NEET-XII-Physics
46: The Nucleus
- #11A 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.Ans : Given:
Half-life period of free neutron beta-decays to a proton, `` {T}_{1/2}`` = 14 minutes
Half-life period, T1/2 = `` \frac{0.6931}{\lambda }``
Here, `` \lambda `` = Decay constant
`` \therefore \lambda =\frac{0.693}{14\times 60}``
`` =8.25\times {10}^{-4}{\,\mathrm{\,s\,}}^{-1}``
If mp is the mass of proton, let mn and me be the mass of neutron and mass of electron, respectively.
`` \therefore \; Energ\,\mathrm{\,y\,}\,\mathrm{\,liberated\,},E=[{m}_{n}-\left({m}_{p}+{m}_{e}\right)]{c}^{2}``
`` =[1.008665\,\mathrm{\,u\,}-\left(1.007276+0.0005486\right)\,\mathrm{\,u\,}]{c}^{2}``
`` =0.0008404\times 931\,\mathrm{\,MeV\,}``
`` =782\,\mathrm{\,keV\,}``
`` ``
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