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
Sp 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
Sp = (MZ–1, N + MH – MZ,N) c2.
Given 119In = 118.9058u, 120Sn = 119.902199u,
121Sb = 120.903824u, 1H = 1.0078252u.
(ii) What does the existence of magic number indicate?
(i) The stablilty of Sn>Sb.
(ii)
Given
The equation for the proton seperation energy is given as 
; The atomic mass is given for In=118.9058u, Sn=119.902199u, Sb=120.903824u, H=1.0078252u.
Formula Used
Separation Energy: The energy required to remove a single proton from a tightly bound nucleus. The formula given in the question is
where
Seperation Energy, 
Atomic mass of Z-1 element, 
atomic mass of Hydrogen, 
Atomic mass of Z element. c is the speed of light.
Therefore, the seperation energy for 
is
And the Seperation Energy for Sb is
As you can see that the value of seperation energy for Sn>Sb, Hence, the stablilty of Sn>Sb.
(ii) Magic number in mordern physics states that the nucleons are arranged in same way as orbit are arranged in an atom. The existance of magic number states similiarity of structure of orbits in a nucleus is same as that of orbit structure in an atom, which in turns tell us that such types of nucleus also have a higher binding energy per nucleon in a nucleus.