CAIE A-Level Physics 23.2.6 Exponential Radioactive Decay

Practise interpreting exponential radioactive decay and using x = x₀e^(−λt) to calculate activity, count rate, nuclei, half-life or decay constant.

Exam points

sketch and interpret exponential radioactive-decay relationships
use x = x₀e⁻λt to calculate activity, count rate or number of undecayed nuclei
determine half-life, decay constant or other quantities from decay data or graphs

[Maximum number: 2]

Fluorine-18 $\left({ }_{9}^{18} \mathrm{~F}\right)$ is a radioactive nuclide that is used as a tracer in positron emission tomography (PET scanning). Fluorine-18 decays to a nuclide of oxygen ( O ) according to

{ }_{9}^{18} \mathrm{~F} \longrightarrow{ }_{P}^{Q} \mathrm{X}+{ }_{8}^{R} \mathrm{O} \text {. }

The half-life of fluorine-18 is T.

A patient is injected with amount of substance n of fluorine-18.

On Fig. 9.1, sketch the variation with time t of R.

Fig. 9.1

sketch: exponential decay curve from t=0 to t=2 T, starting at ( $0, R_{0}$ ) and with a negative gradient of continuously
decreasing magnitude

B1

line with negative gradient passing through ( $T, R_{0} / 2$ ) and ( $2 T, R_{0} / 4$ )

B1

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23.2.6—The exponential nature of radioactive decay, and sketch and use the question 1