First slide

Radioactivity - Nuclei

Question

The activity of a radioactive substance drops to 1 / 32 of its initial value in 7.5h. Find the half-life (in hours).

Moderate

Solution

$\begin{array}{l} \frac{A}{A_{0}} = {(\frac{1}{2})}^{t / T} \\ \Rightarrow \frac{1}{32} = {(\frac{1}{2})}^{7.5 / T} \\ \Rightarrow {(\frac{1}{2})}^{5} = {(\frac{1}{2})}^{7.5 / T} \\ \Rightarrow 5 = \frac{7.5}{T} \\ \Rightarrow T = 1.5 hours \end{array}$

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