Definition
Mass defect and binding energy
Mass defect Δm = Z m_p + N m_n - m_nucleus (always positive). Binding energy B = Δm c². Binding energy per nucleon B/A peaks around A = 56-60 (Fe) at ~8.8 MeV.
-- NCERT Class 12 Physics, Ch. 13, p. 311Mass Defect Binding Energy
8 MCQs2 revision cards9-step worked example
Source: NCERT Atoms and NucleiPYQ coverage: NEET 2021Official key: NTA-verifiedLast updated: 25 Sep 2026
Mass Defect Binding Energy, explained for NEET
The nucleus of an atom weighs less than the protons and neutrons inside it. That difference is the mass defect, and it is where the whole topic lives.
Write it carefully:
Δm = Z·m_p + N·m_n − m_nucleus
Two things go wrong here often enough to be worth naming. First, the subtraction runs one way only — constituents minus the bound nucleus — and a sign slip hands you a negative binding energy, which does not exist for a bound nucleus. Second, the tables you are given usually list the atomic mass, not the nuclear mass. An atomic mass includes Z electrons. If you plug it into the formula above without removing them, your Δm is wrong by Z·m_e. The clean workaround for a neutral atom: use m_H (atomic mass of hydrogen, which already carries one electron) in place of m_p, and the electrons cancel on both sides.
Binding energy is that defect expressed as energy: B = Δm·c². Working in atomic mass units, the conversion 1 u = 931.5 MeV/c² makes this one multiplication — no need to go through kilograms and joules. NCERT Class 12 Physics, Chapter 13, page 311, defines binding energy as the energy required to separate the nucleons of a nucleus to infinite distance. Nothing is destroyed when the nucleus forms; that energy left as radiation, and the missing mass is its receipt.
Divide by A and you get binding energy per nucleon, B/A — the quantity that actually says which nucleus is more tightly bound. A heavy nucleus has a huge total B and yet is less stable than iron. Compare B/A, never B, when the question asks about stability. (How B/A varies across the periodic table is the next lesson's business.)
Watch out for: reading "mass defect" as a measurement error. It is a real, physical mass difference, and it is exactly the mass that became energy.
Can you answer these Mass Defect Binding Energy MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The mass defect of a nucleus is defined as the
Show answer and why every option is right or wrong
Answer: B. B is correct. Δm = Z·m_p + N·m_n − m_nucleus: the free nucleons together are heavier than the bound nucleus, and that excess is the defect (NCERT Class 12 Physics, Chapter 13, page 311).
Why A is wrong: A is wrong because the nucleus-versus-atom difference is simply the mass of the Z electrons, which is an entirely separate correction and not the mass defect.
Why C is wrong: C is wrong because the defect is a real physical mass difference, not an experimental uncertainty — reading it as measurement error is the classic misreading of the word 'defect'.
Why D is wrong: D is wrong because it inverts the subtraction. A bound nucleus is always lighter than its separated nucleons; this direction would give a negative binding energy.
MCQ 2Easy RecallPractice
The binding energy of a nucleus is the energy
Show answer and why every option is right or wrong
Answer: C. C is correct — this is the NCERT definition (Class 12 Physics, Chapter 13, page 311): binding energy is the work needed to dismantle the nucleus into free, well-separated nucleons.
Why A is wrong: A is wrong because that is the ionisation energy, an atomic (electronic) quantity of order eV, while nuclear binding energies are of order MeV.
Why B is wrong: B is wrong because alpha decay energy is the energy released in one particular decay, not the energy needed to disassemble the whole nucleus.
Why D is wrong: D is wrong because proton–proton repulsion opposes binding; the binding energy is the net energy deficit of the bound system, not one repulsive contribution within it.
MCQ 3Easy RecallPractice
In nuclear calculations, the mass 1 u is taken to be equivalent to
Show answer and why every option is right or wrong
Answer: A. A is correct. The standard conversion 1 u = 931.5 MeV/c² lets a mass defect in u be turned into binding energy in MeV by a single multiplication (NCERT Class 12 Physics, Chapter 13, page 311).
Why B is wrong: B is wrong because 13.6 eV is the ionisation energy of hydrogen — an atomic energy scale roughly a hundred million times smaller than the nuclear one.
Why C is wrong: C is wrong because 1.6 × 10⁻¹⁹ J is the joule-equivalent of one electronvolt, a unit conversion, not the energy equivalent of one atomic mass unit.
Why D is wrong: D is wrong because 3.00 × 10⁸ is the numerical value of c in m/s; it has been pasted in as if it were an energy.
MCQ 4Direct ApplicationPractice
For a nucleus, Δm is the mass defect in atomic mass units and A is the mass number. The binding energy per nucleon, in MeV, is
Show answer and why every option is right or wrong
Answer: B. B is correct. Total binding energy B = Δm × 931.5 MeV, and the per-nucleon value divides that total by the number of nucleons A.
Why A is wrong: A is wrong because it multiplies by A instead of dividing — this makes a heavy nucleus appear ever more tightly bound per nucleon, which is the opposite of the trend.
Why C is wrong: C is wrong because it divides by 931.5 rather than multiplying, so the answer is not in MeV at all; the conversion factor turns u into MeV and belongs in the numerator.
Why D is wrong: D is wrong because it also puts 931.5 in the denominator, compounding the wrong-direction conversion with the division by A.
MCQ 5Direct ApplicationPractice
The mass defect of a certain nucleus is 0.2500 u. Its total binding energy is closest to
Show answer and why every option is right or wrong
Answer: A. A is correct: B = 0.2500 u × 931.5 MeV/u = 232.9 MeV ≈ 2.33 × 10² MeV, keeping four significant figures in the data and quoting three.
Why B is wrong: B is wrong because it divides by the defect instead of multiplying (931.5 / 0.2500), inverting the relation between mass defect and energy.
Why C is wrong: C is wrong because the number is right but the unit is not: 931.5 is MeV per u, so the product is in MeV, six orders of magnitude above eV.
Why D is wrong: D is wrong because it is the energy equivalent of 1 u itself, obtained by ignoring the factor 0.2500 entirely.
MCQ 6Direct ApplicationPractice
A ²He⁴ nucleus contains 2 protons and 2 neutrons. Taking m_p = 1.00728 u, m_n = 1.00866 u and the nuclear mass as 4.00151 u, the mass defect is closest to
Show answer and why every option is right or wrong
Answer: D. D is correct. Σm = 2(1.00728) + 2(1.00866) = 4.03188 u; Δm = 4.03188 − 4.00151 = 0.03037 u ≈ 0.03038 u. The integers 2 and 2 are exact counts and do not limit the significant figures.
Why A is wrong: A is wrong because it subtracts a single proton mass from a single neutron mass (1.00866 − 1.00728 = 0.00138 u), a quantity that has nothing to do with the assembled nucleus.
Why B is wrong: B is wrong because it treats all four nucleons as protons, 4m_p = 4.02912 u, leaving out the neutrons' extra mass; the defect must use 2m_p + 2m_n.
Why C is wrong: C is wrong because it compares the nuclear mass with 4 exactly, |4 − 4.00151| = 0.00151 u, treating the mass number as though it were the summed nucleon mass in u; the nucleons are each slightly heavier than 1 u.
MCQ 7Concept TrapPractice
A table gives the atomic mass of a nuclide. A student inserts this value directly as m_nucleus into Δm = Z·m_p + N·m_n − m_nucleus. The computed mass defect is
Show answer and why every option is right or wrong
Answer: A. A is correct. The atomic mass exceeds the nuclear mass by Z·m_e, and since it is subtracted, an inflated subtrahend makes Δm too small by Z·m_e. Using m_H in place of m_p is the standard fix, since the electrons then cancel on both sides.
Why B is wrong: B is wrong because it has the direction backwards: adding mass to the term being subtracted reduces the result, it does not raise it.
Why C is wrong: C is wrong because cancellation only happens if the atomic mass of hydrogen is used on the constituent side too; with the bare proton mass there is nothing on that side to cancel the Z electrons.
Why D is wrong: D is wrong because a neutral atom carries Z electrons, one per proton, not A — the neutrons bring no electrons with them.
MCQ 8CalculationPractice
Nucleus X has mass number 60 and total binding energy 5.20 × 10² MeV. Nucleus Y has mass number 200 and total binding energy 1.56 × 10³ MeV. Which statement is correct?
Show answer and why every option is right or wrong
Answer: C. C is correct. B/A for X is 520/60 = 8.67 MeV and for Y is 1560/200 = 7.80 MeV; stability is judged by binding energy per nucleon, so X is the more tightly bound.
Why A is wrong: A is wrong because total binding energy grows simply because there are more nucleons to bind; it is not a measure of how tightly each one is held.
Why B is wrong: B is wrong because the two mass defects are not equal — 520 MeV and 1560 MeV correspond to defects of about 0.558 u and 1.67 u respectively.
Why D is wrong: D is wrong because the per-nucleon values run the other way: 7.80 MeV for Y against 8.67 MeV for X.
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Mass Defect Binding Energy: quick recall before you leave
How do you solve a Mass Defect Binding Energy question? A worked example
- 1
Given.
Nucleus: ⁷Li (Z = 3, A = 7, so N = 4).
m_p = 1.00728 u, m_n = 1.00866 u, nuclear mass m = 7.01435 u.
1 u = 931.5 MeV/c². - 2
Required.
The binding energy per nucleon of ⁷Li, in MeV.
- 3
Concept.
The bound nucleus is lighter than its separated nucleons. That missing mass, converted by E = mc², is the energy that must be resupplied to pull the nucleons apart — the binding energy. Dividing by the nucleon count gives the per-nucleon figure used to compare stability.
- 4
Formula.
Δm = Z·m_p + N·m_n − m
B = Δm × 931.5 MeV
B/A = B / A - 5
Substitution.
Δm = 3(1.00728) + 4(1.00866) − 7.01435 u
- 6
Calculation.
3 × 1.00728 = 3.02184 u
4 × 1.00866 = 4.03464 u
Sum of constituents = 7.05648 u
Δm = 7.05648 − 7.01435 = 0.04213 u
B = 0.04213 × 931.5 = 39.24 MeV
B/A = 39.24 / 7 = 5.606 MeV
The counting integers 3, 4 and 7 (numbers of protons, neutrons and nucleons) are exact and impose no limit on significant figures; only the measured masses do, and they carry six. - 7
Final answer.
B/A ≈ 5.61 MeV per nucleon.
- 8
Common trap.
Stopping at B = 39.2 MeV and calling it the answer when the question asked for the per-nucleon value — the two differ by a factor of 7 here, and both numbers will be sitting in the options. Read the last four words of the stem before you pick. The second trap is subtracting the wrong way round: 7.01435 − 7.05648 = −0.04213 u would give a negative binding energy, which no bound nucleus has.
- 9
Similar NEET-style question.
The nuclear mass of ¹⁶O is 15.99053 u. Using m_p = 1.00728 u and m_n = 1.00866 u, find its binding energy per nucleon. *(Answer: Δm = 8(1.00728) + 8(1.00866) − 15.99053 = 0.13699 u; B = 127.6 MeV; B/A ≈ 7.97 MeV per nucleon.)*
What to remember before solving Mass Defect Binding Energy questions
Which Mass Defect Binding Energy formulas do you need for NEET?
1 formula — click to collapse
Mass defect and binding energy
Mass defect = sum of constituent masses minus nuclear mass. Binding energy = mass defect in energy units.
| Symbol | Quantity | SI Unit |
|---|---|---|
| Z | proton number | - |
| N | neutron number | - |
| m_p, m_n | proton, neutron mass | u |
| B | binding energy | MeV |
Valid when
- Non-relativistic
- Stable nucleus
More in Atoms and Nuclei: 3 exam traps and mistakes · 5 formulas · 5 question patterns from its other lessons.
Mass Defect Binding Energy questions from past NEET papers
1 question from NEET 2021. Answers verified against NTA official keys. — click to collapse
NEET 2021
1216 MeV
20.9 MeV
39.4 MeV
4804 MeV
NTA Answer: Option 1(final)
Sources
NCERT refs: Class 12 Physics Chapter 13, p.311
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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