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?
[Illustration: _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 observer) 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_ = _mc_²
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.
[Illustration: ENERGY CREATED compared to MATTER (OR MASS) DESTROYED]
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 large 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.