Nuclei for NEET UG
The nucleus is held together by the strongest force in nature. Mass defect and binding energy explain why heavy nuclei split, light ones fuse, and some decay on their own.
PhysicsClass 1260 MCQs2 lessons11 flashcards3 memory tricks
What you'll learn
- Nuclear size, mass defect and binding energy
Calculate nuclear radius, mass defect and binding energy, and read the binding-energy curve. - Radioactivity and half-life
Use the decay law and half-life to find how much of a sample remains.
Key formulas
| Nuclear radius | R = R₀A^(1/3), R₀ ≈ 1.2 fm |
|---|---|
| Mass defect | Δm = [Zm_p + (A − Z)m_n] − M_nucleus |
| Binding energy | E_b = Δm c²; 1 u ≈ 931.5 MeV |
| Decay law | N = N₀e^(−λt) |
| Half-life | T½ = 0.693/λ |
| After n half-lives | N = N₀/2ⁿ |
| Mean life | τ = 1/λ |
Memory tricks
Alpha decay lowers A by 4 and Z by 2. Beta-minus decay raises Z by 1 and leaves A the same. Gamma emission changes neither; it only releases energy.
After n half-lives the fraction remaining is (1/2)ⁿ. Half-life = 0.693/λ.
Binding energy per nucleon peaks near A = 56 (about 8.8 MeV). Moving towards iron, by fusion or fission, releases energy.
Try 3 NEET-style questions
Q1. The total binding energy of the helium-4 nucleus is about 28.3 MeV. Its binding energy per nucleon is about
- 14.15 MeV
- 28.3 MeV
- 3.54 MeV
- 7.07 MeV
Show answer
Answer: (4) 7.07 MeV
BE per nucleon = 28.3/4 ≈ 7.07 MeV.
Q2. A nucleus emits one alpha particle and then two beta-minus particles. The final nucleus is
- an isobar of the original nucleus
- an isotope of the original nucleus
- an isotone of the original nucleus
- identical to the original nucleus
Show answer
Answer: (2) an isotope of the original nucleus
Alpha: A − 4, Z − 2. Two β⁻: Z + 2. Final: A − 4, Z unchanged. Same Z, different A: an isotope.
Q3. A nucleus has a mass defect of 0.1 u. Its binding energy is about (1 u ≈ 931.5 MeV)
- 931.5 MeV
- 9.315 MeV
- 93.15 MeV
- 0.1 MeV
Show answer
Answer: (3) 93.15 MeV
BE = Δm × 931.5 MeV/u = 0.1 × 931.5 = 93.15 MeV.
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