NucleiNEET Physics · Class 12 · NCERT Chapter 13

You can expect 1 to 2 questions in NEET 2027. Common asks: half-life and mean life, binding energy, position of Fe-56 in the BE curve, alpha and beta decay equations, and energy released in fission or fusion.

R = R_0 A^(1/3), where R_0 = 1.2 fm and A is the mass number. Nuclear volume scales as A, so the nuclear density is essentially the same for all nuclei (~2.3 x 10^17 kg/m^3, about 100 trillion times the density of water).

1 u corresponds to 931.5 MeV via E = m c^2. So even a tiny mass defect of 0.05 u corresponds to about 47 MeV of binding energy.

When you add up the masses of the protons and neutrons in a nucleus, the total exceeds the actual nuclear mass. The difference is the mass defect: Delta M = Z m_p + (A - Z) m_n - M_nuc. Multiplied by c^2, it gives the binding energy: BE = Delta M c^2. This is the energy that must be supplied to break the nucleus into individual nucleons.

For light nuclei, adding nucleons rapidly increases the average binding (more nuclear-force partners). Beyond Fe (A ~ 56), the long-range Coulomb repulsion of protons starts to outweigh the gain. So Fe-56 sits at the most stable point. Lighter nuclei release energy on fusion (towards Fe); heavier nuclei release energy on fission (down towards Fe).

Alpha: emission of a He-4 nucleus. Z drops by 2, A drops by 4. Beta-minus: a neutron turns into a proton + electron + antineutrino. Z rises by 1, A unchanged. Beta-plus: proton turns into neutron + positron + neutrino. Z drops by 1, A unchanged. Gamma: nucleus de-excites by emitting a high-energy photon. No change in Z or A.

N(t) = N_0 e^(-lambda t). Activity A(t) = -dN/dt = lambda N. The number of undecayed nuclei drops exponentially. The decay constant lambda has units 1/time.

t_1/2 = (ln 2) / lambda ≈ 0.693 / lambda. Mean life tau = 1 / lambda. So tau = t_1/2 / ln 2 ≈ 1.44 t_1/2. Mean life is always longer than half-life.

Activity A = lambda N is the rate of disintegration. SI unit: becquerel (Bq) = 1 disintegration per second. Older unit: curie (Ci) = 3.7 x 10^10 Bq. Activity decreases by half every t_1/2.

Fission: a heavy nucleus (e.g. U-235) splits into smaller nuclei + neutrons + energy (~200 MeV per fission). Used in nuclear reactors and bombs. Fusion: two light nuclei combine into a heavier one + energy (~26 MeV per cycle of 4 H → He). Powers stars, including the Sun. Hard to do on Earth because of the high temperature needed to overcome Coulomb repulsion.