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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

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The half life period of radioactive element x is same ....

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 and y have same decay rate initially and later on different decay rate.
(B) x and y decay at the same rate always.
(C) x will decay faster than y.
(D) y will decay faster than x.

Solution

Given, ${({t_{1/2}})_x} = {({t_{mean}})_y}$

$\therefore \frac{{0.693}}{{{\lambda _x}}} = \frac{1}{{{\lambda _y}}}$

$ \Rightarrow {\lambda _x} = 0.693{\lambda _y}$

$ \Rightarrow {\lambda _x} < {\lambda _y}$

If N is same, $A \propto \lambda $

$\therefore A_x < A_y $

Answer: (D)