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, (a) x and y have the 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

Answer 1

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.

So, $X_{\frac{1}{2} } = Y$

where $X_{\frac{1}{2} } =$half   life   for   x

           Y = mean life time of y

⇒ $\frac{ln 2}{k_{x}} = \frac{1}{k_{y}}$  

As ln 2 < 1,  $k_{y} > k_{x}$

Decay Constant (k) is proportional to decay rate. Hence y decays at a faster rate than x. So, correct option is C.

Answer 2

Therefore, y will decay at a faster rate than x .

Option (C) is correct.

Explanation:

The formula of half life period is given below:

(t 1/2)x = (t mean )y

or 0.693 / λ = 1 / λy

λx < λy

or Rate of decay=λN

Initially, number of atoms(N) of both are equal but since λy > λx.

Therefore, y will decay at a faster rate than x .