Key Fact
Nuclear composition
Nucleus contains protons (Z) and neutrons (N); A = Z + N (mass number). Nuclear radius: R = R_0 A^(1/3), R_0 ≈ 1.2 fm. Density nearly constant across nuclei.
-- NCERT Class 12 Physics, Ch. 13, p. 309Nuclear Composition Size
8 MCQs1 revision card9-step worked example
Source: NCERT Atoms and NucleiPYQ coverage: NEET 2022, 2024Official key: NTA-verifiedLast updated: 27 Sep 2026
Nuclear Composition Size, explained for NEET
The mistake that costs marks here is treating nuclear radius as proportional to A. A nucleus with twice the mass number is not twice as wide. The relation is
R = R₀ A^(1/3), R₀ ≈ 1.2 fm
so doubling A multiplies R by 2^(1/3) ≈ 1.26, not by 2. Any option offering a factor of 2 for a doubled A, or 4 for a quadrupled A, is the linear-scaling distractor.
Composition. A nucleus contains Z protons and N neutrons; together these are the A = Z + N nucleons. Z fixes the element, A fixes the nuclide. Isotopes share Z and differ in N; isobars share A and differ in Z; isotones share N.
Size. NCERT Class 12 Physics Chapter 13, page 307, records that nuclear radii measured by electron-scattering follow the A^(1/3) law. Nuclear radii sit in femtometres (1 fm = 10⁻¹⁵ m) — about 10⁻⁴ of the atomic radius, so the nucleus occupies roughly 10⁻¹² of the atom's volume.
Why the cube root matters. Volume goes as R³ ∝ A, so volume per nucleon is the same in every nucleus. Density is therefore independent of A:
ρ = mass/volume ≈ (A × 1.66 × 10⁻²⁷ kg) / (4/3 · π · R₀³A) ≈ 2.3 × 10¹⁷ kg m⁻³
for every nuclide from helium to uranium. That constancy is the point of the formula, and it is a standard one-line NEET question: nuclear density does not increase with mass number. A nucleus behaves like an incompressible drop, not a compressible gas.
Watch-outs. Ratio questions ask for R₁/R₂ = (A₁/A₂)^(1/3) — cube-root the ratio of mass numbers, never the ratio of radii. And use A, not Z: a question quoting atomic number alone has not given you enough to find R.
Can you answer these Nuclear Composition Size 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 number of nucleons in a nucleus of mass number A and atomic number Z is
Show answer and why every option is right or wrong
Answer: C. Nucleons are protons and neutrons taken together; their total is the mass number A, as defined in NCERT Class 12 Physics Chapter 13, page 307.
Why A is wrong: A is wrong because Z counts only the protons, which fixes the element but not the total nucleon number.
Why B is wrong: B is wrong because A − Z is the neutron number N alone.
Why D is wrong: D is wrong because A already includes the Z protons; adding Z again double-counts them.
MCQ 2Easy RecallPractice
In the relation R = R₀A^(1/3) used for nuclear radii, the constant R₀ has a value of about
Show answer and why every option is right or wrong
Answer: A. R₀ ≈ 1.2 fm = 1.2 × 10⁻¹⁵ m, the femtometre-scale constant quoted with the radius law in NCERT Class 12 Physics Chapter 13, page 307.
Why B is wrong: B is wrong because 10⁻¹⁰ m is the atomic (ångström) scale, about 10⁵ times larger than any nuclear radius.
Why C is wrong: C is wrong because 0.53 × 10⁻¹⁰ m is the Bohr radius of the hydrogen atom, an electron-orbit length, not a nuclear one.
Why D is wrong: D is wrong because 10⁻¹⁹ is the exponent of the electronic charge in coulomb and has no connection with nuclear size.
MCQ 3Easy RecallPractice
Two nuclides that have the same mass number but different atomic numbers are called
Show answer and why every option is right or wrong
Answer: D. Equal A with different Z defines isobars; the classification of nuclides by Z, N and A is given in NCERT Class 12 Physics Chapter 13, page 307.
Why A is wrong: A is wrong because isotopes share the atomic number Z and differ in mass number A — the opposite pairing.
Why B is wrong: B is wrong because isotones share the neutron number N.
Why C is wrong: C is wrong because isomers are nuclei of the same Z and the same A differing only in energy state.
MCQ 4Direct ApplicationPractice
Nucleus X has mass number 27 and nucleus Y has mass number 125. The ratio of their nuclear radii R_X : R_Y is
Show answer and why every option is right or wrong
Answer: B. R ∝ A^(1/3), so R_X/R_Y = (27/125)^(1/3) = 3/5. The cube-root scaling is stated with the radius law in NCERT Class 12 Physics Chapter 13, page 307.
Why A is wrong: A is wrong because it takes R directly proportional to A, the linear-scaling error the cube root is there to prevent.
Why C is wrong: C is wrong because 9 : 25 is (3 : 5)², i.e. the ratio of surface areas or of A^(2/3), not of radii.
Why D is wrong: D is wrong because it inverts the ratio; the smaller mass number 27 must give the smaller radius.
MCQ 5Direct ApplicationPractice
The nuclear radius of a nuclide of mass number 64 is R. A nuclide whose radius is 2R has mass number
Show answer and why every option is right or wrong
Answer: C. Doubling R requires A to increase by 2³ = 8, so A = 64 × 8 = 512, following directly from R ∝ A^(1/3) as given in NCERT Class 12 Physics Chapter 13, page 307.
Why A is wrong: A is wrong because it doubles A to double R, assuming linear scaling; doubling A raises R only by 2^(1/3) ≈ 1.26.
Why B is wrong: B is wrong because it multiplies A by 4, which raises R by 4^(1/3) ≈ 1.59, not by 2.
Why D is wrong: D is wrong because 8 = √64 takes a square root of the mass number — and 8 would be a smaller nucleus with a smaller radius. Doubling R needs A multiplied by 2³.
MCQ 6Concept TrapPractice
A student computes nuclear density for ⁴He and for ²³⁸U using R = R₀A^(1/3) and nucleon mass m. Comparing the two results, the student should find that the density of ²³⁸U is
Show answer and why every option is right or wrong
Answer: D. Volume ∝ R³ ∝ A, so mass and volume both scale with A and the ratio is constant at about 2.3 × 10¹⁷ kg m⁻³ for all nuclides — the constant-density result that the A^(1/3) law implies, per NCERT Class 12 Physics Chapter 13, page 307.
Why A is wrong: A is wrong because it scales the mass with A but forgets that the volume scales with A as well, so the ratio does not grow.
Why B is wrong: B is wrong because it applies the cube root to the density ratio; the cube root belongs to the radius, and once cubed in the volume it cancels the mass factor exactly.
Why C is wrong: C is wrong because nucleon packing is the same throughout the nuclear volume; there is no loosening with increasing A.
MCQ 7CalculationPractice
For a nucleus of mass number A, the surface area of the nuclear sphere is proportional to
Show answer and why every option is right or wrong
Answer: A. Surface area = 4πR², and R ∝ A^(1/3), so area ∝ (A^(1/3))² = A^(2/3) — a two-step consequence of the radius law in NCERT Class 12 Physics Chapter 13, page 307.
Why B is wrong: B is wrong because A is the volume scaling (R³ ∝ A), not the surface scaling; this is the source of constant density, not of area.
Why C is wrong: C is wrong because A^(1/3) is the radius scaling itself; squaring it is the step this question requires.
Why D is wrong: D is wrong because it squares A rather than squaring R, assuming R ∝ A.
MCQ 8Direct ApplicationPractice
A nucleus of mass number 216 splits into two spherical fragments of mass numbers 64 and 152. The ratio of the radius of the lighter fragment to that of the original nucleus is
Show answer and why every option is right or wrong
Answer: B. R ∝ A^(1/3), so R_light/R_parent = (64/216)^(1/3) = 4/6 = 2/3, using the radius law of NCERT Class 12 Physics Chapter 13, page 307. The mass number 152 is not needed.
Why A is wrong: A is wrong because 8 : 27 is (2 : 3)³, the ratio of volumes rather than of radii.
Why C is wrong: C is wrong because 4 : 9 is (2 : 3)², the ratio of surface areas.
Why D is wrong: D is wrong because it takes the radii directly proportional to the mass numbers, the linear-scaling error.
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Nuclear Composition Size: quick recall before you leave
How do you solve a Nuclear Composition Size question? A worked example
- 1
Given.
Mass number of aluminium nuclide A₁ = 27 (exact, a nucleon count). Radius R₁ = 3.6 × 10⁻¹⁵ m (2 significant figures). Mass number of tellurium nuclide A₂ = 125 (exact, a nucleon count).
- 2
Required.
R₂, the nuclear radius of the ¹²⁵Te nuclide, in metres.
- 3
Concept.
Nuclear radius grows as the cube root of mass number, because each nucleon occupies the same volume. Taking a ratio of the two nuclei removes R₀ entirely, so no value of R₀ is needed.
- 4
Formula.
R = R₀A^(1/3). Dividing one instance by the other:
R₂/R₁ = (A₂/A₁)^(1/3) - 5
Substitution.
R₂ = R₁ × (125/27)^(1/3) = (3.6 × 10⁻¹⁵ m) × (125/27)^(1/3)
- 6
Calculation.
125^(1/3) = 5 and 27^(1/3) = 3, so the factor is 5/3 = 1.666…
R₂ = 3.6 × 10⁻¹⁵ × 1.666… = 6.0 × 10⁻¹⁵ m
The mass numbers 27 and 125 are exact counting integers, and the 3 in the exponent 1/3 is an exact mathematical constant; none of them contributes to the significant-figure count. Only R₁, with 2 significant figures, limits the answer. - 7
Final answer.
R₂ = 6.0 × 10⁻¹⁵ m, i.e. 6.0 fm, to 2 significant figures. Written as 6.0 × 10⁻¹⁵ rather than 60 × 10⁻¹⁶ so that the two significant figures are unambiguous.
- 8
Common trap.
Scaling linearly: 3.6 × (125/27) = 16.7 fm. That answer is almost always offered as an option. Nuclear radius is a cube-root quantity — the ratio 125/27 must be cube-rooted to 5/3 before it multiplies R₁. A quick check: the factor between two nuclear radii is nearly always small, because even a tenfold rise in A only raises R by about 2.15.
- 9
Similar NEET-style question.
The radius of a ¹⁶O nucleus is 3.0 × 10⁻¹⁵ m. What is the radius of a ²⁵⁶Fm nucleus? *(Answer: (256/16)^(1/3) = 16^(1/3) ≈ 2.52, so R ≈ 7.6 × 10⁻¹⁵ m.)*
What to remember before solving Nuclear Composition Size questions
Which Nuclear Composition Size formulas do you need for NEET?
1 formula — click to collapse
Nuclear radius scaling
Nuclear radius scales with cube root of mass number A. Implies constant nuclear density.
| Symbol | Quantity | SI Unit |
|---|---|---|
| R | nuclear radius | m |
| A | mass number | - |
| R0 | ~1.2e-15 | m |
Valid when
- Spherical nucleus assumption
Where do students lose marks on Nuclear Composition Size?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
1 item — click to collapse
Root cause: formula misuse
Correction
R = R_0 A^(1/3). Doubling A multiplies R by 2^(1/3) ≈ 1.26 (not 2). Implies constant nuclear density.
More in Atoms and Nuclei: 2 exam traps and mistakes · 5 formulas · 4 question patterns from its other lessons.
Nuclear Composition Size questions from past NEET papers
2 questions from NEET 2022, 2024. Answers verified against NTA official keys. — click to collapse
NEET 2024Revised key
1280, 81
2286, 80
3288, 82
4286, 81
NTA Answer: Option 4(revised_final)
NEET 2022
In the given nuclear reaction, the element X is ²²₁₁Na → X + e⁺ + ν
1²²₁₂Mg
2²³₁₁Na
3²³₁₀Ne
4²²₁₀Ne
NTA Answer: Option 4(final)
How does NEET ask about Nuclear Composition Size?
1 recurring pattern from past papers — click to collapse
Nuclear radius scales as A^(1/3). Compare two nuclei.
Direct ApplicationEasy
Common distractors
uses A or A squared
Uses linear or quadratic instead of cube root
Sources
NCERT refs: Class 12 Physics Chapter 13, p.307
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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