A one-gram sample of thorium  contains 2.64 × 1021 atoms and undergoes a decay with a half-life of 1.913 yr (1.677 × 104 h). Each disintegration releases an energy of 5.52 MeV (8.83 × 10^–13 J). Assume that all of the energy is used to heat a 3.8-kg sample of water.

Concepts:

(i) How much heat Q is needed to raise the temperature of a mass m of water by ΔT degrees?

(ii) The energy released by each disintegration is E. What is the total energy E_total released by a number n of disintegrations?

(iii) What is the number n of disintegrations that occur during a time t? Calculations: Find the change in temperature of the 3.8-kg sample of water that occurs in one hour.

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