First slide

Radioactivity - Nuclei

Question

The activity of a radioactive sample falls from 700 $s^{- 1}$ to 500 $s^{- 1}$ in 30 minute. Its half-life is close to:

Moderate

A

66
B

62
C

52
D

72

Solution

$\begin{array}{l} A c t i v i t y, A = A_{0} e^{- λ t} \\ \Rightarrow \frac{A_{0}}{A} = e^{λ t} \\ \Rightarrow \ln [\frac{Α_{0}}{A}] = λ t \\ \Rightarrow \ln [\frac{700}{500}] = (\frac{\ln 2}{t_{1 / 2}}) (30 \min) \\ \Rightarrow \frac{\ln 2}{\ln (7 / 5)} = \frac{t_{1 / 2}}{(30 \min)} \\ \Rightarrow t_{1 / 2} = (2.06004) 30 = 61.8 \min ≃ 62 m i n \end{array}$

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