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The existence of energy of motion also explains why a cup of coffee is heavier when hot than when cold. Heat is microscopic motion. The atoms in a liquid or solid jiggle about, while the atoms in a gas fly hither and thither. Because the atoms in a cup of hot coffee are jiggling faster than the atoms in a stone-cold cup, they possess more energy of motion. Consequently, the coffee weighs more.

RABBITS OUT OF HATS

So much for energy having an equivalent mass, or weighing something. The fact that mass is a form of energy also has profound implications. Since one form of energy can be converted into another, mass-energy can be transformed into other forms of energy and, conversely, other forms of energy can be changed into mass-energy.

Take the latter process. If mass-energy can be made out of other forms of energy, it follows that mass can pop into existence where formerly no mass existed. This is exactly what happens in giant particle accelerators, or atom smashers. At CERN, the European centre for particle physics near Geneva, for instance, subatomic particles—the building blocks of atoms—are whirled around a subterranean racetrack and slammed together at speeds approaching that of light. In the violent smash-up, the tremendous energy of motion of the particles is converted into mass-energy—the mass of new particles that physicists wish to study. At the collision point, these particles appear apparently out of nothing, like rabbits out of a hat.

This phenomenon is an instance of one type of energy changing into mass-energy. But what about mass-energy changing into another type of energy? Does that happen? Yes, all the time.

A MILLION TIMES THE DESTRUCTIVE POWER OF DYNAMITE

Think of a piece of burning coal. Because the heat it gives out weighs something, the coal gradually loses mass. So if it were possible to collect and weigh all the products of burning—the ash, the gases given off, and so on—they would turn out to weigh less than the original lump of coal.

The amount of mass-energy turned into heat-energy when coal burns is so small as to be essentially unmeasurable. Nevertheless, there is a place in nature where a significant mass is converted into other forms of energy. It was identified by the English physicist Francis Aston in 1919 while he was “weighing” atoms.

Recall that each of the 92 naturally occurring atoms contains a nucleus made from two distinct subatomic particles—the proton and neutron.

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Since the masses of these two nucleons are essentially the same, the nucleus, at least as far as its weight is concerned, can be thought of as being made from a single building block. Think of it as a Lego brick. Hydrogen, the lightest nucleus, is therefore made from one Lego brick; uranium, the heaviest, is made from 238 Lego bricks.

Now, there had been a suspicion since the beginning of the 19th century that perhaps the Universe had started out with only one kind of atom—the simplest, hydrogen. Since that time, all the other atoms have somehow been built up from hydrogen, by the process of sticking together hydrogen Lego bricks. The evidence for the idea, which had been proposed by a London physician named William Prout in 1815, was that an atom like lithium appeared to weigh exactly six times as much as hydrogen, an atom like carbon exactly 12 times as much, and so on.

However, when Aston compared the masses of different kinds of atoms more precisely with an instrument he invented called a mass spectrograph, he discovered something different. Lithium in fact weighed a shade less than six hydrogen atoms; carbon weighed a shade less than 12 hydrogen atoms. The biggest discrepancy was helium, the second lightest atom. Since a helium nucleus was assembled from four Lego bricks, by rights it should weigh four times as much as a hydrogen atom. Instead, it weighed 0.8 per cent less than four hydrogen atoms. It was like putting four 1-kilogram bags of sugar on a set of scales and finding that they weighed almost 1 per cent less than 4 kilograms!

If all atoms had indeed