Q1. Find the energy released if a mass defect of 0.2 u occurs in a reaction.
E = 931.5 × Δm
E = 931.5 × 0.2
E = 186.3 MeV
Nuclei — Class 12
A tiny loss of mass releases enormous energy (E = mc²). Learn mass defect, binding energy and half-life, and compute the energy of nuclear reactions.
Nucleus & isotopesThe nucleus contains protons and neutrons (nucleons). Isotopes have the same Z but different mass number A. Nuclear radius R = R₀A^(1/3).
Mass defectThe mass of a nucleus is slightly LESS than the sum of its nucleons; this missing mass Δm is converted to binding energy.
Binding energyThe energy that holds the nucleus together, E = Δm·c². Using 1 u = 931.5 MeV, E = 931.5 × Δm MeV. Higher BE/nucleon = more stable.
Radioactivity & half-lifeUnstable nuclei decay (α, β, γ). The half-life T is the time for half the nuclei to decay; N = N₀/2^(t/T).
Binding-energy calculator Interactive
Enter the mass defect (in atomic mass units) to get the energy released, using 1 u = 931.5 MeV.
Energy, E = 931.5·Δm—MeV
Just 1 atomic mass unit of "lost" mass releases 931.5 MeV — the reason nuclear energy dwarfs chemical energy.
Numericals practice Interactive
Mass-defect energy and half-life problems with steps.
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Solved numericals
Q2. A radioactive substance has a half-life of 4 days. What fraction remains after 12 days?
12 days = 3 half-lives
Fraction left = (1/2)³ = 1/8
So 1/8 (12.5%) of the sample remains.
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Nuclear radius | R = R₀ A^(1/3) | m (R₀ = 1.2 fm) |
| Mass–energy | E = Δm c² | joule (J) |
| Binding energy (shortcut) | E = 931.5 × Δm | MeV (Δm in u) |
| Radioactive decay | N = N₀ e^(−λt) | — |
| Half-life | T = 0.693 / λ | second (s) |
Common mistakes & exam wins
- Use E = 931.5 × Δm(in u) to get the energy in MeV directly.
- Binding energy per nucleon peaks near iron (A ≈ 56) — the most stable nuclei.
- Fusion (light nuclei joining) and fission (heavy nuclei splitting) both move towards higher BE/nucleon, releasing energy.
- After n half-lives, the fraction remaining is (1/2)ⁿ.
Frequently asked questions
What is mass defect?
The difference between the sum of the masses of the individual nucleons and the actual (smaller) mass of the nucleus; this missing mass becomes the binding energy.
What is binding energy?
The energy needed to break a nucleus into its separate nucleons (or released when they combine), E = Δm·c² = 931.5 × Δm MeV.
What is half-life?
The time taken for half the radioactive nuclei in a sample to decay; after n half-lives, (1/2)ⁿ of the sample remains.
What is the difference between nuclear fission and fusion?
Fission is the splitting of a heavy nucleus into lighter ones; fusion is the joining of light nuclei into a heavier one. Both release energy.