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: 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

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.

mass defectbinding energyE = mc^2nucleonsenergy releasednuclear stabilitydelta m c squared

Marking Scheme

11 mark: correct option (C).
2Assertion 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.

Analysis & Explanation

Concept:

When protons and neutrons combine to form a stable nucleus, the system settles into a lower energy state. Energy must leave the system for it to become bound.

Assertion analysis:

Mass defect: $\Delta m = [Z \cdot m_p + (A-Z) \cdot m_n] - M_{\text{nucleus}} > 0$ .
The bound nucleus is therefore lighter than its separated constituents — assertion is true.

Reason analysis:

Binding requires energy to be given out (released), equal to $\Delta m \cdot c^2$ .
To pull the nucleons apart again you must supply that energy.
So "energy is absorbed when nucleons bind" is false; it is released.

Exam trap:

Absorbed vs released is the classic reversal. Binding energy released on formation = energy needed to disassemble the nucleus.

Real-world:

This released binding energy powers the Sun (fusion of light nuclei) and nuclear reactors (fission of heavy nuclei), where tiny mass losses yield enormous energy via $E = mc^2$ .

Common Mistakes

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

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.

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Frequently Asked Questions

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.

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?

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.