Energy and Mass

Physicist Albert Einstein (1879—1955), shown in Figure 15, developed his special theory of relativity in 1905. This theory included the now-famous equation E = mc². In Einstein's equation, E is energy, m is mass, and c is the speed of light. This seemingly ordinary equation has surprising consequences. Einstein's equation, E = mc², says that energy and mass are equivalent and can be converted into each other. In other words, energy is released as matter is destroyed, and matter can be created from energy.

Notice that the speed of light is squared in Einstein's equation. The speed of light is an extremely large number, $3.0 \times {10}^8$ meters per second. Thus, a tiny amount of matter can produce an enormous amount of energy. Suppose 1 gram of matter were entirely converted into energy.

$E=m{c}^2=\left({10}^{-3}kg\right)\times (3\times {10}^{8}m/s)\times (3\times {10}^{8}m/s)=9\times {10}^{13}kg.m^2{s}^2=9\times {10}^{13}J$

In comparison, 1 gram of TNT produces only 2931 joules of energy. In nuclear fission and fusion reactions, however, large amounts of energy are released by the destruction of very small amounts of matter. Therefore, the law of conservation of energy has been modified to say that mass and energy together are always conserved.

Figure 15 Albert Einstein made important contributions to many areas of physics. His theory of special relativity showed that energy and mass are equivalent.

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