Nuclear physics

What nuclear physics covers

The evidence for a small, massive nucleus, then radioactive decay, nuclear size and density, binding energy, and the two ways of releasing energy from nuclei. It reuses the exponential mathematics from capacitance and the inverse-square law from fields. AQA's required practical 12 on gamma radiation is examined here.

The main ideas

• The alpha scattering results, and the argument from them to a nucleus that is small, massive and positive.
• Alpha, beta and gamma identified by absorption, with their compositions, ranges, hazards and uses, and the inverse-square law for gamma.
• Decay as a random process, activity and the decay constant, the exponential law, and half-life from a decay curve or a log graph.
• Predicting a decay mode from a nuclide's place on the neutron against proton graph, and writing balanced decay equations.
• Nuclear radius from closest approach and from electron diffraction, and the cube-root law that makes nuclear density the same for every nucleus.
• Mass difference, binding energy, binding energy per nucleon and the shape of its curve.
• Induced fission, the chain reaction and critical mass, then the moderator, control rods, coolant and the safety case of a reactor.

Key equations

A = λN$A = \lambda N$A = λN

activity from the decay constant and the number of nuclei

N = N₀e^-λt$N = N_{0}e^{-\lambda t}$N = N_0e^(-λt)

the decay law, in nuclei, activity or corrected count rate

half-life = (ln 2)/λ$\text{half-life} = (\text{ln}\,2)/\lambda$half-life = (ln 2)/λ

converting between half-life and decay constant

R = R₀A^1/3$R = R_{0}A^{1/3}$R = R_0A^(1/3)

nuclear radius from nucleon number

E = mc²      1 u = 931.5 MeV$E = mc^{2} \qquad 1 \text{ u} = 931.5 \text{ MeV}$E = mc^2 1 u = 931.5 MeV

converting a mass difference into an energy

I = kx²$I = \frac{k}{x^2}$I = k/x^2

the inverse-square law for a gamma source

Every equation the nuclear physics notes display is collected, with its conditions, on the nuclear physics equations page.

Common errors

• A half-life has to be converted to a decay constant first, and it must be in seconds if the activity is to come out in becquerels.
• A mass in grams has to become a number of nuclei through the molar mass and the Avogadro constant before A = lambda N can be used.
• Binding energy is the energy to separate a nucleus into nucleons, and the mass difference is the parts minus the whole. Energy is released when the products sit higher on the binding energy per nucleon curve, which is why fission suits heavy nuclei and fusion light ones.
• Background count rate must be subtracted from every reading before an inverse-square check, since the background does not fall with distance.

Suggested order

Rutherford scattering first for the evidence, then alpha, beta and gamma radiation. Radioactive decay and the decay constant comes next, with half-life and nuclear instability straight after, since half-life follows directly from the decay constant. Nuclear radius next, then binding energy, which fission and fusion both depend on. Reactors last, since that lesson is mostly description.