Question

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 very stable. (i) Verify this by calculating the proton separation energy S_p for ¹²⁰Sn (Z = 50) and ¹²¹Sb = (Z = 51). 

The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by 

S_p = (M_Z–1, _N + M_H – M_Z,N) c². 

Given ¹¹⁹In = 118.9058u, ¹²⁰Sn = 119.902199u, ¹²¹Sb = 120.903824u, ¹H = 1.0078252u. 

(ii) What does the existance of magic number indicate?

Answer 1

Since S_pSn > S_pSb, Sn nucleus is more stable than Sb nucleus.

(ii) It indicates shell structure of nucleus similar to the shell structure of an atom. This also explains the peaks in BE/ nucleon curve.