What is the half-life (in years) period of a | vedclass

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Question

$A=A_{0} e^{-\lambda t}$

$-\lambda t =\ln \left(\frac{ A }{ A _{0}}ight)$

$-\frac{\ln 2}{ t _{1 / 2}} 	imes 30=\ln \left(\frac{1}{16}ight)$

Vedclass · Accepted Answer

$7.5$

Vedclass · Answer

$A=A_{0} e^{-\lambda t}$

$-\lambda t =\ln \left(\frac{ A }{ A _{0}}ight)$

$-\frac{\ln 2}{ t _{1 / 2}} 	imes 30=\ln \left(\frac{1}{16}ight)$

$-\frac{\ln 2}{t_{1 / 2}} 	imes 30=-4 \ln 2$

$t _{1 / 2}=\frac{30}{4}=7.5\,yrs$

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?

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