JEE Main · 2007 · 29 Apr 2007 · Offline · Modern Physics

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The half-life period of a radioactive element X is the 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✓ Correct
(C)X and Y have the same decay rate initially
(D)X and Y decay at the same rate always

Answer: (B)

Solution

The half-life of X equals the mean life of Y, so

\frac{l n 2}{λ _{X}} = \frac{1}{λ _{Y}}

, which rearranges to

λ_{X} = 0.693 λ_{Y}

. Thus Y has the larger decay constant. With the same initial number of atoms the initial activity

λ N

is greater for Y, so Y decays faster at the outset.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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