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Conversion of Mass to Energy

Einstein's association of the term m c² with a REST MASS ENERGY E₀ naturally led to a great deal of speculation about what might be done to convert mass into useable energy, since for a little mass you get a lot of energy! Let's see just how much: in S.I. units  1 J $\equiv$ 1 kg-m²/s²  so a 1 kg mass has a rest mass energy of  (1 kg) $\times(2.9979 \times 10^8$ m/s $)^2 \; = \; 8.9876 \times 10^{16}$ J  -- i.e.,

$$1 \hbox{\rm ~kg} \; \longleftrightarrow \; 8.9876 \times 10^{16} \hbox{\rm ~J}$$ (24.10)

which is a lot of joules. To get an idea how many, remember that one WATT is a unit of power equal to one joule per second, so a JOULE is the same thing as a WATT-SECOND. Therefore a device converting one millionth of a gram (1 $\mu$g) of mass to energy every second would release approximately 90 megawatts [millions of watts] of power!

Contrary to popular belief, the first conclusive demonstration of mass-energy conversion was in a controlled nuclear reactor. However, not long after came the more unpleasant manifestation of mass$\to$energy conversion: the fission bomb. An unpleasant subject, but one about which it behooves us to be knowledgeable. For this, we need a new energy unit, namely the KILOTON [kt], referring to the energy released in the explosion of one thousand tons of TNT [trinitrotoluene], a common chemical high explosive. The basic conversion factor is

$$1 \hbox{\rm ~kt} \; \equiv \; \hbox{\rm ~a trillion {\sc calories}} \; = \; 4.186 \times 10^{12} \hbox{\rm ~J}$$ (24.11)

which, combined with Eq. (10), gives a rest-mass equivalent of

$$1 \hbox{\rm ~kt} \; \longleftrightarrow \; 4.658 \times 10^{-5} \hbox{\rm ~kg}$$ (24.12)

That is, one KILOTON's worth of energy is released in the conversion of 0.04658 grams [46.58 mg] of mass. Thus a MEGATON [equivalent to one million tons of TNT or 10³ kt] is released in the conversion of 46.58 grams of mass; and the largest thermonuclear device [bomb] ever detonated, about 100 megatons' worth, converted some 4.658 kg of mass directly into raw energy.