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Question
The masses of 11C and 11B are respectively 11.0114 u and 11.0093 u. Find the maximum energy a positron can have in the β*-decay of 11C to 11B.
(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.)
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Solution
Given:-
Mass of 11C, m(11C) = 11.0114 u
Mass of 11B, m(11B) = 11.0093 u
Energy liberated in the β+ decay (Q) is given by
`Q = [m(""^11C) - m(""^11B) - 2m_e]c^2`
= (11.0114 u − 11.0093 u - 2 × 0.0005486 u)c2
= 0.0010028 × 931 MeV
= 0.9336 MeV = 933.6 keV
For maximum KE of the positron, energy of neutrino can be taken as zero.
∴ Maximum KE of the positron = 933.6 keV
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