Question

Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is
∆E=(MZ-1,N+MB-MZ,N)c2
where MZ,N = mass of an atom with Z protons and N neutrons in the nucleus and MB = mass of a hydrogen atom. This energy is known as proton-separation energy.

Answer 1

The minimum energy required for separating a proton from the nucleus with N neutrons and Z protons is shown as $\Delta E=(M Z-1, N+M H-M Z, N) c 2$.

Explanation:

It is given that

An atom’s mass with N neutrons and Z protons = MZ,N

An hydrogen atom has the mass = MH

It is to be noted that hydrogen is made only of protons. And, the reaction can be shown as

$\mathrm{EZ}, \mathrm{N} \rightarrow \mathrm{EZ}-1, \mathrm{N}+\mathrm{p} 1$

$\Rightarrow \mathrm{EZ}, \mathrm{N} \rightarrow \mathrm{E} z-1, \mathrm{N}+1 \mathrm{H} 1$

Therefore, to separate a proton, the required minimum energy is

$\Delta E=(M Z-1, N+M H-M Z, N) c 2$