The half-life period of a radioactive element X is same as the mean lifetime of another radioactive element Y . Initially they have the same number of - Physics MCQ AIEEE 2007 2026 | ExamTest.live

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The half-life period of a radioactive element X is same as the mean lifetime of another radioactive element Y . Initially they have the same number of atoms. Then:

Solution & Step-by-step Explanation

Given: (t_{1/2})_{X} = (τ)_{Y} .We know: (t_{1/2})_{X} = \frac{ln 2}{λ _{X}} (τ)_{Y} = \frac{1}{λ _{Y}} Therefore, \frac{l n 2}{λ _{X}} = \frac{1}{λ _{Y}} ⟹ λ_{Y} = \frac{λ _{X}}{l n 2} .Since ln 2 \approx 0.693, we have λ_{Y} = \frac{λ _{X}}{0.693} \approx 1.44 λ_{X} .This means λ_{Y} > λ_{X} .The decay rate is given by R = λ N . Since λ_{Y} > λ_{X} and initially N_{X} = N_{Y}, element Y decays faster initially.

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The half-life period of a radioactive element X is same as the mean lifetime of another radioactive element Y . Initially they have the same number of atoms. Then:

X will decay faster than Y

Y will decay faster than X

X and Y have same decay rate initially

X and Y decay at same rate always

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