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Physics LibreTexts

11.7 Mass-Energy Conversion

In 1905, a young scientist named Albert Einstein startled the scientific world with a series of papers on the nature of mass, energy, and time. Extending ideas of earlier scientists, he postulated that the speed of light is an absolute limit. More profoundly, he suggested that the speed of light is a universal constant, always with the same value regardless of the motion of the person emitting o receiving the light. From this he deduced that mass could be converted into energy, and energy into mass. In the everyday world, mass and energy appear to be quite distinct and this remarkable process is not apparent. However, physicists observe it routinely when tiny particles are accelerated to very high speeds.

How can it be that the speed of light is never exceeded? As a particle is accelerated towards the speed of light, its mass steadily increases. The effect is only pronounced at extremely high speeds. Energy is being turned into mass. You will recall that a more massive object has more inertia and so resists any change in its motion. But as a tiny particle is accelerated closer and closer to the speed of light, the energy given to it goes more and more into increasing its mass and less and less into increasing its speed. Kinetic energy turns into mass. The particle gets heavier and heavier and approaches, but never reaches, the speed of light. This process also works in reverse: particles can convert mass into pure energy. The most dramatic form of this is when a particle and its anti-particle meet, like an electron and a positron. When that happens, they both disappear and their combined mass is turned into pure energy!

There is a fantastic amount of energy associated with even tiny amounts of normal matter. Normally, this energy is safely tucked away in the familiar mass of everyday objects. This energy can be liberated in two ways. In one process, naturally occurring heavy elements can split their nuclei and release energy. This is nuclear fission. We have learned to purify and concentrate these rare elements and harness this energy source. The other process involves merging the nuclei of light elements. When atomic nuclei fuse, a small percentage of the mass is released in the form of radiant energy in a process called mass-energy conversion. This is nuclear fusion.

The nucleus of the atom contains a prodigious energy source. Mass and energy are related by Einstein's famous and simple equation E = mc2. Since c is a very large number, a tiny amount of mass is equivalent to a fantastic amount of energy. The "frozen" energy in a mass about the size of an adult man is enough to power the entire energy needs of the United States for a year. Compare that to the energy you would get from the same mass of a fossil fuel, probably enough to run a single car for a month, or heat a single home for a week. Einstein doubted that there would ever be any practical use for this form of energy. Unfortunately for us, in a world full of nuclear weapons, he was wrong.

The equivalence between mass and energy has some profound consequences for the way we look at the physical world. Energy can be stored and can appear in many different forms. Mass is another of those forms. We can consider it potential energy since it is normally frozen in the form of stable particles. However, under certain extreme conditions this mass-energy can be released. The equation E = mc2 works in both directions. Just as mass can be considered a form of energy, energy can be considered a form of mass. A rapidly moving car has very slightly more mass than a stationary car. A spent battery has very slightly less mass than a fully charged battery. These effects are tiny since mass equals energy divided by c2, which is a very small number. Yet they are real. Lastly, when we apply the law of conservation of energy, we must include mass-energy as well.