Read the following passage and answer the questions.
The oxygen nucleus \({}^{16}_{8}\mathrm{O}\) contains 8 protons and 8 neutrons. A student adds up the masses of 8 free protons and 8 free neutrons. She then compares this total with the mass of the oxygen nucleus. The mass of the oxygen atom is measured very precisely with a mass spectrometer, and the mass of the nucleus is found from it. The nucleus turns out to be lighter than its separate nucleons put together. This difference in mass is called the mass defect. The nucleons stay together in the nucleus because of the nuclear force. The student also looks at a graph of the binding energy per nucleon against the mass number A for a large number of nuclei. The curve is smooth and changes slowly. At nuclides such as \({}^{4}\mathrm{He}\) and \({}^{16}\mathrm{O}\), it shows small peaks.
Consider the following statements about the \({}^{16}_{8}\mathrm{O}\) nucleus:
(A) To split it into 8 protons and 8 neutrons, an energy equal to its mass defect times \(c^{2}\) must be supplied.
(B) Its binding energy per nucleon is its binding energy divided by 16.
(C) Energy is absorbed when 8 free protons and 8 free neutrons come together to form it.
(D) Its binding energy per nucleon is greater than that of \({}^{56}\mathrm{Fe}\).
Which of the above statements are incorrect?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (C) and (D) only
A nucleus is lighter than its free nucleons. So energy is given out when the nucleons come together, and the same energy must be supplied to pull them apart.
(A) To split it into 8 protons and 8 neutrons, an energy equal to its mass defect times \( c^{2} \) must be supplied. — Correct statement. This energy, \( E_b=\Delta M\,c^{2} \), is the binding energy of the nucleus.
(B) Its binding energy per nucleon is its binding energy divided by 16. — Correct statement. The binding energy per nucleon is \( E_b/A \), and \( A=16 \) for this nucleus.
(C) Energy is absorbed when 8 free protons and 8 free neutrons come together to form it. — Incorrect statement. The nucleus has less mass than the free nucleons, so energy equal to the binding energy is released when it forms.
(D) Its binding energy per nucleon is greater than that of \( {}^{56}\mathrm{Fe} \). — Incorrect statement. The binding energy per nucleon is the largest, about 8.75 MeV, near \( A=56 \). A light nucleus such as oxygen lies below this, even with its small peak.
NCERT (2026-27):
Nuclear binding energy – “… If one wants to break the oxygen nucleus into 8 protons and 8 neutrons, this extra energy ΔM c2, has to be supplied. …”
Nuclear binding energy – “… binding energy per nucleon, Ebn, which is the ratio of the binding energy Eb of a nucleus to the number of the nucleons, A, in that nucleus: …”
Nuclear binding energy – “If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy Eb will be released in the process. …”
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.”