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Question

A free neutron beta-decays to a proton with a half-life of 14 minutes. (a) What is the decay constant? (b) Find the energy liberated in the process.

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Solution

Given:
Half-life period of free neutron beta-decays to a proton, T1/2 = 14 minutes

Half-life period, T1/2 = 0.6931λ

Here, λ = Decay constant

λ=0.69314×60 =8.25×10-4 s-1

If mp is the mass of proton, let mn and me be the mass of neutron and mass of electron, respectively.

∴ Energy liberated, E=[mn-mp+me]c2 =[1.008665 u-1.007276+0.0005486 u]c2 =0.0008404×931 MeV =782 keV

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