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Nuclei
Physics · Class 12 · Part 2NCERT pp. 306–3182 sets × 25 questions
Key facts and formulas for Nuclei, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Nuclear radius | R = R₀ A^(1/3), R₀ = 1.2 fm; volume ∝ A; density is the same for all nuclei |
| Composition | A = Z + N; isotopes same Z, isobars same A, isotones same N |
| Mass-energy | E = mc²; 1 u = 931.5 MeV; mass defect Δm = Zm_p + Nm_n − M |
| Binding energy | E_b = Δm × 931.5 MeV; E_bn = E_b / A; peak about 8.75 MeV near A = 56 |
| Energy release | Q = (mass of reactants − mass of products) × 931.5 MeV; fission and fusion raise E_bn |
| Decay law | N = N₀ e^(−λt) = N₀ (1/2)^(t/T½); ln N has slope −λ |
| Half-life and mean life | T½ = 0.693/λ; τ = 1/λ = 1.44 T½; 1 Ci = 3.7 × 10¹⁰ Bq |
| Decay types | α: A − 4, Z − 2; β⁻: Z + 1; β⁺: Z − 1; γ: no change in A or Z |
| Fission and reactor | 200 MeV per fission; moderator slows neutrons; control rods are Cd or B; k = 1 is steady |
| Fusion and closest approach | Fusion needs about 10⁸ K plasma; r = (1/4πε₀)(2Ze²)/K |
Three sample questions
Q1. The radius of a nucleus is smaller than the radius of its atom by a factor of about
- 10⁴
- 10²
- 10⁶
- 10¹²
Hint and solution
Hint: Alpha scattering shows the nucleus is a tiny speck at the centre. Compare the volumes: they differ by about 10⁻¹², and volume goes as radius cubed.
- V(nucleus)/V(atom) ≈ 10⁻¹² — Scattering experiments give a nuclear volume about 10⁻¹² of the atomic volume.
- V ∝ R³, so R ratio = (10⁻¹²)^(1/3) — Volume goes as the cube of the radius, so the radius ratio is the cube root of the volume ratio.
- R(nucleus)/R(atom) ≈ 10⁻⁴ — The cube root of 10⁻¹² is 10⁻⁴. The nucleus is about ten thousand times smaller in radius.
- Answer: 10⁴ times smaller — So the radius is smaller by a factor of about 10⁴. Option A.
Answer: A. R(nucleus) is about 10⁻⁴ of R(atom); the volumes differ by about 10⁻¹².
Q2. An element has two isotopes: 63 u (70 %) and 65 u (30 %). Its atomic mass is
- 64.0 u
- 63.3 u
- 63.6 u
- 64.4 u
Hint and solution
Hint: Atomic mass of an element is a weighted mean, with abundance as the weight. It lies closer to the more abundant isotope.
- M = Σ (abundance × mass) — Atomic mass is the abundance weighted mean of isotope masses.
- M = 0.70 × 63 + 0.30 × 65 — Convert the percentages to fractions 0.70 and 0.30, then multiply each by its mass.
- M = 44.1 + 19.5 = 63.6 u — Add the two contributions. The result is nearer to 63 because that isotope is more abundant.
- Answer: 63.6 u — So the atomic mass is 63.6 u. Option C.
Answer: C. Weighted mean = 0.70 × 63 + 0.30 × 65 = 63.6 u.
Q3. Which statements about the proton and neutron are correct?
(i) m_p equals the mass of a hydrogen atom minus one electron mass.
(ii) The neutron was discovered by Chadwick in 1932.
(iii) A free neutron is stable for ever.
(iv) The neutron is slightly heavier than the proton.
- (i) and (iii) only
- (ii) and (iii) only
- (i), (ii) and (iv) only
- (i), (ii), (iii) and (iv)
Hint and solution
Hint: Check each statement alone. One of them says a free neutron lasts for ever; recall that a free neutron decays after about 1000 s.
- Test each statement — Go through (i) to (iv) one by one against NCERT facts.
- (i) true, (ii) true — The proton mass is the hydrogen atom mass minus one electron mass. Chadwick discovered the neutron in 1932.
- (iii) false, (iv) true — A free neutron decays with mean life near 1000 s. The neutron mass 1.00866 u exceeds the proton mass 1.00727 u.
- Correct set: (i), (ii), (iv) — So the correct statements are (i), (ii) and (iv) only. Option C.
Answer: C. A free neutron decays with a mean life near 1000 s, so (iii) is false. The others are correct.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.