The half-life period of a radioactive element | vedclass

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Question

(C) According to the question,the half-life of $X$ is equal to the mean life of $Y$.$T_{1/2}(X) = 	au_{av}(Y)$Using the relations $T_{1/2} = \frac{0.

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$Y$ will decay faster than $X$.

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(C) According to the question,the half-life of $X$ is equal to the mean life of $Y$.$T_{1/2}(X) = 	au_{av}(Y)$Using the relations $T_{1/2} = \frac{0.693}{\lambda}$ and $	au_{av} = \frac{1}{\lambda}$,we get:$\frac{0.693}{\lambda_X} = \frac{1}{\lambda_Y}$$\lambda_X = 0.693 \cdot \lambda_Y$Since $0.693 The rate of decay is given by $R = \lambda N$.Since both elements have the same number of atoms $N$ initially,the element with the larger decay constant $\lambda$ will have a higher decay rate.Therefore,$Y$ will decay faster 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,they have the same number of atoms. Then:

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