Which of the following statements about the binding energy per nucleo…

The correct answer is Option (3) → \( E_{bn} \) of a nucleus with \( A=238 \) is greater than that of a nucleus with \( A=120 \).

The binding energy per nucleon, \( E_{bn}=E_b/A \), is the average energy needed to pull one nucleon out of a nucleus. So it measures how tightly the nucleus is bound. Its plot against the mass number \( A \) has a long, nearly flat middle part and lower values at both ends.

Option (1) \( E_{bn} \) is nearly constant, at about 8 MeV, for nuclei with \( 30\lt A\lt 170 \). — Correct statement. For nuclei of middle mass number the value is practically independent of the atomic number.

Option (2) \( E_{bn} \) has its maximum value, about 8.75 MeV, for nuclei with \( A=56 \). — Correct statement. The curve reaches its highest point at \( A=56 \) (iron), with a value of about 8.75 MeV.

Option (3) \( E_{bn} \) of a nucleus with \( A=238 \) is greater than that of a nucleus with \( A=120 \). — Not correct. Beyond the peak the curve falls slowly, and for \( A=238 \) it is only about 7.6 MeV. A very heavy nucleus is less tightly bound than a nucleus with \( A=120 \). This is why the fission of a heavy nucleus releases energy.

Option (4) \( E_{bn} \) shows small peaks for nuclides such as \( {}^{4}\mathrm{He} \) and \( {}^{16}\mathrm{O} \). — Correct statement. The curve is smooth on the whole, but it rises above its neighbours at these nuclides. This is taken as evidence of a shell structure in nuclei.

NCERT (2026-27):
Nuclear Binding Energy – “(i) the binding energy per nucleon, E_bn, is practically constant, i.e. practically independent of the atomic number for nuclei of middle mass number ( 30 < A < 170). The curve has a maximum of about 8.75 MeV for A = 56 and has a value of 7.6 MeV for A = 238.”

Nuclear Binding Energy – “(iii) A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. …”

Points to Ponder – “6. Although the binding energy (per nucleon) curve is smooth and slowly varying, it shows peaks at nuclides like ⁴He, ¹⁶O etc. This is considered as evidence of atom-like shell structure in nuclei.”