Question 151 markSection A

$Assertion (A): The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R): Energy is absorbed when the nucleons are bound together to form a nucleus.$

Q: Assertion (A): The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R): Energy is absorbed when the nucleons are bound together to form a nucleus.

**Correct option: (C)** — Assertion is true, but Reason is false. **Why A is true:** The measured nuclear mass is less than the sum of the free nucleon masses. This difference is the *mass defect* Δm, related to binding energy by $E_b = \Delta m \cdot c^2$. **Why R is false:** Energy is **released**, not absorbed, when free nucleons bind into a nucleus. The lost mass is converted into this released binding energy — that is exactly why the nucleus is lighter.

Q: Why is a nucleus lighter than its nucleons?

When nucleons bind, energy equal to $\Delta m \cdot c^2$ is released; the mass corresponding to this energy is 'missing' from the nucleus, giving the mass defect Δm.

Q: How is mass defect linked to binding energy?

By Einstein's relation $E_b = \Delta m \cdot c^2$, where Δm is the difference between the summed nucleon masses and the actual nuclear mass.

Nuclei

Mass defect and binding energy

Options

(A)

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

(B)

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

(C)

Assertion (A) is true, but Reason (R) is false.

(D)

Both Assertion (A) and Reason (R) are false.

Official answer

E_b = \Delta m \cdot c^2

mass defect

binding energy

E = mc^2

nucleons

energy released

nuclear stability

delta m c squared

Marking scheme

1. $1 mark: correct option (C).$
2. $Assertion recognised true (mass defect), Reason recognised false (energy released, not absorbed).$

Hint

$Mass defect is real, but binding releases energy — it is not absorbed.$

Quick oral answer

$Assertion is true — the nucleus is lighter by the mass defect — but the Reason is false because binding releases energy equal to delta-m c squared; you must absorb energy only to break the nucleus apart.$

Common mistakes

1. $Confusing 'absorbed' with 'released' — forming a bound nucleus releases energy; separating it absorbs energy.$
2. $Marking (A) by assuming R correctly explains the mass defect, when R itself states the wrong energy direction.$
3. $Thinking mass is destroyed rather than converted into released binding energy (mass-energy equivalence).$

Analysis and explanation

\Delta m = [Z \cdot m_p + (A-Z) \cdot m_n] - M_{\text{nucleus}} > 0

Interesting facts

$1 atomic mass unit corresponds to 931.5 MeV of energy, the conversion factor used to turn mass defect into binding energy.$

$Iron-56 sits near the peak of the binding-energy-per-nucleon curve (~8.8 MeV/nucleon), making it among the most tightly bound nuclei.$

$The Sun converts about 4 million tonnes of mass into energy every second through fusion, all traceable to nuclear mass defect.$

Question details

Q15 of 39 questions

Board: CBSE
Class: Class 12
Subject: Physics
Year: 2026
Section: Section A
Marks: 1
Chapter: Nuclei
Topic: $Mass defect and binding energy$
Bloom's level: understand
Syllabus topic: $Unit VIII: Atoms and Nuclei — Mass defect; binding energy of a nucleus$
Author: CBSE
Reviewed by: Padhantu Academic Team

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Frequently asked questions

$Why is a nucleus lighter than its nucleons?$

$\Delta m \cdot c^2$

$Is energy absorbed or released when a nucleus forms?$

$It is released. Binding energy is given out on formation; the same amount must be supplied to break the nucleus back into free nucleons, so the Reason is false.$

$How is mass defect linked to binding energy?$

$E_b = \Delta m \cdot c^2$