For a certain radioactive process graph between In, {R} and {t},({sec}) is obtained as shown in figu

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13.Nuclei

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For a certain radioactive process the graph between $In\, {R}$ and ${t}\,({sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately $....\,{sec}.$

A

$6.93$

B

$4.62$

C

$2.62$

D

$9.15$

(JEE MAIN-2021)

Solution

${R}=R_{o} e^{-\lambda t}$

$\ell n R=\ell n R_{o}-\lambda t$

$-\lambda$ is slope of straight line

$\lambda=\frac{3}{20}$

$t_{1 / 2}=\frac{\ell n 2}{\lambda}=4.62$

Standard 12

Physics

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