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 120 Sn (Z = 50) and 121 Sb = (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 = (M Z–1, N + M H – M Z,N ) c 2 . Given 119 In = 118.9058u, 120 Sn = 119.902199u, 121 Sb = 120.903824u, 1 H = 1.0078252u. (ii) What does the existence of magic number indicate?

Question

Philoid · Accepted Answer

(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.