The Story of Nuclear Energy, Volume 2 (of 3): Mass and Energy

A field-ion microscope view of atoms in a crystal. Each tiny white dot is a single atom, and each ring system is a crystal facet or plane. The picture is magnified 1,500,000 times.

Worlds Within Worlds: The Story of Nuclear Energy, Volume 2 (of 3), by Isaac Asimov is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here. Volume II: MASS AND ENERGY

MASS AND ENERGY

In 1900 it began to dawn on physicists that there was a vast store of energy within the atom; a store no one earlier had imagined existed. The sheer size of the energy store in the atom—millions of times that known to exist in the form of chemical energy—seemed unbelievable at first. Yet that size quickly came to make sense as a result of a line of research that seemed, at the beginning, to have nothing to do with energy.

Suppose a ball were thrown forward at a velocity of 20 kilometers per hour by a man on top of a flatcar that is moving forward at 20 kilometers an hour. To someone watching from the roadside the ball would appear to be travelling at 40 kilometers an hour. The velocity of the thrower is added to the velocity of the ball.

If the ball were thrown forward at 20 kilometers an hour by a man on top of a flatcar that is moving backward at 20 kilometers an hour, then the ball (to someone watching from the roadside) would seem to be not moving at all after it left the hand of the thrower. It would just drop to the ground.

There seemed no reason in the 19th century to suppose that light didn’t behave in the same fashion. It was known to travel at the enormous speed of just a trifle under 300,000 kilometers per second, while earth moved in its orbit about the sun at a speed of about 30 kilometers per second. Surely if a beam of light beginning at some earth-bound source shone in the direction of earth’s travel, it ought to move at a speed of 300,030 kilometers per second. If it shone in the opposite direction, against earth’s motion, it ought to move at a speed of 299,970 kilometers per second.

Could such a small difference in an enormous speed be detected?

Albert A. Michelson

The German-American physicist Albert Abraham Michelson (1852-1931) had invented a delicate instrument, the interferometer, that could compare the velocities of different beams of light with great precision. In 1887 he and a co-worker, the American chemist Edward Williams Morley (1838-1923), tried to measure the comparative speeds of light, using beams headed in different directions. Some of this work was performed at the U. S. Naval Academy and some at the Case Institute.

The results of the Michelson-Morley experiment were unexpected. It showed no difference in the measured speed of light. No matter what the direction of the beam—whether it went in the direction of the earth’s movement, or against it, or at any angle to it—the speed of light always appeared to be exactly the same.

To explain this, the German-Swiss-American scientist Albert Einstein (1879-1955) advanced his “special theory of relativity” in 1905. According to Einstein’s view, speeds could not merely be added. A ball thrown forward at 20 kilometers an hour by a man moving at 20 kilometers an hour in the same direction would not seem to be going 40 kilometers an hour to an observer at the roadside. It would seem to be going very slightly less than 40 kilometers an hour; so slightly less that the difference couldn’t be measured.

However, as speeds grew higher and higher, the discrepancy in the addition grew greater and greater (according to a formula Einstein derived) until, at velocities of tens of thousands of kilometers per hour, that discrepancy could be easily measured. At the speed of light, which Einstein showed was a limiting velocity that an observer would never reach, the discrepancy became so great that the speed of the light source, however great, added or subtracted zero to or from the speed of light.

Accompanying this were all sorts of other effects. It could be shown by Einstein’s reasoning that no object possessing mass could move faster than the speed of light. What’s more, as an object moved faster and faster, its length in the direction of motion (as measured by a stationary 72observer) grew shorter and shorter, while its mass grew greater and greater. At 260,000 kilometers per second, its length in the direction of movement was only half what it was at rest, and its mass was twice what it was. As the speed of light was approached, its length would approach zero in the direction of motion, while its mass would approach the infinite.

Could this really be so? Ordinary objects never moved so fast as to make their lengths and masses show any measurable change. What about subatomic particles, however, which moved at tens of thousands of kilometers per second? The German physicist Alfred Heinrich Bucherer (1863-1927) reported in 1908 that speeding electrons did gain in mass just the amount predicted by Einstein’s theory. The increased mass with energy has been confirmed with great precision in recent years. Einstein’s special theory of relativity has met many experimental tests exactly ever since and it is generally accepted by physicists today.

Einstein’s theory gave rise to something else as well. Einstein deduced that mass was a form of energy. He worked out a relationship (the “mass-energy equivalence”) that is expressed as follows:

E = mc²

where E represents energy, m is mass, and c is the speed of light.

If mass is measured in grams and the speed of light is measured in centimeters per second, then the equation will yield the energy in a unit called “ergs”. It turns out that 1 gram of mass is equal to 900,000,000,000,000,000,000 (900 billion billion) ergs of energy. The erg is a very small unit of energy, but 900 billion billion of them mount up.

The energy equivalent of 1 gram of mass (and remember that a gram, in ordinary units, is only ¹/₂₈ of an ounce) would keep a 100-watt light bulb burning for 35,000 years.

It is this vast difference between the tiny quantity of mass and the huge amount of energy to which it is equivalent that obscured the relationship over the years. When a chemical reaction liberates energy, the mass of the materials undergoing the reaction decreases slightly—but very slightly.

Suppose, for instance, a gallon of gasoline is burned. The gallon of gasoline has a mass of 2800 grams and combines with about 10,000 grams of oxygen to form carbon dioxide and water, yielding 1.35 million billion ergs. That’s a lot of energy and it will drive an automobile for some 25 to 30 kilometers. But by Einstein’s equation all that energy is equivalent to only a little over a millionth of a gram. You start with 12,800 grams of reacting materials and you end with 12,800 grams minus a millionth of a gram or so that was given off as energy.

No instrument known to the chemists of the 19th century could have detected so tiny a loss of mass in such a 74large total. No wonder, then, that from Lavoisier on, scientists thought that the law of conservation of mass held exactly.

Radioactive changes gave off much more energy per atom than chemical changes did, and the percentage loss in mass was correspondingly greater. The loss of mass in radioactive changes was found to match the production of energy in just the way Einstein predicted.

It was no longer quite accurate to talk about the conservation of mass after 1905 (even though mass was just about conserved in ordinary chemical reactions so that the law could continue to be used by chemists without trouble). Instead, it is more proper to speak of the conservation of energy, and to remember that mass was one form of energy and a very concentrated form.

The mass-energy equivalence fully explained why the atom should contain so great a store of energy. Indeed, the surprise was that radioactive changes gave off as little energy as they did. When a uranium atom broke down through a series of steps to a lead atom, it produced a million times as much energy as that same atom would release if it were involved in even the most violent of chemical changes. Nevertheless, that enormous energy change in the radioactive breakdown represented only about one-half of 1% of the total energy to which the mass of the uranium atom was equivalent.

Once Rutherford worked out the nuclear theory of the atom, it became clear from the mass-energy equivalence that the source of the energy of radioactivity was likely to be in the atomic nucleus where almost all the mass of the atom was to be found.

The attention of physicists therefore turned to the nucleus.

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Isaac Asimov. 2015. Worlds Within Worlds: The Story of Nuclear Energy, Volume 2 (of 3). Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from https://www.gutenberg.org/files/49820/49820-h/49820-h.htm#c16

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