil. Behind the foil, he placed a screen painted with his new coating (see Figure 15-5). Rutherford asked Geiger to take data and to change the location of the screen around, to see how the alphas were being deflected.

Figure 15-5: Rutherford’s famous experiment.

Figure 15-5: Rutherford’s famous experiment.

Recall that J.J. Thomson had found that atoms contain negative electrons. But Thomson and other scientists knew that something positive must be in the atom as well, to balance the negative electrons, because atoms are electrically neutral. What was that positive something, and where was it? That’s what Rutherford wanted to know.

The flashes on Rutherford’s screen provided the answer. Geiger was back in the lab taking data. He saw most of the flashes when the screen was placed right on the other side of the gold foil or within a couple of degrees. Rutherford was expecting that. A fast alpha particle would pass through the crowd of electrons in the gold atom and, in general, continue on its path. Every once in a while, one alpha might go closer to an electron or two so that their electrical repulsion would push it away a bit. But the repulsion wouldn’t push it much, because the alphas were coming through fast.

Rutherford wanted to see what would happen if they moved the screen farther out still. He asked a bright undergraduate by the name of Ernest Marsden to move the screen up to about 45 degrees and to take the data. Marsden did and got a few flashes. Encouraged by this result, Marsden decided to move the screen out farther. Fifty degrees, sixty. He got some flashes. Seventy? Still some. He was getting counts with the screen at 75 and 80 degrees. Surely, if you placed the screen at right angles with the incoming alphas, you wouldn’t get anything. He did, and he saw some flashes.

What if he went to the other side? Still a few counts. All the way to the back? A few counts even there. He reported his results to Rutherford. Rutherford, who understood fully what he was doing, was astonished. It was like firing a 15-inch shell at tissue paper and expecting to see the bullet bounce back at you, he said later.

Creating a new model

These fast alphas were encountering something very strong inside the nucleus that made them bounce back. Rutherford made some calculations and decided that for that phenomenon to happen, the atom had to have a very small core of positive charge in the middle — a positively charged nucleus. And the nucleus would contain most of the mass of the atom (see Figure 15-6).

Figure 15-6: A close-up of Rutherford’s experiment.

Figure 15-6: A close-up of Rutherford’s experiment.


Rutherford published his results in 1911. In his paper, he proposed a new model of the atom, with a tiny, positively charged nucleus containing 99.9 percent of the mass of the entire atom. In this model, the negatively charged electrons are distributed throughout the volume of the atom, like a planetary system (see Figure 15-7). The total charge of the electrons is equal and opposite to the charge of the nucleus.

Figure 15-7: Rutherford’s nuclear model of the atom.

Figure 15-7: Rutherford’s nuclear model of the atom.

And, Rutherford said, the atom is very small. If you line up ten trillion atoms next to each other, they measure one centimeter (about half an inch). Also, the atom is almost empty. If the atom was the size of a concert hall, the nucleus would look like a pea at the center with the electrons like bees flying around.

Things were looking bright now. There was even a candidate for the positive particle that lived in the atomic nucleus: the proton. In Germany in 1886, Eugen Goldstein had observed positively charged particles that were 1,836 times more massive than the electron. Although they were more massive, the amount of electric charge these particles carried was the same as that of the electron.

Predicting an unrealized collapse

Soon, physicists calculated that the nucleus of hydrogen is a single proton. Hydrogen is simple: a proton at the center forming the nucleus, and a single electron moving around it.

Other atoms are more complex and were more challenging. Measurements and calculations were not working out for these atoms. The main problem was with the electrons moving around the nucleus. James Clerk Maxwell’s electromagnetism said that such an electric charge that moved around in a curved path would radiate energy. That meant the electrons should lose energy as they moved around in the atom, spiraling down and collapsing into the nucleus. Physicists calculated that it would take about a microsecond for this collapse to happen. But the collapse doesn’t happen; atoms are stable.

The solution came from two scientists who weren’t even working on the physics of the atom at the time, Max Planck and Einstein.

Discovering Quanta

At about the time that J.J. Thomson was doing his experiments with cathode ray tubes, Max Planck in Germany was trying to resolve another big unexplained problem in physics. This problem had to do with the way hot objects radiate energy. His explanation eventually helped scientists explain why the electron in an atom doesn’t collapse into the nucleus. But before it did that, Planck’s solution needed Einstein’s interpretation.


To understand the problem physicists were grappling with, consider an example close to home. When you turn on an electric stove, you can feel the element getting hot before there’s any appreciable change in color. Within a couple minutes, the element begins to glow red, and eventually, when it’s hot, it has an orange glow.

This thermal radiation is an electromagnetic wave. Sometimes you can’t see it, if the radiation is in the infrared range, for example. But sometimes the wavelength is in the visible range of the spectrum. And other times, the radiation is in the short wavelengths of the ultraviolet region.


Max Planck

Planck was born in Kiel, Germany, in 1858, the sixth son of a professor of Law at the University of Kiel. Planck came from a long line of academics; his grandfather and great-grandfather had also been professors.

When Planck was 9, his father accepted a position at the University of Munich. The high school that Planck attended in Munich had a great math and physics teacher, and Planck became very interested in these two subjects. He was always a top student.

Planck entered the University of Munich to study physics but didn’t get along with his professor, Philipp von Jolly. Von Jolly told Planck that there wasn’t anything new to be discovered in physics. Unhappy with the university, Planck decided to move to the University of Berlin, where the famous physicists Hermann von Helmholtz and Gustav Kirchhoff taught.

Like Einstein would do some years later, Planck became interested in areas that weren’t taught in courses, and he studied Rudolf Clausius’s work in thermodynamics from original journal papers. After getting his undergraduate degree, Planck wrote a thesis on the second law of thermodynamics and submitted it as a PhD dissertation to the University of Munich. The dissertation was approved, and Planck obtained his PhD in physics when he was only 21 years old.

Like most PhD physicists at the time, Planck was interested in an academic career. At the time in Germany, if you wanted to be a professor, you started as an instructor, or Privatdozent — an unpaid position with teaching duties. Privatdozents collected small fees from the students for administering exams. But you needed another job to survive. Planck was a Privatdozent in Munich from 1880 to 1885. In 1885, he was promoted to associate professor, which meant he finally got a regular salary for teaching.

With a steady income, he married his childhood girlfriend, Marie Merck. In 1889, Planck moved to the University of Berlin as a full professor, replacing Kirchhoff, who was retiring.

Planck was also a gifted pianist and seriously considered a career in music before deciding on physics. He became one of the most important scientists of all time, earning the Nobel Prize in physics in 1918 for his discovery of the quantum of energy.


Pitting theory against the real world

What is the source of this thermal radiation? When Planck began to study the problem, the prevalent model assumed that the thermal energy emitted by an object was formed by the continuous changes in energy of charged particles oscillating within the matter (see Figure 15-8). In this model, the distribution of energies at shorter and shorter wavelengths grew larger and larger, eventually tending toward infinity. This prediction was not only impossible; it was completely opposite to what Planck and other scientists were observing.

Figure 15-8: The heat radiated by an object comes from the energy changes of charged particles oscillating inside the body.

Figure 15-8: The heat radiated by an object comes from the energy changes of charged particles oscillating inside the body.

What physicists were observing was that at short wavelengths, the energy distributions actually grew smaller and smaller, moving toward zero at the very short wavelengths. These very short wavelengths are in the ultraviolet part of the spectrum, and physicists refer to this problem as the ultraviolet catastrophe.

The model predicted that bodies should radiate more energy at short wavelengths. The observations showed that bodies emit less energy at these wavelengths. The problem was serious, because the solutions that physicists were proposing were based on a very solid theoretical framework, but the real world data wasn’t matching. Physicists were worried because their failure to explain these new observations meant that thermodynamics, the study of heat and thermal effects (see Chapter 5), was flawed.

In 1900, when Planck was a professor of physics at the University of Munich, he decided to tackle the radiation problem. He used Maxwell’s electromagnetism to develop a theory that connected the heat or thermal energy of the radiating body and the charged oscillating particles. To do that, he had to use the statistical methods that Ludwig Boltzmann had invented for the distribution of energies in molecular collisions.

Splitting energy bundles


To derive his formula using Boltzmann’s statistical methods, Planck first had to split the total energy being radiated from an object into a number of bundles or packets all with the same energy. He then counted the possible ways of distributing these bundles among all the oscillating particles. Planck published his results in a series of papers between 1897 and 1900.

Planck’s formula, known today as Planck’s law, agreed perfectly with the observations. Planck, however, didn’t like the method he’d used to derive his equation. He wasn’t happy about using statistical methods in physics. But his equation worked.

At first, scientists didn’t appreciate the importance of Planck’s discovery. Planck himself didn’t fully understand what he’d done. His idea of splitting the total energy of the oscillators into bundles, or quanta (as they are called today), marked a turning point in the history of physics and made possible the development of the physics of the atom by Einstein and others.

Exploring the Bohr Atom

Planck’s law with the total energy radiated by a hot object split into bundles or quanta of energy was later generalized by Einstein into a revolutionary idea that started quantum theory. I discuss that development in Chapter 16. Here, I return to the problem of the collapse of the electron in orbit about the nucleus in Rutherford’s model.

In James Clerk Maxwell’s theory of electromagnetism, the charged electron moving around the nucleus gives off energy. (In the same way, Planck’s oscillating charges give off the energy of radiation in a hot object.) As these charges give off energy, they should fall into the nucleus in about a microsecond. But they don’t. Atoms are stable.

Rutherford proposed his model in 1911. Planck had published his solution to the ultraviolet catastrophe and the explanation of the energy distribution of objects in 1900. During his year of miracles, in 1905, Einstein generalized Planck’s idea of the energy quanta into a property of light and radiation.

All the elements were there to solve the riddle of the collapsing atom. But no one did. At least not right away.

Kicking marbles on a staircase

In 1913, the Danish physicist Niels Bohr came up with a new model of the atom that avoided the collapse of the electron. His model was similar to Rutherford’s planetary model but had an important difference. In Bohr’s model, the electrons orbit the nucleus in very specific orbits that he called stationary orbits. In these orbits, the electrons are safe. They don’t radiate any energy.


In Bohr’s theory, the electrons are allowed to move between orbits. When they jump to a lower orbit, they give off energy. After they arrive there, they are safe again, in another stationary orbit. If they gain energy, they jump to a higher orbit.

The electrons in Bohr’s atom are like marbles on a staircase (see Figure 15-9). If you carefully place a marble at the edge of one of the steps, it stays there safe. You can give the marble some energy by kicking it up. If you do that, the marble will land one, two, or any other number of steps higher and stay there. When the marble loses energy, it falls down, landing one, two, or several steps down. You can’t kick a marble so that it moves two and a half steps up. A marble that rolls off a given step won’t move down and stop in the middle of two steps, floating there. The allowed orbits for the marble are the steps.

Bohr said the same is true with electrons. Electrons can stay only in the allowed orbits. The places in between aren’t allowed.

Figure 15-9: Electrons in the Bohr atom are like marbles on a staircase. They are allowed only on certain specific orbits.

Figure 15-9: Electrons in the Bohr atom are like marbles on a staircase. They are allowed only on certain specific orbits.

The energies that the electrons give off or gain when they jump around in their orbits are Planck’s bundles or quanta. Electrons are allowed to give off or gain energy only in the form of these quanta.

Bohr used Planck’s theory to calculate the energies of the allowed stationary orbits for the atom. When he compared his calculations with experimental data, his theory agreed exactly.

Needing a new physics

Bohr’s theory provided a great advance toward the understanding of the atom. But it wasn’t the final word. When Bohr tried to apply his theory to other more complicated atoms, things didn’t work out as nicely. The energies of his allowed orbits didn’t quite match the energies measured for those atoms.

Soon, physicists realized that they needed something else. The physics of Newton and Maxwell, patched up with Planck’s and Bohr’s discoveries, wasn’t cutting it. A few physicists knew that a new physics was needed. The 26-year-old Einstein would give them the key to this new physics. Take a look at Chapter 16 for the details.

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