How NEET Tests This Chapter

Nuclei is a reliable 1-2 question NEET topic, drawn from a compact pool:

  1. Vocabulary & notation: isotopes/isobars/isotones; Z, N, A counting.
  2. Size & density: R=R0A1/3R = R_0A^{1/3} ratios; density constant for all nuclei.
  3. Binding energy: mass defect × 931.5; EbnE_{bn} curve readings (plateau, peak at A = 56, droops); stability comparisons.
  4. Nuclear force: strength ordering, short range, charge independence, the 0.8 fm potential minimum.
  5. Radioactivity: alpha/beta/gamma character and displacement rules; half-life/mean-life/activity numericals.
  6. Fission & fusion: equation balancing, ~200 MeV and 26.7 MeV energy facts, the temperature story.

Everything below is NEET-style previous-year material with fully worked explanations. Years are attached only where attribution is certain; otherwise the tag is the generic [NEET].

Constants: 1 u = 931.5 MeV/c2c^2; R0R_0 = 1.2 fm; mHm_H = 1.007825 u; mnm_n = 1.008665 u.

NEET PYQ Worked Set A: Structure & Size

PYQ 1. The number of neutrons in 92238^{238}_{92}U is: [NEET]

Solution:

  1. N = A - Z = 238 - 92 = 146.

PYQ 2. If R is the radius of a nucleus with mass number 27… the radius for A = 216 is: [NEET]

Solution:

  1. (21627)1/3=2\left(\dfrac{216}{27}\right)^{1/3} = 2 → radius 2R.

PYQ 3. A nucleus with A = 64 and one with A = 8: ratio of radii and densities? [NEET]

Solution:

  1. Radii: (64/8)1/3=2(64/8)^{1/3} = 2 → 2 : 1.
  2. Densities: 1 : 1 (always).

PYQ 4. 1940^{40}_{19}K and 2040^{40}_{20}Ca are: [NEET]

Solution:

  1. Same A = 40, different Z → isobars.

PYQ 5. The nuclear force's strength ordering with Coulomb and gravitational forces? [NEET]

Solution:

  1. Nuclear > Coulomb > gravitational — with nuclear ~100× Coulomb at fm range and gravity ~103610^{36}× weaker than Coulomb.

NEET PYQ Worked Set B: Binding Energy & Mass-Energy

PYQ 6. The mass defect of 4^{4}He is 0.0304 u. Its binding energy per nucleon: [NEET]

Solution:

  1. Eb=0.0304×931.5≈28.3E_b = 0.0304 \times 931.5 \approx 28.3 MeV.
  2. Ebn=28.3/4≈7.08E_{bn} = 28.3/4 \approx 7.08 MeV.

PYQ 7. For heavier stability, which is the best indicator: binding energy, or binding energy per nucleon? [NEET]

Solution:

  1. Binding energy per nucleon — total EbE_b grows with size regardless of stability.
  2. EbnE_{bn} measures how tightly the AVERAGE nucleon is held: the true stability index (max at A ≈ 56).

PYQ 8. When a heavy nucleus fissions, the binding energy per nucleon of the fragments: [NEET]

Solution:

  1. Increases (from ~7.6 toward ~8.5 MeV) — the gain is the released energy.

PYQ 9. The energy equivalent of 1 mg of mass: [NEET]

Solution:

  1. E=10−6×9×1016=9×1010E = 10^{-6} \times 9 \times 10^{16} = 9 \times 10^{10} J.

PYQ 10. In a nuclear reaction, which pair is separately conserved (ordinary energies)? [NEET]

Solution:

  1. Proton number and neutron number — atoms of elements are NOT (transmutation), and binding energy changes by design.

NEET PYQ Worked Set C: Radioactivity & Nuclear Energy

PYQ 11. A nucleus 90220X^{220}_{90}X emits one alpha and two beta-minus particles. The resulting nuclide is: [NEET]

Solution:

  1. Alpha: (216, 88); two β−\beta^-: Z + 2 → (216, 90).
  2. 90216X^{216}_{90}X — same element, four units lighter.

PYQ 12. The half-life of a sample is 30 minutes. Fraction decayed in 90 minutes: [NEET]

Solution:

  1. 3 half-lives → remaining 1/8; decayed 7/8.

PYQ 13. Which radiation from radioactive decay has the greatest penetrating power? [NEET]

Solution:

  1. Gamma rays — neutral, massless photons; alphas are stopped by paper, betas by aluminium foil, gammas need thick lead/concrete.

PYQ 14. The fusion reaction chain in the Sun ultimately converts: [NEET]

Solution:

  1. Four hydrogen nuclei (protons) into one helium-4 (+ 2 positrons/neutrinos, net 26.7 MeV with annihilations).

PYQ 15. Fission is possible at room temperature but fusion is not, because: [NEET]

Solution:

  1. Fission's trigger — the neutron — is uncharged: no Coulomb barrier to enter the nucleus.
  2. Fusion partners are both positive: they need ~100s of keV (→ 10710^7-10910^9 K) to overcome mutual repulsion.

PYQ 16. A radioactive sample's mean life is 1000 s. Its half-life is: [NEET]

Solution:

  1. T1/2=0.693τ=693T_{1/2} = 0.693\tau = 693 s.