10. 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 :
Select the correct option:
A
x–will decay faster than y.
B
y– will decay faster than x.
C
x and y have same decay rate initially and later on different decay rate.
D
xand y decay at the same rate always.
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$
\left(t_{1 / 2}\right)_x=(\tau)_y \Rightarrow \frac{\Rightarrow_x}{\lambda_x}=\frac{1}{\lambda_y} \Rightarrow \lambda_x=0.693 \lambda_y
$$
Also initially $\mathrm{N}_{\mathrm{x}}=\mathrm{N}_{\mathrm{y}}=\mathrm{N}_0$
Activity $\mathrm{A}=\lambda \mathrm{N}$
As $\lambda_x<\lambda_y \Rightarrow \mathrm{~A}_x<\mathrm{A}_y$
$\Rightarrow \mathrm{y}$ will decay faster than x
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