PhysicsNucleiClass 12

Nuclear physics: binding energy and radioactivity: interactive simulation

A nucleus weighs less than its separate protons and neutrons. The missing mass is the binding energy, and how it changes from one nucleus to another decides whether energy comes from joining nuclei (fusion) or splitting them (fission).

Useful for: JEE Main, JEE Advanced, NEET, CBSE Boards, AP Physics 2, A-level Physics, IB Physics, GCSE Physics · 3 modes in one lab

What you can explore

  1. 1

    Binding energy curve

    BE per nucleon for 21 real nuclei with the liquid-drop trend, fusion and fission estimates.
  2. 2

    Radioactive decay

    400 nuclei decaying at random against N₀e^(−λt), with half-life, mean life and activity.
  3. 3

    α, β, γ radiation

    Penetration through paper, aluminium and lead, and deflection in a magnetic field.

Try this

Step along the binding energy curve, watch 400 nuclei decay at random yet trace a perfect exponential, and block α, β and γ radiation with paper, aluminium and lead.

  1. 1

    Move along the curve to ⁵⁶Fe and ⁶²Ni.

    What you should see

    About 8.8 MeV per nucleon — the most tightly bound nuclei. Energy is released by moving towards them from either side.

  2. 2

    Press Show fusion.

    What you should see

    ²H + ²H → ⁴He: 4 × 7.074 − 4 × 1.112 ≈ 23.8 MeV released.

  3. 3

    Press Show fission.

    What you should see

    ²³⁵U splitting into two nuclei near A ≈ 117 releases about 235 × 0.9 ≈ 200 MeV.

  4. 4

    In Radioactive decay, set T½ = 4 s and run.

    What you should see

    λ ≈ 0.173 s⁻¹, τ ≈ 5.77 s. About 200 remain at 4 s and 100 at 8 s, with random scatter.

  5. 5

    In α, β, γ radiation, add paper, then aluminium, then lead.

    What you should see

    Paper stops α, aluminium stops β, and every ~0.9 cm of lead halves the γ rays (1 cm lets about 46 % through).

Formulas behind it

Binding energy

Eb=Δm c2,1 u=931.5 MeV/c2E_b = \Delta m\,c^2,\qquad 1\ \text{u} = 931.5\ \text{MeV}/c^2

Radioactive decay law

N=N0e−λtN = N_0e^{-\lambda t}

Half-life and mean life

T1/2=0.693λ,τ=1λ=1.44 T1/2T_{1/2} = \frac{0.693}{\lambda},\qquad \tau = \frac{1}{\lambda} = 1.44\,T_{1/2}

Activity

R=λNR = \lambda N

After n half-lives

N=N02nN = \frac{N_0}{2^n}

Common mistakes

  • Saying binding energy is energy stored in the nucleus that comes out. It is the energy needed to pull the nucleus apart.
  • Thinking half the sample decays in each half-life “in turn” for a single nucleus. Half-life is a statistical property of many nuclei.
  • Confusing mean life and half-life: τ is 1.44 times longer.
  • Saying γ rays are stopped completely by lead. They are only reduced exponentially.
Practise 239 questionsCheck your answer instantly, with a worked solution.Modern Physics chapter guideFormula sheet, solved examples and PYQ patterns.Stuck on a nuclear physics: binding energy and radioactivity question?Snap it and get a whiteboard video solution.

FAQ

Why do light nuclei fuse and heavy nuclei split?

Both processes move the products towards the peak of the binding energy curve near iron, where nucleons are most tightly bound, so the total binding energy rises and the difference is released.

Does temperature or pressure change the half-life?

No. Radioactive decay is a nuclear process; ordinary physical or chemical conditions do not affect it.

Why are α particles the most dangerous inside the body but the least dangerous outside?

They ionise very strongly but cannot get through skin. Swallowed or inhaled, they deposit all that energy in living cells.

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