The atomic mass of a helium‑4 nucleus is $4.002603 u$ , the mass of a proton is $1.007276 u$ and the mass of a neutron is $1.008665 u$ . Calculate the binding energy per nucleon of the helium‑4 nucleus. (1 u = $931.5 MeV / c^{2}$ ).

easy 3 marks Class 12 · Physics · Nuclei

Answer

6.82 MeV per nucleon

The correct answer is 6.82 MeV per nucleon — Obtain the binding energy per nucleon by dividing by the number of nucleons (4): $\frac{27.27}{4} = 6.82 MeV$ .

Step-by-step solution

Find the total mass of the separate nucleons: $2 \times m_{p} + 2 \times m_{n} = 2 (1.007276) + 2 (1.008665) = 4.031882 u$ .
Calculate the mass defect: $Δ m = mass of nucleons - mass of nucleus = 4.031882 - 4.002603 = 0.029279 u$ .
Convert the mass defect to energy using $E = Δ m c^{2} = Δ m \times 931.5 MeV$ : $E = 0.029279 \times 931.5 = 27.27 MeV$ .
Obtain the binding energy per nucleon by dividing by the number of nucleons (4): $\frac{27.27}{4} = 6.82 MeV$ .

Common mistake: Using

931 MeV

instead of

931.5 MeV

or forgetting to multiply the mass defect by

c^{2}

Concept tested: Binding energy per nucleon

Published 29 August 2026 · How this solution was prepared and checked

The atomic mass of a helium‑4 nucleus is 4.002603u, the mass of a proton is 1.007276u and the mass of a neutron is 1.008665u. Calculate the binding energy per nucleon of the helium‑4 nucleus. (1 u = 931.5MeV/c2).

Step-by-step solution

Related questions

The atomic mass of a helium‑4 nucleus is $4.002603 u$ , the mass of a proton is $1.007276 u$ and the mass of a neutron is $1.008665 u$ . Calculate the binding energy per nucleon of the helium‑4 nucleus. (1 u = $931.5 MeV / c^{2}$ ).