A proton-rich atom has parent-minus-daughter neutral atomic mass difference 0.00090 u. Neglect atomic electron-binding energies. Take 1 u·c² = 931.5 MeV. Which statement is correct regarding β⁺ emission and electron capture?
Options

Question

A proton-rich atom has parent-minus-daughter neutral atomic mass difference 0.00090 u. Neglect atomic electron-binding energies. Take 1 u·c² = 931.5 MeV. Which statement is correct regarding β⁺ emission and electron capture?

Options

G1 Physics · Accepted Answer

First calculate the available mass-energy difference: ΔE = 0.00090×931.5 = 0.83835 MeV. For β⁺ emission using neutral atomic masses, at least 2mₑc² = 1.022 MeV is required. Since 0.83835 MeV < 1.022 MeV, β⁺ emission is forbidden. For electron capture, ignoring small electron-binding corrections, Q(EC) = [M(parent)−M(daughter)]c². Since this is positive, electron capture is allowed. Correct option: C.