Set 57 Problem number 12

Problem

If in an atomic explosion a sample of .103% of the total 20 kg of fissionable material is converted to energy, how much energy is released?

Solution

The mass converted to energy is called the mass defect. In this situation we have

mass defect = .103 % ( initial mass ) = .00103 * 20 kg = .0206 kg.

The energy equivalent of .0206 kg is

energy equivalent: E = m c^2 = .0206 kg ( 3 * 10^8 m/s) ^ 2 = 185.4 * 10^14 Joules.

This energy is released in the explosion.

Note that the energy in a kg of typical high explosives is around 3 * 10^7 J. In a metric ton, or 1000 kg, the energy would be approximately 3 * 10^10 J. So the energy in this explosion would be equivalent to on the order of 10,000 tons of high explosive.

This energy might also be released slowly in a nuclear power facility. One kilowatt-hour is approximately 3.6 * 10^6 Joules, so the energy released by this mass conversion would be on the order of 10^8 kilowatt-hours. At 7 cents per kwh, this energy would be worth on the order of ten million dollars.