Consider the following statements about nuclear properties and select the correct statements only:
(A) 56Fe has the maximum binding energy per nucleon.
(B) In the fission reaction, 10n + 23592U → 23692U → x56Ba + 89yKr + 3 10n , x = 144 and y = 36
(C) Density of nuclei is independent of mass number.
(D) Nuclear forces are conservative and central in nature.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
Nuclear properties follow from the short-range, strongly attractive nuclear force and the conservation of mass number and charge in reactions.
(A) 56Fe has the maximum binding energy per nucleon. — Correct. The binding energy per nucleon curve peaks near A = 56, at about 8.8 MeV, which is why iron-group nuclei are the most stable.
(B) In the fission reaction, 10n + 23592U → 23692U → x56Ba + 89yKr + 3 10n , x = 144 and y = 36 — Correct. Mass number and atomic number are conserved:
\( \text{Mass number}: 236 = x + 89 + 3 \Rightarrow x = 144 \)
\( \text{Atomic number}: 92 = 56 + y + 0 \Rightarrow y = 36 \)
(C) Density of nuclei is independent of mass number. — Correct. The nuclear radius is \( R = R_0 A^{1/3} \), so the volume is proportional to A, and so is the mass. Their ratio, the density (about \( 2.3\times10^{17} \) kg m−3), is the same for all nuclei.
(D) Nuclear forces are conservative and central in nature. — Incorrect. The nuclear force is non-central: it depends on the spins of the nucleons and their orientation, not only on the distance between them.
NCERT (2026-27):
Size of the Nucleus – “… Thus the density of nucleus is a constant, independent of A, for all nuclei. Different nuclei are like a drop of liquid of constant density.”
Nuclear Binding Energy – “… The curve has a maximum of about 8.75 MeV for A = 56 and has a value of 7.6 MeV for A = 238.”