OxfordAQA International AS and A-level Physics: Atomic structure and elementary particles (9630) – Revision Notes

These are condensed notes for the final weeks on sections 3.3.1 and 3.3.2 of the OxfordAQA International AS and A-level Physics (9630) specification, Version 4.4. Both sections are shared International AS and A-level content. For full explanations and worked examples, read the study guide, then test yourself with the practice set.

Related pages: physics hub, printable checklist and the free 10-minute diagnostics. The atomic mass unit is not required at International AS (it is in section 3.12.2, International A-level), so keep masses in kg or in relative units.

3.3.1 Constituents of the atom

Simple model. A small, dense, positive nucleus (protons and neutrons, called nucleons) surrounded by electrons. A neutral atom has Z electrons.

Scale. Atomic radii are about 10⁻¹⁰ m; nuclear radii are about 10⁻¹⁵ m. Nearly all the mass is in the nucleus.

Rutherford scattering in one box

Set-up	Why
Alpha source, thin gold foil, detector that moves round	Count alpha particles at different angles
Vacuum	Air would absorb or scatter alpha particles
Very thin foil	Each alpha particle scatters at most once

Result	Meaning
Most pass straight through	The atom is largely empty space
Few deflected through large angles	Small concentrated positive charge (repulsion)
Very few rebound	Nucleus is massive as well as positive

How the model changed

1. Positive charge spread through the atom with electrons embedded (“plum pudding”). This predicts only small deflections.
2. Scattering evidence led to the nuclear atom.
3. The neutron was identified in 1932, explaining why nuclear mass exceeds what the proton count suggests.
4. Protons and neutrons are now known to have internal structure (not needed for this section).

Key idea: a model stays until evidence contradicts it.

Properties table

Particle	Relative charge	Relative mass	Charge (C)	Mass (kg)
Proton	+1	1	+1.60 × 10⁻¹⁹	1.67 × 10⁻²⁷
Neutron	0	1	0	1.67 × 10⁻²⁷
Electron	−1	about 1/1840	−1.60 × 10⁻¹⁹	9.11 × 10⁻³¹

Nuclide notation

 A
   X      A = nucleon number (protons + neutrons)
 Z        Z = proton number

Neutrons = A − Z. Electrons in a neutral atom = Z. Isotopes: same Z, different A.

Specific charge

specific charge = charge / mass, in C kg⁻¹.

Method in steps:

1. Find the net charge: (protons − electrons) × 1.60 × 10⁻¹⁹ C. For a bare nucleus, use Z protons only.
2. Find the mass: A × 1.67 × 10⁻²⁷ kg (ignore electrons unless the question gives their mass).
3. Divide, keep the sign, give units and 3 significant figures.

Reference values: proton 9.58 × 10⁷ C kg⁻¹. Electron 1.76 × 10¹¹ C kg⁻¹.

Quick check: a nucleus with Z protons and A nucleons has specific charge Z/A times the proton value. For helium-4 that is 2/4, so half the proton value.

3.3.2 Elementary particles

For every type of particle there is a corresponding antiparticle. Know these four pairs:

Particle	Antiparticle	Charge	Rest energy (MeV)
Electron	Positron	opposite	0.511 for both
Proton	Antiproton	opposite	938.3 for both
Neutron	Antineutron	both 0	939.6 for both
Neutrino	Antineutrino	both 0	negligible at this level

Must-know distinction. A particle and its antiparticle share mass and rest energy but carry opposite charge. Neutral particles still have distinct antiparticles.

E = mc² is not required in calculations. Use rest energies in MeV. Convert: 1 MeV = 1.60 × 10⁻¹³ J.

Annihilation

A particle and its antiparticle vanish together, and photons carry off the energy. Charge, energy and momentum are conserved. At least two photons, in opposite directions.

Energy of photons = both rest energies + both kinetic energies.

Example: electron and positron at rest give two photons of 0.511 MeV each (1.022 MeV in total).

Pair production

Photon becomes particle + antiparticle, near a nucleus. Minimum photon energy = twice the rest energy of one particle.

Pair	Minimum photon energy
Electron and positron	1.022 MeV
Proton and antiproton	1876.6 MeV

Extra energy becomes kinetic energy of the pair.

Method in steps for energy questions

1. Write the rest energy of each particle in MeV.
2. Add kinetic energy for annihilation, or subtract the rest energies from the photon energy for pair production.
3. Divide by two if the two products share energy equally (symmetrical case).
4. Convert to joules only if asked.

Worked reminders

Ion. Find the specific charge of the magnesium ion with 12 protons, 12 neutrons and 10 electrons.

1. Net charge = (12 − 10)e = +2e = 3.20 × 10⁻¹⁹ C.
2. Nucleon number = 24, so mass ≈ 24 × 1.67 × 10⁻²⁷ = 4.01 × 10⁻²⁶ kg.
3. Specific charge = 3.20 × 10⁻¹⁹ ÷ 4.01 × 10⁻²⁶ = 7.98 × 10⁶ C kg⁻¹.

Annihilation. An electron and a positron, each with 0.30 MeV of kinetic energy, meet head-on.

1. Each has 0.511 + 0.30 = 0.811 MeV.
2. Total = 1.622 MeV, shared by two photons.
3. Each photon: 0.811 MeV, or 0.811 × 1.60 × 10⁻¹³ = 1.30 × 10⁻¹³ J.

Pair production check. A photon must carry at least 1.022 MeV. If it has 2.022 MeV, the pair shares 1.000 MeV of kinetic energy.

Writing a Rutherford answer

A full answer has three linked parts: the observation, the physics, and the conclusion.

• Observation: “A small number of alpha particles were deflected through large angles.”
• Physics: “Alpha particles are positive and are repelled by a positive charge.”
• Conclusion: “The positive charge must be concentrated in a very small region, the nucleus.”

Do the same for the other two observations in the table, and always mention that the experiment was done in a vacuum with a thin foil.

Quick links between ideas

• The specific charge of a nucleus is Z/A times that of a proton. Isotopes of one element therefore have slightly different specific charges, because A differs while Z is fixed.
• Particle and antiparticle rest energies are equal, so the pair-production threshold is always twice one rest energy.
• A neutral atom has no overall charge. An ion has a net charge, so its specific charge is not zero.

Quick self-test

1. How many neutrons are in the nucleus of uranium-238, which has proton number 92?
2. How many protons, neutrons and electrons does a 39K⁺ ion contain (proton number 19).
3. Calculate the specific charge of the lithium-7 nucleus (proton number 3), giving units.
4. State the relative charge and approximate relative mass of an electron.
5. What is the minimum photon energy needed to produce a proton and an antiproton?
6. Why must at least two photons be produced when a stationary electron and positron annihilate?
7. A photon of energy 1.50 MeV produces an electron-positron pair. Find the kinetic energy of each, assuming they share it equally.
8. Give the antiparticle of the neutrino, and state its charge.
9. Convert a photon energy of 2.40 MeV to joules.
10. Explain why a photon of energy 0.90 MeV cannot produce an electron-positron pair.
11. Which observation in the scattering experiment shows that the target is more massive than the alpha particles?
12. Why was the foil in the scattering experiment very thin?

Answers

1. 238 − 92 = 146 neutrons.
2. Nucleon number 39, so neutrons = 20. Electrons = 19 − 1 = 18. 19 protons, 20 neutrons, 18 electrons.
3. Three protons carry 4.80 × 10⁻¹⁹ C in total. Mass ≈ 7 × 1.67 × 10⁻²⁷ = 1.17 × 10⁻²⁶ kg. Specific charge = 4.11 × 10⁷ C kg⁻¹.
4. Relative charge −1; relative mass about 1/1840.
5. 2 × 938.3 = 1876.6 MeV.
6. Momentum must be conserved. The total momentum before is zero, and one photon carries momentum, so there must be at least two, moving in opposite directions.
7. Available = 1.50 − 1.022 = 0.478 MeV; each gets 0.239 MeV.
8. The antineutrino, with zero charge.
9. 2.40 × 1.60 × 10⁻¹³ = 3.84 × 10⁻¹³ J.
10. The minimum energy is 1.022 MeV, and 0.90 MeV is less than this, so there is not enough energy to create two particles of rest energy 0.511 MeV each.
11. The small number of alpha particles that rebounded through angles above 90 degrees.
12. So each alpha particle is scattered by at most one nucleus and few are absorbed.

Where marks are usually lost

• Giving the neutron count as A instead of A − Z.
• Leaving out the negative sign on the specific charge of a negative ion or the electron.
• Using Z protons for the charge of an ion instead of the net charge.
• Stating only “most of the atom is empty space” for Rutherford. Write each observation with its own conclusion.
• Saying “attraction” instead of repulsion between the nucleus and the alpha particles.
• Using a single rest energy as the pair-production threshold.
• Mixing MeV and joules in one calculation.
• Writing that antimatter has negative mass or that the neutron and antineutron are identical.

Official syllabus

OxfordAQA International AS and A-level Physics (9630), sections 3.3.1 and 3.3.2, Version 4.4 (for exams May/June 2020 onwards), published by OxfordAQA.