The half-life of a radioactive element A is t | vedclass

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(D) Given: $(T_{1/2})_A = (	au)_B$, where $	au$ is the mean life.We know that $T_{1/2} = \frac{0.693}{\lambda}$ and $	au = \frac{1}{\lambda}$.There

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$B$ will decay at a faster rate than $A.$

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(D) Given: $(T_{1/2})_A = (	au)_B$, where $	au$ is the mean life.We know that $T_{1/2} = \frac{0.693}{\lambda}$ and $	au = \frac{1}{\lambda}$.Therefore, $\frac{0.693}{\lambda_A} = \frac{1}{\lambda_B}$.This implies $\lambda_A = 0.693 \lambda_B$, which means $\lambda_A The rate of decay is given by $R = \lambda N$.Initially, the number of atoms $N$ is the same for both elements.Since $\lambda_B > \lambda_A$, the decay rate $R_B = \lambda_B N$ will be greater than $R_A = \lambda_A N$.Thus, $B$ will decay at a faster rate than $A$.

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially, both substances have the same number of atoms, then

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