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

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7 months ago

$A = - \frac{d N}{d t} = λ N = λ N_{0} e^{- λ t} \Rightarrow λ \frac{N_{0}}{16} = λ N_{0} e^{- 80 λ} \Rightarrow \frac{1}{16} = e^{- 80 λ} \Rightarrow \frac{1}{16} = e^{- 80 λ}$

$\Rightarrow 80 λ = l n (16) = 4 l n (2) \Rightarrow t_{\frac{1}{2}} = \frac{l n (2)}{λ} = \frac{80}{4} = 20 d a y s$

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