# The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then : `
Question:

The half life period of radioactive element $x$ is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :

1. $x$-will decay faster than $y$.

2. $\mathrm{y}-$ will decay faster than $\mathrm{x}$.

3. $x$ and $y$ have same decay rate initially and later on different decay rate.

4. x and y decay at the same rate always.

Correct Option: , 2

Solution:

$\left(t_{1 / 2}\right)_{x}=(\tau)_{y}$

$\Rightarrow \frac{\ell \mathrm{n} 2}{\lambda_{\mathrm{x}}}=\frac{1}{\lambda_{\mathrm{y}}} \Rightarrow \lambda_{\mathrm{x}}=0.693 \lambda_{\mathrm{y}}$

Also initially $\mathrm{N}_{\mathrm{x}}=\mathrm{N}_{\mathrm{y}}=\mathrm{N}_{0}$

Activity $\mathrm{A}=\lambda \mathrm{N}$

As $\lambda_{x}<\lambda_{y} \Rightarrow A_{x}$\Rightarrow y$will decay faster than$\mathrm{x}\$

Option (2)
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