Half-life (in years) period of a radioactive material if its activity drops to 1 / 16^{text {th }} o

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13.Nuclei

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What is the half-life (in years) period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of its initial value of $30$ years?

A

$9.5$

B

$8.5$

C

$7.5$

D

$10.5$

(JEE MAIN-2022)

Solution

$A=A_{0} e^{-\lambda t}$

$-\lambda t =\ln \left(\frac{ A }{ A _{0}}\right)$

$-\frac{\ln 2}{ t _{1 / 2}} \times 30=\ln \left(\frac{1}{16}\right)$

$-\frac{\ln 2}{t_{1 / 2}} \times 30=-4 \ln 2$

$t _{1 / 2}=\frac{30}{4}=7.5\,yrs$

Standard 12

Physics

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