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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.
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
Solution
Given:
Half-life period of free neutron beta-decays to a proton, `T_"1/2"` = 14 minutes
Half-life period , `T_"1/2" = 0.6931/lambda`
Here, `lambda` = Decay constant
`therefore lambda = 0.693/(14 xx 60)`
= `8.25 xx 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.
`therefore "Energy liberated" , E = [m_n - (m_p + m_e)] c^2`
= `[1.008665 "u" - (1.007276 + 0.0005486) "u"]c^2`
= `0.0008404 xx 931 "MeV"`
= `782 "keV"`
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