Question

(15 markah) 1. (a) Binding energy of a nucleus is the difference in the mass energy between nucleus X and its constituent Z protons and N neutrons: From the binding energy, define proton separation energy and neutron separation energy in terms of binding energy (10 marks) SMES3201 (b) From part (a), find the binding energy per nucleon for 12C and their proton and (15 marks) (c) Sketch a graph showing the distribution of binding energy per nucleon vs (20 marks) (d) The attempt to understand the curve of binding energy leads us to the neutron separation energies mass number from light to heavy nuclei and describe its characteristics semiempirical mass formula. The complete binding energy in semi empirical formula are A-2Z with constants a, 15.5 MeV, a, 16.8MeV,a. 0.72MeV, am 23 MeV a 34 MeV Explain what are these terms and explain each contribution to the curve of (40 marks) (e) Compute the the binding energy per nucleon using the semi empirical mass binding energy per nucleon formula for 2C nucleus and compared with part (b). How much is the (15 marks) difference?

Answer 1

Proton separation energy is the energy required to remove one proton from the nucleus.

Thus

$S_{p}=[BE(X_{N}^{A-1})- BE(X_{N}^{A})]$ , where Sp = Proton separation energy

Neutron separation energy is the energy required to remove 1 neutron from the nucleus

$S_{n}=[BE(X_{N-1}^{A-1})- BE(X_{N}^{A})]$ , where Sn = Neutron separation energy

The original mass 12C nucleus = 12.00000 amu

$ZM_{p}+NM_{n}+6M_{e}-M(12C)+ = 6\times(1.00864u)+6\times (1.007276)u+6\times0.00054858u-12.00000u$

= 0.098931u

Energy released per amu = 931.5 MeV

Total BE = 92.15 MeV

12C ,if bereft of 1 proton becomes 11B

BE of 11B = 92.15MeV ( as per tables)

Sp = BE of 11B-BE of 12C = 76.20 Mev - 92.15 MeV = -15.95 MeV

BE of 11C = 6x 1.00864u + 5 x 1.007276u + 6 x 0.000054858u - 11.000 u = 0.088554 u = 82.44 MeV

12C bereft of 1 neutron becomes 11C = 92.15 MeV - 82.44 MeV = 9.71 MeV

Note: I am allowed to solve only one problem and upto 4 parts of the same problem. In this case part(c) onwards is diffrent problems.Hence can not be solved.