Question

Show that the minimum energy needed to separate a proton from a nucleus with Zprotons and N neutrons is `ΔE = (M_(Z-1,N) + M_B - M_(Z,N))c^2` 

where M_Z,N = mass of an atom with Z protons and N neutrons in the nucleus and M_B = mass of a hydrogen atom. This energy is known as proton-separation energy.

Answer 1

Given:
Mass of an atom with Z protons and N neutrons = M_Z,_N
Mass of hydrogen atom = M_H
As hydrogen contains only protons, the reaction will be given by 

`E_(Z,N) → E_(Z-1,N) + p_1`

⇒ `E_(Z,N) → E_(Z-1,N) + ""^1H_1`

∴ Minimum energy needed to separate a proton, `ΔE = (M_(Z-1,N) + M_H - M_(Z,N))C^2`