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13.Nuclei
medium
A radioactive substance decays to $\left(\frac{1}{16}\right)^{t h}$ of its initial activity in $80\, days.$ The half life of the radioactive substance expressed in days is ... .
A
$20$
B
$200$
C
$2$
D
$4$
(JEE MAIN-2021)
Solution
$N_{o} \stackrel{t_{\frac{1}{2}}}{\longrightarrow} \frac{N_{o}}{2} \stackrel{t_{\frac{1}{2}}}{\longrightarrow} \frac{N_{o}}{4} \stackrel{t_{\frac{1}{2}}}{\longrightarrow} \frac{N_{o}}{8} \stackrel{t_{\frac{1}{2}}}{\longrightarrow} \frac{N_{o}}{16}$
$4 \times t_{1 / 2}=80$
$t_{1 / 2}=20 \text { days }$
Standard 12
Physics
