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:

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Answer & Solution

Correct Answer

(B) \({y}\) - will decay faster than \({x}\).

Step-by-step Solution

Detailed explanation

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

\(\Rightarrow \frac{\ell n 2}{\lambda_{x}}=\frac{1}{\lambda_{y}} \Rightarrow \lambda_{x}=0.693 \lambda_{y}\)

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 \({x}\)

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