Edexcel A-Level Physics Half-Life and Decay Equations

Practise Edexcel A-Level Physics half-life and radioactive decay equations by calculating activity, decay constant, nuclei number and time.

Exam points

use λ = ln2/t½ with A = λN to calculate activity, nuclei number or decay constant
solve A = A0e^-λt or N = N0e^-λt problems for time, activity or original atoms
determine half-life or λ from decay graphs and assess activity-age claims

[Maximum number: 4]

Actinium-225 is a radioactive isotope. It decays to francium by emitting alpha particles. Actinium-225 has a short half-life, which makes it suitable for medical applications.

The activity of a sample of actinium-225 is 7.4 × 10^7 Bq when it is prepared.

Calculate the number of actinium atoms in the sample 7.0 days later.
half-life of actinium-225 = 9.9 days

Number of actinium atoms after 7.0 days =

$\lambda=\ln2/(9.9\times24\times3600)=8.10\times10^{-7}\,\mathrm{s^{-1}}$ . Initially $N_0=A_0/\lambda=(7.4\times10^7)/(8.10\times10^{-7})=9.13\times10^{13}$ . After 7.0 days, $N=N_0e^{-\lambda t}=9.13\times10^{13}e^{-(8.10\times10^{-7})(7.0\times24\times3600)}=5.59\times10^{13}$ , about $5.6\times10^{13}$ .

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5.4.142 - Half-life and radioactive decay equations question 1