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Nucleus: Common Terms

A radioactive...

Question

A radioactive substance decays to ${(\frac{1}{16})}^{t h}$ of its initial activity in $80$ days. The half life of the radioactive substance expressed in days is ______.

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Solution

$N_{0} t_{1 / 2} - - \to \frac{N_{0}}{2} t_{1 / 2} - - \to \frac{N_{0}}{4} t_{1 / 2} - - \to \frac{N_{0}}{8} t_{1 / 2} - - \to \frac{N_{0}}{16}$

$∴ 4 \times t_{1 / 2} = 80$

$\Rightarrow t_{1 / 2} = 20$ days

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