First slide

Radio activity

Question

The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

Moderate

A

X and Y havethe same decay rate initially
B

X and Y decay at the same rate always
C

Y will decay at a faster rate than X
D

X will decay at a faster rate than Y

Solution

${(T_{1 / 2})}_{x} = {(t_{mean})}_{y} \Rightarrow \frac{0.693}{λ_{x}} = \frac{1}{λ_{y}} \Rightarrow λ_{x} = 0.693 λ_{y} or λ_{x} < λ_{y}$
Also rate of decay = $λN$
Initially number of atoms (N) of both are equal but
since $λ_{y} > λ_{x},$ therefore, y will decay at a faster rate than x.

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