IB Physics Radioactive Decay & Half-Life: Your Questions Answered

It's tested across Papers 1, 2 and 3 as part of Topic 7. Expect multiple-choice questions on decay types and nuclear equations, calculation questions using the decay constant and half-life formula, and data-analysis questions where you read a decay graph or half-life from experimental count-rate data.

The core half-life and decay constant maths ($N=N_0{e}^{-\lambda t}$) is identical for SL and HL. HL students go further into nuclear binding energy, mass defect calculations and the physics behind alpha, beta and gamma emission at a level of detail SL doesn't require.

You need $A=A_0{e}^{-\lambda t}$ for activity, $N=N_0{e}^{-\lambda t}$ for undecayed nuclei, and the link between decay constant and half-life: $t_{1/2}=\frac{\ln 2}{\lambda }$. All three are on the IB Physics data booklet, so you don't need to memorise them — just know when to use each one.

Find the initial activity or count on the y-axis, then read across to find the time at which that value has halved. Repeat from that new point to check consistency — a genuine exponential decay gives you the same half-life value no matter which starting point you pick on the curve.

The decay constant ($\lambda$) is the probability per unit time that a given nucleus decays — a fixed property of the isotope. Half-life ($t_{1/2}$) is the time for half a sample to decay. They're mathematically linked but conceptually different: one's a rate, the other's a duration.

Not conceptually — the physics is straightforward once you accept decay is random and exponential. Where students lose marks is arithmetic: mixing up natural log and log base 10, or forgetting activity decreases exponentially, not linearly. Get comfortable with the exponential function on your calculator and this topic becomes one of the easier ones in Topic 7.

Three recurring reasons: using $\log$ instead of $\ln$ in the half-life formula, forgetting units (seconds vs years vs days must match the decay constant's units), and writing 'radioactive decay is affected by temperature or pressure' — it isn't, and examiners specifically flag this misconception in mark schemes.

That you can predict when a specific nucleus will decay. You can't — decay is genuinely random at the level of an individual atom. Half-life only works statistically, across huge numbers of nuclei. IB examiners regularly award marks for stating this randomness explicitly in extended-response answers.

Master the three data-booklet equations, practise rearranging them under time pressure, and get fast at reading count-rate graphs. Then go further: understand why decay is random at nucleus level but statistically predictable across a sample — that distinction is what separates a grade 6 answer from a grade 7 one in extended response questions.

Don't just memorise them — practise deriving $t_{1/2}=\frac{\ln 2}{\lambda }$ from $N=N_0{e}^{-\lambda t}$ yourself once, so you understand where it comes from. Then drill past-paper questions until the rearrangement is automatic. Topical worksheets on RevisionPrep group these by difficulty so you can build up speed systematically.

Prioritise questions that combine a decay graph with a calculation — that's the most common format across recent Physics papers. Also practise short-answer questions asking you to name the type of decay (alpha, beta-minus, beta-plus) from a nuclear equation, since that's a frequent easy-mark question students still get wrong.

IB Physics goes noticeably further than GCSE or IGCSE: your child will need to work with the exponential decay equation and natural logarithms, not just qualitative half-life graphs. If your child found GCSE physics manageable, the maths jump here is the main thing to prepare for, not the concepts themselves.

Yes — it connects directly to nuclear energy in Topic 8 (energy production), since fission and radioactive decay both rely on binding energy per nucleon. It also links to the exponential functions used in capacitor discharge (Topic 5), so understanding one genuinely reinforces the other.