The half-life period of a radioactive element | vedclass

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(C) Given that the half-life of $X$ is equal to the mean life of $Y$: $({T_{1/2}})_X = ({	au})_Y$ We know that ${T_{1/2}} = \frac{0.693}{\lambda}$ an

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$Y$ will decay at a faster rate than $X$.

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(C) Given that the half-life of $X$ is equal to the mean life of $Y$: $({T_{1/2}})_X = ({	au})_Y$ We know that ${T_{1/2}} = \frac{0.693}{\lambda}$ and ${	au} = \frac{1}{\lambda}$. Substituting these,we get: $\frac{0.693}{\lambda_X} = \frac{1}{\lambda_Y}$ $\Rightarrow \lambda_X = 0.693 \lambda_Y$ Since $0.693 The rate of decay is given by $R = \lambda N$. Initially,the number of atoms $N$ is the same for both. Since $\lambda_Y > \lambda_X$,the decay rate $R_Y = \lambda_Y N$ will be greater than $R_X = \lambda_X N$. Therefore,$Y$ will decay at a faster rate than $X$.

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

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