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

These notes condense 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. For full explanations, read the study guide; to test yourself, use the practice questions.

Course pages: OCR A Level Physics hub | checklist | free diagnostics. Values used: r₀ = 1.2 fm, u = 1.66 × 10⁻²⁷ kg, 1 fm = 10⁻¹⁵ m. In an exam, use the values the question gives.

Key terms

Term	Meaning
Nucleon	A proton or a neutron
Proton number Z	Number of protons in the nucleus
Nucleon number A	Protons plus neutrons
Isotopes	Same Z, different A (different neutron numbers)
Strong nuclear force	Holds nucleons together; short range
Hadron	Particle that feels both the strong and the weak force; made of quarks
Lepton	Particle that feels the weak force but not the strong force
Antiparticle	Same mass as its particle; opposite charge if charged

Equations and values

Item	Result	Notes
Neutron number	N = A − Z
Nuclear radius	R = r₀A^(1/3)	r₀ is a constant, about 1.2 fm; A is the nucleon number
Nuclear volume	proportional to A	R³ is proportional to A
Nuclear density	ρ = 3u / (4πr₀³)	Same for every nucleus, about 2.3 × 10¹⁷ kg m⁻³
Atom radius	about 10⁻¹⁰ m
Nucleus radius	about 10⁻¹⁵ to 10⁻¹⁴ m
Atom : nucleus width	about 10⁴ to 10⁵

Alpha scattering (6.4.1(a)-(b))

Thin gold foil, alpha beam, vacuum, moving detector.

• Most pass straight through: the atom is mostly empty space.
• A few swing through large angles: positive charge packed into a small region repels the alpha particles.
• Very few rebound back: the nucleus is also massive.

Say “small, charged nucleus” and link each observation to its conclusion. The result replaced the plum pudding picture, in which positive charge is spread through the whole atom.

Simple nuclear model: nucleus of protons (+e) and neutrons (0), electrons (−e) outside. A neutral atom has the same number of electrons as protons.

Notation and isotopes (6.4.1(d))

ᴬ_Z X: A is at the top, Z at the bottom.

Method in steps:

1. Read Z from the element or the subscript.
2. N = A − Z.
3. Neutral atom: electrons = Z.
4. Isotopes: same Z, different N.

Worked reminder. ¹³⁷₅₆Ba has 56 protons, 137 − 56 = 81 neutrons, and 56 electrons if neutral. ¹³⁸₅₆Ba is an isotope with 82 neutrons.

Strong nuclear force (6.4.1(e))

Separation	Behaviour
Under 0.5 fm (approximately)	Repulsive
Around 0.5 fm	Zero resultant force
Between roughly 0.5 fm and 3 fm	Attractive
Beyond a few fm	Negligible: short range

Why it matters: it must beat the electrostatic repulsion between protons, but the repulsive core stops collapse. 1 fm = 10⁻¹⁵ m.

Radius and density (6.4.1(c), (f), (g))

Method in steps for a radius question:

1. Write R = r₀A^(1/3).
2. Take the cube root of A before multiplying.
3. Give the answer in fm or m, and say which.

Worked reminder (radius). Iron-56: R = 1.2 × 56^(1/3) = 1.2 × 3.83 = 4.6 fm. For a nucleus with A = 216: R = 1.2 × 6 = 7.2 fm.

Worked reminder (scaling). Multiplying A by 8 multiplies R by 8^(1/3) = 2, and the volume by 8.

Worked reminder (finding A). If R = 6.0 fm, A^(1/3) = 6.0/1.2 = 5.0, so A = 5.0³ = 125.

Density in words. Mass is proportional to A and volume is proportional to A, so the A cancels. All nuclei have the same density, of the order of 10¹⁴ times the mean density of an atom, because nearly all the mass of the atom is in about 10⁻¹⁴ of its volume.

Worked reminder (density estimate). Using ρ = 3u / (4πr₀³) with r₀ = 1.2 × 10⁻¹⁵ m: ρ = 3 × 1.66 × 10⁻²⁷ / (4π × 1.73 × 10⁻⁴⁵) = 2.3 × 10¹⁷ kg m⁻³. A volume of 1.0 cm³ (1.0 × 10⁻⁶ m³) of nuclear matter would have a mass of about 2.3 × 10¹¹ kg. Compare a typical solid, around 10³ kg m⁻³: the ratio is of the order of 10¹⁴.

Worked reminder (atom against nucleus). An atom of radius 1.0 × 10⁻¹⁰ m and a nucleus of radius 5.0 × 10⁻¹⁵ m: radius ratio 2.0 × 10⁴, volume ratio (2.0 × 10⁴)³ = 8.0 × 10¹². Cube the radius ratio for volumes.

Worked reminder (nucleus after decay). In beta-minus decay a nucleus with Z = 30 becomes Z = 31 with the same A, because one neutron has become a proton. In beta-plus decay Z falls by 1 and A is unchanged, because one proton has become a neutron.

Antiparticles, hadrons and leptons (6.4.2(a)-(d))

Particle	Antiparticle	Charge relation
e⁻	e⁺	opposite
p	p̄	opposite
n	n̄	both neutral
ν	ν̄	both neutral

Class	Strong force?	Weak force?	Examples
Hadron	yes	yes	proton, neutron
Lepton	no	yes	electron, neutrino

Memory aid: hadrons are the ones made of quarks, and so feel the strong force; leptons are not made of quarks.

Quarks (6.4.2(e)-(g))

Quark	Charge / e	Antiquark	Charge / e
u	+2/3	ū	−2/3
d	−1/3	d̄	+1/3
s	−1/3	s̄	+1/3

• Proton uud = +1. Neutron udd = 0.
• Antiproton ūūd̄ = −1. Antineutron ūd̄d̄ = 0.
• Total charge of any hadron is a whole number times e. If your sum is not, check for a missed bar.

Beta decay (6.4.2(h)-(k))

	β⁻	β⁺
Quark change	d → u	u → d
Equation	d → u + e⁻ + ν̄	u → d + e⁺ + ν
Nucleon equation	n → p + e⁻ + ν̄	p → n + e⁺ + ν
Charge check	−1/3 → +2/3 − 1	+2/3 → −1/3 + 1
Force	weak	weak

Method in steps for balancing a quark equation:

1. Identify which quark changes; the others are spectators.
2. Add the charges on the left in units of e.
3. Add the charges on the right, including the lepton.
4. Check they match, then choose neutrino or antineutrino. Beta-minus gives an antineutrino; beta-plus gives a neutrino.

Worked reminder (6.4.2(l)). A strange quark in a hadron can decay as s → u + e⁻ + ν̄. Charge: −1/3 on the left and +2/3 − 1 = −1/3 on the right. Balanced.

Must-know distinctions

• Proton number is about identity (which element); nucleon number is about mass.
• Isotopes share chemistry because they share electrons.
• Neutron and antineutron are both neutral but are different particles.
• Hadrons feel the strong force; leptons do not.
• Antiquarks have the opposite charge: ū is −2/3, not +2/3.

Quick self-test

1. How many neutrons are in ¹⁴⁰₅₈Ce?
2. State what the deflection of a few alpha particles through large angles shows.
3. Calculate the radius of a nucleus with A = 216.
4. A nucleus has A = 8 times that of another. State the ratio of their radii.
5. State the separations over which the strong force is attractive and repulsive.
6. State which of the strong and weak forces a proton feels, and which an electron feels.
7. Find the charge, in units of e, of ūd.
8. Write the quark equation for beta-plus decay.
9. State the antiparticle of the neutrino and its charge.
10. Explain why nuclear density does not depend on A.

Answers

1. 140 − 58 = 82.
2. A small region holds a concentrated positive charge (and most of the mass): the nucleus.
3. 1.2 × 216^(1/3) = 1.2 × 6 = 7.2 fm.
4. 2 (8^(1/3) = 2).
5. Attractive from about 0.5 fm to about 3 fm; repulsive below about 0.5 fm.
6. The proton, a hadron, feels the strong and weak forces; the electron, a lepton, feels the weak force only (not the strong force).
7. −2/3 − 1/3 = −1.
8. u → d + e⁺ + ν.
9. The antineutrino; its charge is zero.
10. Mass ∝ A and volume ∝ R³ ∝ A, so the ratio mass/volume has no A in it.

Where marks are usually lost

• Saying the nucleus is “small” without saying it is charged, or without linking to the large-angle deflections.
• Writing that most alpha particles go through “because the nucleus is small” without saying the atom is mostly empty space.
• Giving R = r₀A, or forgetting to take the cube root.
• Leaving a radius in metres when the question asks in fm, or mixing 10⁻¹⁵ and 10⁻¹⁰.
• Saying the strong force is attractive at all separations.
• Putting a neutrino where the antineutrino belongs in beta-minus decay.
• Adding quark charges but using +2/3 for an antiup quark.
• Writing a bare equation with no charge check when the question says “show”.

Next steps

Work through the practice questions, then go back to the study guide for any weak spot.

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.