A radionuclide with half life T = 693.1 days emits β -particles of average kinetic energy E = 8.4 × 10 –14 joule. This radionuclide is used as source in a machine which generates electrical energy with efficiency η = 12.6%. Calculate number of moles of the nuclide required to generate electrical energy at an initial rate P = 441 KW. (Take Avogadro number N = 6 × 10 23 , log e 2 = 0.6931)
Text Solution
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Sol. Let number of moles of the radio nuclide be ‘n’.
Number of nuclei in the nuclide = n.N
Since, half life of the nuclide is T, therefore, its decay constant λ = 
∴ Activity or rate of decay, A = λ (n. N) = 
Energy released per decay = average kinetic energy E of β -particles.
∴ Rate of release of the energy = AE
But efficiency of conversion of this energy into electrical energy is η , therefore, rate of generation of electrical energy is
P = η AE = 
or n = 
= 6000
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