OCR A Level Physics A: The nuclear atom, nuclear size and fundamental particles (H556) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover sections 6.4.1 (The nuclear atom) and 6.4.2 (Fundamental particles) of the OCR Advanced GCE in Physics A specification (H556), Version 3.0 (March 2026), for first assessment in 2017. Use the data given in each question; where a constant is needed it is stated. Revise first with the study guide or the revision notes.

Course pages: OCR A Level Physics hub | checklist | free diagnostics.

Questions

1. A neutral atom of argon-36 is written ³⁶₁₈Ar. (a) Give the numbers of protons, neutrons and electrons in this atom. [3] (b) Argon-38 is an isotope of argon-36. State what is the same and what is different about the two nuclei. [2]

2. An atom has a radius of 1.3 × 10⁻¹⁰ m and its nucleus has a radius of 4.2 × 10⁻¹⁵ m. (a) Calculate the ratio of the atomic radius to the nuclear radius. [1] (b) Calculate the fraction of the volume of the atom occupied by the nucleus. [2] (c) State what your answer suggests about the structure of an atom. [1]

3. Describe the alpha-particle scattering experiment and explain how its results provide evidence for a small, charged nucleus. [6]

4. The strong nuclear force acts between nucleons. (a) State the separations over which it is attractive and the separations over which it is repulsive. [2] (b) State why the repulsive part of the force is needed. [1] (c) Protons in a nucleus repel one another electrostatically. Explain why the nucleus does not fly apart. [1] (d) Explain why a nucleon at one edge of a large nucleus is hardly affected by a nucleon at the opposite edge. [1]

5. Take r₀ = 1.25 fm, where 1 fm = 10⁻¹⁵ m. (a) Calculate the radius of a gold-197 nucleus. [2] (b) A nucleus has a radius of 5.5 fm. Calculate its nucleon number. [2] (c) Radii R of several nuclei are plotted against A^(1/3). State the shape of the graph and what its gradient represents. [2]

6. Use r₀ = 1.25 fm, u = 1.66 × 10⁻²⁷ kg, and for a hydrogen atom a mass of 1.67 × 10⁻²⁷ kg and a radius of 5.3 × 10⁻¹¹ m. (a) Show that the density of nuclear matter does not depend on the nucleon number A. [3] (b) Calculate the density of nuclear matter. [2] (c) Calculate the ratio of this density to the mean density of the hydrogen atom. [2]

7. (a) State the antiparticle of the electron, giving one way in which it is the same and one way in which it is different. [3] (b) A neutron and an antineutron are both uncharged. State, in terms of quarks, how they differ. [1]

8. The particles listed are an electron, a proton, a neutrino and a neutron. (a) State which are hadrons. [1] (b) State which are leptons. [1] (c) State the force that hadrons feel but leptons do not. [1] (d) State a force felt by both hadrons and leptons. [1]

9. The charge on an up quark is +2/3 e and on a down quark −1/3 e. A strange quark has the same charge as a down quark. (a) State the quark composition of the antiproton and show that its charge is −e. [2] (b) Calculate the charge of a particle made of a down quark and an anti-up quark. [1] (c) Calculate the charge of a particle made of an up quark and an anti-strange quark. [1] (d) Explain why a particle made of two up quarks and an anti-down quark would not be a possible hadron. [1]

10. (a) Write down the quark-level equation for beta-minus decay and show that charge is conserved. [3] (b) Write down the quark-level equation for beta-plus decay. [1] (c) State the change in the proton number of a nucleus in beta-plus decay and name the fundamental force responsible. [2]

11. The sigma-minus particle has quark composition dds. One of its decay modes produces a neutron (udd), an electron and an antineutrino. (a) Calculate the charge of the sigma-minus particle in units of e. [1] (b) State which quark changes and write the quark transformation. [2] (c) Show that charge is conserved in the decay. [2] (d) State why the neutral particle emitted is an antineutrino and not a neutrino. [1] (e) Name the force responsible. [1] (f) State what this decay shows about which forces the sigma-minus particle and the electron feel. [1]

Answers

1. (a) Protons = 18 [1]. Neutrons = 36 − 18 = 18 [1]. Electrons = 18, because the atom is neutral [1] [3] (b) Same number of protons (18) [1]. Argon-38 has 20 neutrons against 18, so a different nucleon number [1] [2] Examiner insight: “Same element” is weaker than “same number of protons”; say the number, and give the neutron numbers to show the difference.

2. (a) 1.3 × 10⁻¹⁰ / 4.2 × 10⁻¹⁵ = 3.1 × 10⁴ [1] [1] (b) Volume fraction = (4.2 × 10⁻¹⁵ / 1.3 × 10⁻¹⁰)³ [1] = 3.4 × 10⁻¹⁴ [1] [2] (c) The atom is mostly empty space [1] [1] Examiner insight: Volume goes as radius cubed, so cube the ratio. Squaring it, or quoting the radius ratio, answers a different question.

3. A narrow beam of alpha particles is fired at a thin metal foil, such as gold, in a vacuum [1]. A detector is moved round to count particles at different angles [1]. Most particles go straight on, so the atom is largely empty space [1]. A small fraction turn through large angles, because the positive alpha particles are repelled by positive charge concentrated in one place [1]. A very few rebound by more than 90°, so the charge is in a very small region that is also massive [1]. Positive charge spread through the whole atom could only give small deflections, so there must be a small, charged nucleus [1] [6] Examiner insight: Pair each observation with its own conclusion. A list of observations followed by one general sentence leaves the reasoning for the examiner to supply.

4. (a) Attractive from about 0.5 fm to about 3 fm [1]. Repulsive below about 0.5 fm [1] [2] (b) It stops the nucleons being pulled together into a single point (the nucleus would collapse) [1] [1] (c) At these separations the attractive strong force is larger than the electrostatic repulsion [1] [1] (d) The strong force has a short range, so it is negligible beyond a few femtometres [1] [1] Examiner insight: Quote the numbers with the unit, fm. “Short range” alone does not say how short.

5. (a) R = r₀A^(1/3) = 1.25 × 197^(1/3) [1] = 1.25 × 5.82 = 7.3 fm [1] [2] (b) A^(1/3) = 5.5 / 1.25 = 4.4 [1]. A = 4.4³ = 85.2, so A = 85 [1] [2] (c) A straight line through the origin [1]. The gradient is r₀ [1] [2] Examiner insight: Show the cube root step. A common slip in (b) is to divide R by r₀ and stop, forgetting to cube.

6. (a) Mass of nucleus ≈ A × u [1]. Volume = (4/3)πR³ = (4/3)π r₀³A [1]. A cancels in mass/volume, giving 3u / (4π r₀³), which is constant [1] [3] (b) ρ = 3 × 1.66 × 10⁻²⁷ / (4π × (1.25 × 10⁻¹⁵)³) [1] = 2.0 × 10¹⁷ kg m⁻³ [1] [2] (c) Hydrogen atom density = 1.67 × 10⁻²⁷ / ((4/3)π(5.3 × 10⁻¹¹)³) = 2.7 × 10³ kg m⁻³ [1]. Ratio = 2.0 × 10¹⁷ / 2.7 × 10³ = 7.6 × 10¹³ [1] [2] Examiner insight: A “show that” answer needs the cancellation written out. Stating that density is constant without the algebra is a conclusion rather than a demonstration.

7. (a) The positron [1]. Same mass [1]. Opposite charge, +e rather than −e [1] [3] (b) Neutron: udd. Antineutron: ū d̄ d̄ (three antiquarks) [1] [1] Examiner insight: “Opposite charge” cannot be the answer for a neutral pair; the difference is in the antiquarks.

8. (a) Proton and neutron [1] [1] (b) Electron and neutrino [1] [1] (c) The strong nuclear force [1] [1] (d) The weak nuclear force [1] [1] Examiner insight: If asked for a force felt by leptons, name the weak force. The electromagnetic force is also felt by charged particles but is not what the specification classification is based on.

9. (a) Antiproton = ū ū d̄ [1]. Charge = −2/3 − 2/3 + 1/3 = −1 e [1] [2] (b) d ū: −1/3 − 2/3 = −1 e [1] [1] (c) u s̄: +2/3 + 1/3 = +1 e [1] [1] (d) u u d̄ has charge 2/3 + 2/3 + 1/3 = 5/3 e, which is not a whole number of e [1] [1] Examiner insight: Write each quark’s charge before adding. The usual error is giving an antiquark the same sign as its quark.

10. (a) d → u + e⁻ + ν̄ [1]. Left: −1/3 [1]. Right: +2/3 − 1 + 0 = −1/3, so charge is conserved [1] [3] (b) u → d + e⁺ + ν [1] [1] (c) The proton number decreases by 1 [1]. The weak nuclear force [1] [2] Examiner insight: Beta-minus emits an antineutrino and beta-plus emits a neutrino. Learn the pair, since charge balance cannot tell them apart.

11. (a) Charge = −1/3 − 1/3 − 1/3 = −1 e [1] [1] (b) The strange quark changes to an up quark [1]. dds → udd + e⁻ + ν̄ (that is, s → u + e⁻ + ν̄) [1] [2] (c) Before: −1 e [1]. After: neutron 0, electron −1, antineutrino 0, total −1 e, so charge is conserved [1] [2] (d) An electron is emitted, as in beta-minus decay, and beta-minus decay emits an antineutrino [1] [1] (e) The weak nuclear force [1] [1] (f) The sigma-minus particle is a hadron, so it feels the strong and weak forces, while the electron is a lepton and feels the weak force but not the strong force [1] [1] Examiner insight: In (b) name the quark that changes and give its equation, and leave the other two quarks out of the change. Quoting only the whole-particle equation does not show which quark is responsible.

Where marks are usually lost

• Describing alpha scattering without saying why a vacuum or a thin foil is used, or without tying each observation to a conclusion.
• Saying “the nucleus is small” but not “charged” or “massive”.
• Using R = r₀A instead of the cube root, or reading R off in metres when fm is asked for.
• Squaring instead of cubing the radius ratio when comparing volumes.
• Claiming the strong force is attractive at every separation, or leaving out the numbers 0.5 fm and 3 fm.
• Stating that nuclear density increases with A.
• Giving an antiquark the same sign of charge as its quark.
• Putting a neutrino in beta-minus decay and an antineutrino in beta-plus decay.
• Adding charges without writing the left and right totals side by side.

Next steps

• Re-read the revision notes and the study guide.
• Return to the OCR A Level Physics hub and the checklist.
• Take the free 10-minute diagnostics.
• Want help with a weak spot? Book a free trial class.

Official syllabus

OCR Advanced GCE in Physics A (H556) specification, Version 3.0 (March 2026), for first assessment in 2017, published by OCR. Sections 6.4.1 The nuclear atom and 6.4.2 Fundamental particles.