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(D) The mean life $(T)$ is given by $T = 1/\lambda = 100 \, 	ext{s}$.The half-life $(T_{1/2})$ is related to the decay constant $(\lambda)$ by the fo

Vedclass · Accepted Answer

$1.155$

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(D) The mean life $(T)$ is given by $T = 1/\lambda = 100 \, 	ext{s}$.The half-life $(T_{1/2})$ is related to the decay constant $(\lambda)$ by the formula $T_{1/2} = \frac{\ln(2)}{\lambda} \approx \frac{0.693}{\lambda}$.Substituting $\lambda = 1/T$,we get $T_{1/2} = 0.693 	imes T$.Given $T = 100 \, 	ext{s}$,the half-life in seconds is $T_{1/2} = 0.693 	imes 100 = 69.3 \, 	ext{s}$.To convert the half-life into minutes,divide by $60$:$T_{1/2} = \frac{69.3}{60} \, 	ext{min} = 1.155 \, 	ext{min}$.

Mean life of a radioactive sample is $100$ seconds. Then its half-life (in minutes) is

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