Question 230: Atoms & Nuclei

Question

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 :

Accepted Answer

Given, ($$	au$$
1/2
)
x
= ($$	au$$)
y
Here, $$	au$$
1/2
= half-life period of radioactive element and $$	au$$ = mean life period of radioactive element.
As we know the expression,
Half-life of the radioactive element x,
$${	au _{1/2}} = {{\ln (2)} \over {{\lambda _x}}}$$
Mean life of the radioactive element y,
$$	au  = {1 \over {{\lambda _y}}}$$
Substituting the values in Eq. (i), we get
$${{\ln 2} \over {{\lambda _x}}} = {1 \over {{\lambda _y}}} \Rightarrow {\lambda _x} = 0.693{\lambda _y}$$
Initially they have same number of atoms,
$${N_x} = {N_y} = {N_0}$$
As we know that,
Activity, $$A = \lambda N$$
As, $${\lambda _x} < {\lambda _y} \Rightarrow {A_x} < {A_y}$$
Therefore, y will decay faster than x.

Answer

x-will decay faster than y.

Answer

y-will decay faster than x.

Answer

x and y have same decay rate initially and later on different decay rate.

Answer

x and y decay at the same rate always.

Atoms & Nuclei

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 :

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