OCR OCR 2018-style practice: A nucleus of iron-56 has a mass defect of 8.8 × 10^-28\ kg. Calculate its total binding energy and its binding energy per nucleon. Take c = 3.0 × 10^8\ m s^-1 and 1\ MeV = 1.6 × 10^-13\ J.

Binding energy: E_b = m\, c^2 = (8.8 × 10^-28)(3.0 × 10^8)^2 = (8.8 × 10^-28)(9.0 × 10^16) = 7.92 × 10^-11\ J. In MeV: 7.92 × 10^-111.6 × 10^-13 = 495\ MeV. Per nucleon (56 nucleons): (495)/(56) = 8.8\ MeV per nucleon. Markers reward E_b = m\, c^2, converting to MeV, and the binding energy per nucleon about 8.8\ MeV (near the peak, so iron is very stable).

EnglandPhysicsSyllabus dot point

What is the nucleus made of, and how do the standard model and binding energy explain matter and nuclear energy?

Nuclear and particle physics: alpha-particle scattering and the nuclear radius, the strong nuclear force, the standard model with quarks and leptons, beta decay, and mass-energy with binding energy, fission and fusion.

A focused answer to the OCR H556 nuclear and particle physics content, covering alpha-particle scattering and the nuclear radius equation, the strong nuclear force, the standard model with quarks and leptons, beta-minus and beta-plus decay with conservation laws, and mass-energy equivalence with binding energy, fission and fusion.

Generated by Claude Opus 4.813 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

Alpha-particle scattering showed the atom has a tiny, dense, positively charged nucleus. The nuclear radius follows $R = R_0 A^{1/3}$ (with $R_0 \approx 1.2 \times 10^{-15}\ \text{m}$ ), so nuclear density is roughly constant. The strong nuclear force holds the nucleus together: attractive over a very short range but repulsive at the very shortest separations. In the standard model, hadrons (made of quarks) include baryons such as the proton ( $uud$ ) and neutron ( $udd$ ), while leptons such as the electron and neutrino are fundamental. In beta-minus decay a neutron becomes a proton, emitting an electron and an antineutrino. Mass-energy equivalence $E = mc^2$ gives the binding energy $E_b = \Delta m\, c^2$ ; both fission of heavy nuclei and fusion of light nuclei release energy by moving towards the peak of the binding-energy-per-nucleon curve at iron.

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What this dot point is asking

OCR wants you to interpret alpha-particle scattering and use the nuclear radius equation, describe the strong nuclear force, classify particles in the standard model with quarks and leptons, write beta-decay equations and apply conservation laws, and use mass-energy equivalence with binding energy to explain fission and fusion.

The answer

Alpha-particle scattering and the nuclear radius

The strong nuclear force

The standard model

Beta decay

Mass-energy, binding energy, fission and fusion

Examples in context

Nuclear fission powers reactors and weapons, releasing the binding-energy difference as heavy uranium or plutonium nuclei split. Nuclear fusion powers the Sun and stars and is the goal of experimental reactors that aim for a clean, abundant energy source. The standard model and conservation laws underpin all of particle physics, tested at accelerators such as the LHC, and beta decay is the basis of carbon-14 dating and many medical tracers. Mass-energy equivalence is confirmed every time particles are created or annihilated.

Try this

Q1. State the equation for the nuclear radius and what it implies about nuclear density. [2 marks]

Cue. $R = R_0 A^{1/3}$ ; since volume is proportional to $A$ , nuclear density is approximately constant.

Q2. Give the quark composition of a proton and a neutron. [2 marks]

Cue. Proton $uud$ , neutron $udd$ .

Q3. Explain why both fission and fusion can release energy. [2 marks]

Cue. Both produce nuclei with a higher binding energy per nucleon (closer to the iron peak), so energy is released; fusion from light nuclei and fission from heavy nuclei.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR 20184 marksA nucleus of iron-56 has a mass defect of

8.8 \times 10^{-28}\ \text{kg}

. Calculate its total binding energy and its binding energy per nucleon. Take

c = 3.0 \times 10^{8}\ \text{m s}^{-1}

and

1\ \text{MeV} = 1.6 \times 10^{-13}\ \text{J}

Show worked answer →

Binding energy: $E_b = \Delta m\, c^2 = (8.8 \times 10^{-28})(3.0 \times 10^{8})^2 = (8.8 \times 10^{-28})(9.0 \times 10^{16}) = 7.92 \times 10^{-11}\ \text{J}$ .

In MeV: $\frac{7.92 \times 10^{-11}}{1.6 \times 10^{-13}} = 495\ \text{MeV}$ .

Per nucleon (56 nucleons): $\frac{495}{56} = 8.8\ \text{MeV per nucleon}$ .

Markers reward $E_b = \Delta m\, c^2$ , converting to MeV, and the binding energy per nucleon about $8.8\ \text{MeV}$ (near the peak, so iron is very stable).

OCR 20214 marksWrite the nuclear equation for the beta-minus decay of carbon-14 into nitrogen, and explain in terms of quarks what happens to the decaying nucleon. State the conservation laws that must be satisfied.

Show worked answer →

Nuclear equation: $^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e} + \bar{\nu}_e$ .

In beta-minus decay a neutron (quark content $udd$ ) changes into a proton ( $uud$ ): one down quark becomes an up quark, emitting an electron and an electron antineutrino.

Conserved: charge ( $6 = 7 - 1$ ), nucleon (baryon) number ( $14 = 14$ ), and lepton number ( $0 = 1 - 1$ for the electron and antineutrino), as well as energy and momentum.

Markers reward the balanced equation with the antineutrino, the down-to-up quark change, and the conservation laws.

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Sources & how we know this

OCR AS and A Level Physics A (H156, H556) specification — OCR (2015)