Arrange the following nuclei in the ascending order of their stability.
(A) Oxygen \( ({}^{16}\mathrm{O}) \) with binding energy 127.5 MeV
(B) Uranium \( ({}^{238}\mathrm{U}) \) with binding energy 1808.8 MeV
(C) Helium \( ({}^{4}\mathrm{He}) \) with binding energy 28.3 MeV
(D) Iron \( ({}^{56}\mathrm{Fe}) \) with binding energy 490 MeV
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C), (B), (A), (D)
The stability of a nucleus is measured by its binding energy per nucleon, \( E_{bn} = E_b/A \), not by the total binding energy, which simply grows with the number of nucleons.
\( (A)\ \mathrm{O}: 127.5/16 \approx 7.97\,\mathrm{MeV} \)
\( (B)\ \mathrm{U}: 1808.8/238 \approx 7.60\,\mathrm{MeV} \)
\( (C)\ \mathrm{He}: 28.3/4 \approx 7.08\,\mathrm{MeV} \)
\( (D)\ \mathrm{Fe}: 490/56 = 8.75\,\mathrm{MeV} \)
In ascending order of binding energy per nucleon:
\( 7.08\ (\mathrm{C}) \lt 7.60\ (\mathrm{B}) \lt 7.97\ (\mathrm{A}) \lt 8.75\ (\mathrm{D}) \)
The order is C, B, A, D. Iron, near the peak of the binding energy curve, is the most stable.