Question

The following plot (Fig. 8.7) shows the average binding energy per nucleon for stable nuclei as a function of mass number. 

Explain how the mass of a nucleus can be calculated from this plot and estimate the mass of ²³⁵₉₂U. 

Briefly describe the main features of the plot in the context of nuclear models such as the liquid Drop Model, the Fermi Gas Model and the Nuclear Shell Model. 

In terms of the Liquid Drop Model, explain why nuclear fission and fusion are possible and estimate the energy released when a nucleus of ²³⁵₉₂U undergoes fission into the fragments ⁸⁷₃₅Br and ¹⁴⁵₅₇La with the release of three prompt neutrons.

 

Answer 1

The plot is based on the semi-empirical mass formula obtained in the Liquid Drop Model. In this formula the lowering of binding energy at low mass numbers due to surface tension effects as well as at high Z (and hence large A) due to coulomb energy, are predicted by this model. The jumps in the curves at low mass numbers (A = 2–20) are attributed to the shell effects explained by the shell Model. The asymmetry term occurring in the mass formula is explained by the Fermi Gas Model. From the plot the binding energy per nucleon for 87Br is found to be 8.7 MeV and that for ¹⁴⁵La it is 8.2 MeV. The energy released in the fission is 

Q = [B(Br) + B(La)] − B(U) 

= 8.7 × 87 + 8.2 × 145 − 1786 

= 160 MeV