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Nuclear physics deals with the structure of atomic nuclei and the processes by which they change. This topic covers the nuclear model, radioactivity, nuclear decay, the exponential decay law, binding energy, and the processes of fission and fusion. It is tested in AQA Paper 2 (Section 8) . This material also connects with the particle physics covered earlier in the course.
The nucleus contains protons and neutrons (collectively called nucleons). The nucleus is described by:
Ernest Rutherford's alpha-particle scattering experiment (1909, conducted by Geiger and Marsden) was pivotal in establishing the nuclear model of the atom.
The experiment: A beam of alpha particles was fired at a thin gold foil. Detectors (zinc sulphide screens) around the foil recorded where the alpha particles arrived.
Key observations:
Conclusions:
flowchart LR
A["Alpha source"] --> B["Narrow beam of<br/>alpha particles"]
B --> C["Thin gold foil"]
C -->|"Most particles"| D["Pass straight through<br/>(atom is mostly empty space)"]
C -->|"Small fraction"| E["Deflected at large angles<br/>(pass close to nucleus)"]
C -->|"Very few (~1 in 8000)"| F["Bounced back > 90 degrees<br/>(head-on approach to nucleus)"]
The closest approach of an alpha particle to the nucleus gives an upper estimate of the nuclear radius, found by equating kinetic energy to electrical potential energy: ½mv² = kQαQnucleus/r.
Described diagram — Rutherford alpha scattering experiment setup and results: On the left, an alpha source emits a narrow beam of alpha particles directed at a thin gold foil at the centre. A movable detector (zinc sulphide screen viewed through a microscope) is positioned around the foil to detect scattered alpha particles at various angles. The results show that the vast majority of alpha particles pass straight through the foil with little or no deflection (shown as straight arrows continuing beyond the foil). A small number are deflected through moderate angles (shown as arrows bending away from their original path). A very small number (about 1 in 8000) are deflected through angles greater than 90°, some bouncing almost straight back towards the source. These large-angle deflections occur when an alpha particle passes very close to a gold nucleus and is repelled by the strong positive charge concentrated in the tiny nucleus.
The nuclear radius can be estimated using:
r = r₀A^(1/3)
where r₀ ≈ 1.2 × 10⁻¹⁵ m (1.2 fm). This shows that the nuclear radius increases with the cube root of the mass number.
This implies that the volume of the nucleus (V = 4/3 πr³) is directly proportional to A, meaning each nucleon occupies approximately the same volume. Therefore, nuclear density is approximately constant — about 10¹⁷ kg m⁻³, which is enormously greater than the density of ordinary matter.
High-energy electrons can also be used to determine nuclear radius. When electrons with de Broglie wavelength comparable to the nuclear size are fired at nuclei, a diffraction pattern is produced. The first minimum in the diffraction pattern occurs at:
sin θ ≈ 1.22λ/2r
where r is the nuclear radius and λ is the de Broglie wavelength of the electrons. Electron diffraction gives more precise measurements than alpha scattering because electrons interact via the electromagnetic force (well understood) rather than the strong force, and their wavelength can be precisely controlled.
Before studying radioactive sources, it is important to understand that we are all constantly exposed to background radiation from natural and artificial sources.
| Source | Approximate Contribution |
|---|---|
| Radon gas (from rocks and soil) | ~50% |
| Medical uses (X-rays, scans) | ~14% |
| Cosmic rays | ~10% |
| Food and drink (e.g. potassium-40) | ~12% |
| Gamma rays from rocks and buildings | ~14% |
| Nuclear power and weapons testing | <1% |
In any experiment measuring radioactive decay, the background count rate must be measured separately and subtracted from the total count rate to obtain the corrected count rate from the source alone.
Exam Tip: In practical and calculation questions involving count rate, always subtract the background count rate first. If you are told the background count is 30 counts per minute and the measured count rate is 250 counts per minute, the corrected count rate from the source is 220 counts per minute.
Key Definition: Radioactive decay is the spontaneous and random emission of radiation from an unstable nucleus. "Spontaneous" means it is not affected by external conditions (temperature, pressure, chemical state). "Random" means it is impossible to predict which particular nucleus will decay next or when.
graph TD
A["Unstable Nucleus"] --> B["Alpha Decay<br/>Z decreases by 2<br/>A decreases by 4"]
A --> C["Beta-minus Decay<br/>Z increases by 1<br/>A unchanged"]
A --> D["Beta-plus Decay<br/>Z decreases by 1<br/>A unchanged"]
A --> E["Gamma Emission<br/>Z and A unchanged<br/>(nucleus loses energy)"]
B --> F["Emits: ⁴₂He nucleus"]
C --> G["Emits: e⁻ + antineutrino<br/>(via W⁻ boson)"]
D --> H["Emits: e⁺ + neutrino<br/>(via W⁺ boson)"]
E --> I["Emits: high-energy photon"]
An alpha particle is a helium nucleus (⁴₂He) — 2 protons and 2 neutrons. Alpha decay reduces the atomic number by 2 and the mass number by 4:
ᴬ_Z X → ᴬ⁻⁴_(Z−2) Y + ⁴₂α
Alpha particles are strongly ionising (they create many ion pairs per cm of path), have a short range in air (~3–7 cm), and are stopped by a sheet of paper or a few centimetres of air. They have a discrete (single) energy for a given decay.
A neutron transforms into a proton, emitting an electron and an electron antineutrino:
n → p + e⁻ + ν̄ₑ
The atomic number increases by 1, and the mass number remains unchanged. At the quark level: d → u + e⁻ + ν̄ₑ (mediated by a W⁻ boson).
Beta-minus particles are moderately ionising, have a range of several metres in air, and are stopped by a few millimetres of aluminium. They have a continuous energy spectrum (the energy is shared between the electron and the antineutrino).
A proton transforms into a neutron, emitting a positron and an electron neutrino:
p → n + e⁺ + νₑ
The atomic number decreases by 1, and the mass number remains unchanged. At the quark level: u → d + e⁺ + νₑ (mediated by a W⁺ boson).
Beta-plus decay occurs in proton-rich nuclei. The emitted positron quickly annihilates with an electron, producing two gamma photons travelling in opposite directions — this is the basis of PET (positron emission tomography) scanning in medical imaging.
Gamma rays are high-energy photons emitted when a nucleus transitions from an excited state to a lower energy state. They carry no charge and no mass, so they do not change the atomic number or mass number.
Gamma rays are weakly ionising, very penetrating, and require several centimetres of lead or metres of concrete for significant attenuation.
| Property | Alpha (α) | Beta-minus (β⁻) | Beta-plus (β⁺) | Gamma (γ) |
|---|---|---|---|---|
| Identity | ⁴₂He nucleus | Electron | Positron | Photon |
| Charge | +2e | −e | +e | 0 |
| Mass | 4u | ~1/1840 u | ~1/1840 u | 0 |
| Speed | ~5% c | Up to ~99% c | Up to ~99% c | c |
| Ionising ability | Strong | Moderate | Moderate | Weak |
| Penetrating ability | Low | Moderate | Moderate | High |
| Stopped by | Paper/skin | Few mm aluminium | Annihilates with e⁻ | cm of lead |
| Deflection in E/B fields | Small deflection | Large deflection (opposite to α) | Large deflection (same as α) | None |
Gamma radiation obeys an inverse square law: the intensity (I) at a distance r from a point source is:
I = k/r²
or equivalently, I₁r₁² = I₂r₂². Doubling the distance from the source reduces the intensity to one quarter. This is because gamma photons spread out uniformly in all directions, and the area of a sphere increases as r².
When working with radioactive sources:
Key Definition: The decay constant (λ) is the probability of a given nucleus decaying per unit time. Its unit is s⁻¹ (or min⁻¹, year⁻¹ depending on the context).
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