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The maximum energy Emax of the electrons emitted in the decay of the isotope 14C is 0.156 MeV. If the number of electrons with energy between E and E + dE is assumed to have the approximate form 

N(E)dE ∝ √E (Emax − E)2dE 

find the rate of evolution of heat by a source of 14C emitting 3.7 × 107 electrons per sec.

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The mean energy of electrons

If all the electrons emitted are absorbed then the kinetic energy of the electrons is converted into heat. 

Heat evolved/sec = (mean energy)(no. of electrons emitted/second) 

= (0.156) × (3.7 × 107)/3 MeV/s = 1.92 × 106 MeV/s. 

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