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13.Nuclei
hard
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:
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
${x}$ and ${y}$ decay at the same rate always.
(JEE MAIN-2021)
Solution
$\left(t_{1 / 2}\right)_{x}=(\tau)_{y}$
$\Rightarrow \frac{\ell n 2}{\lambda_{x}}=\frac{1}{\lambda_{y}} \Rightarrow \lambda_{x}=0.693 \lambda_{y}$
Also initially ${N}_{{x}}={N}_{{y}}={N}_{0}$
Activity ${A}=\lambda {N}$
As $\lambda_{{x}}<\lambda_{{y}} \Rightarrow {A}_{{x}}<{A}_{{y}}$
$\Rightarrow {y}$ will decay faster than ${x}$
Standard 12
Physics
