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 m_p = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_n = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c²,1 u = 931 MeV/c².)

Answer 1

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