Nuclei with magic no. of proton Z=2,8,20,28,50,52 and magic no. of neutrons N=2,8,20,28,50,82 and 126 are found to be stable. (i) Verify this by calculating the proton separation energy `S_(p)` for `.^(120)Sn (Z=50)` and `.^(121)Sb =(Z=51)`.
The proton separation energy for a nuclide is the minimum energy required to separated the least tightly bound proton form a nucleus of that nuclide. It is given by
`S_(p)=(M_(z-1,N)+M_(H)-M_(Z,N))c^(2)`.
given `.^(119)Sn =118.9058u, .^(120) Sn =119.902199u, .^(121)Sb=120.903824u, .^(1)H=1.0078252u`
(ii) what does the existence of magic number indicate?

Explanation

(i) The proton separation energy is given by `S_(p)=(M_(Z-1,N)+M_(H)-M_(Z,N))c^(2)......(i)`
for sn, `M_(Z-1,N)=118.9058u, M_(H)=1.0078252u`
and `M_(Z,N)=119.902199u`
`:.` form (i), `S_(pSn)=(118.9058+1.0078252-119.902199)c^(2)=0.0114362c^(2)`
Similarly, `S_(pSb)=(M_(50,70)+M_(H)-M_(51,70)) c^(2)=(119.902199+1.0078252-120.903824)c^(2)`
`=0.0059912c^(2)`
Since `S_(pSn)gtS_(pSb)`, therefore, `S_(n)` nucleus is more stable than Sb nucleus, which was to be proved.
(ii) The existance of magic numbers indicates the shell structure of nucleus similar to the shell structure of an atom. It also accounts for the peaks in Binding energy/nucleon curve.