Question 213: Atoms & Nuclei

Question

A radioactive nucleus decays by two different
processes. The half life for the first process is
10 s and that for the second is 100 s. The
effective half life of the nucleus is close to :

Accepted Answer

T
1
= 10 sec
$$\lambda $$
1
= $${{\ln 2} \over {{T_1}}}$$
T
2
= 100 sec
$$\lambda $$
2
= $${{\ln 2} \over {{T_2}}}$$
$$\lambda $$
eq
= $${{\ln 2} \over {{T_{eq}}}}$$
We know,
$$\lambda $$
eq
= $$\lambda $$
1
+ $$\lambda $$
2
$$ \Rightarrow $$ $${{\ln 2} \over {{T_{eq}}}}$$ = $${{\ln 2} \over {{T_1}}}$$ + $${{\ln 2} \over {{T_2}}}$$
$$ \Rightarrow $$ $${1 \over {{T_{eq}}}}$$ = $${1 \over {10}} + {1 \over {100}}$$
$$ \Rightarrow $$ T
eq
= $${{100} \over {11}}$$ = 9 sec

Answer

12 sec

Answer

9 sec

Answer

55 sec

Answer

6 sec

Atoms & Nuclei

A radioactive nucleus decays by two different processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is close to :

Choose the correct answer: