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13.Nuclei
medium
The half-life period of a radio-active element $X$ is same as the mean life time of another radio-active element $Y$ Initially they have the same number of atoms. Then
A
$X$ and $Y$ have same decay rate initially
B
$X$ and $ Y$ decay at same rate always
C
$Y$ will decay faster than $X$
D
$X$ will decay faster than $Y$
(AIEEE-2007)
Solution
According to question,
Half life of $X, T_{1 / 2}=\tau_{\text {av }},$ average life of $Y$
$\Rightarrow \frac{0.693}{\lambda_{X}}=\frac{1}{\lambda_{Y}} \Rightarrow \lambda_{X}=(0.693) \cdot \lambda_{Y}$
$\therefore \lambda_{X}<\lambda_{Y}$
Now, the rate of decay is given by
$-\frac{d N}{d t}=\lambda N$
$Y$ will decay faster than $X .[\because N \text { is some }]$
Standard 12
Physics
