CAIE A-Level Physics 23.2.5 Half-Life and Decay Constant

Practise converting between half-life and decay constant with λ = ln 2/t₁/₂, then interpreting the corresponding radioactive-decay behaviour.

Exam points

use λ = 0.693 / t½ to calculate decay constant or half-life
rearrange the half-life relationship and use consistent time units

[Maximum number: 2]

Show that the decay constant $\lambda$ is related to the half-life $t_{\frac{1}{2}}$ of a radioactive isotope by the expression

\lambda t_{\frac{1}{2}}=\ln 2

$A=A_{0} \mathrm{e}^{-\lambda t}$

after one half-life, $1 / 2 A_{0}=A_{0} \mathrm{e}^{-\lambda t 1 / 2}$

M1

$\frac{1}{2}=\exp \left(-\lambda t_{\frac{1}{2}}\right)$ and hence taking logs, $\ln 2=\lambda t_{\frac{1}{2}}$

A1

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23.2.5—Λ = 0.693 / t 1/2 question 1