Calculate the binding energy per nucleon of the $^{56}$ Fe nucleus. The nuclear mass is $55.934937$ u, mass of a proton $1.007276$ u, mass of a neutron $1.008665$ u. Use $1, u = 931.5, MeV / c^{2}$ .

hard 3 marks Class 12 · Physics · Nuclei

Answer

8.56 MeV per nucleon

The correct answer is $8.56 MeV per nucleon$ — Divide by the total nucleons $56$ to get binding energy per nucleon: $479.3/56 a pp r o x 8.56$  MeV.

Step-by-step solution

Determine the total mass of the 26 protons and 30 neutrons: $26 (1.007276) + 30 (1.008665) = 56.449926$  u.
Compute the mass defect: $D e l t am = 56.449926 - 55.934937 = 0.514989$  u.
Convert to energy: $E_{bind} = Δ m \times 931.5 = 479.3$  MeV.
Divide by the total nucleons $56$ to get binding energy per nucleon: $479.3/56 a pp r o x 8.56$  MeV.

Common mistake: Using atomic mass instead of nuclear mass or forgetting to subtract the nuclear mass

Concept tested: binding energy per nucleon, mass defect

Published 15 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

← All Nuclei questions

Calculate the binding energy per nucleon of the 56Fe nucleus. The nuclear mass is 55.934937 u, mass of a proton 1.007276 u, mass of a neutron 1.008665 u. Use 1,u=931.5,MeV/c2.

Step-by-step solution

Calculate the binding energy per nucleon of the $^{56}$ Fe nucleus. The nuclear mass is $55.934937$ u, mass of a proton $1.007276$ u, mass of a neutron $1.008665$ u. Use $1, u = 931.5, MeV / c^{2}$ .