A radioactive nucleus can decay in two different processes with half life 0.7 hr and 0.3 hr .
The

Options

A. 14
B. 18
C. 24
D. 26

Answer

B

Explanation

Key Idea If a radioactive sample has more than one radioactive material then the effective half life.
`(1)/(T_("eff" T//2))=(1)/(T_(1 1/2))+(1)/(T_(2 1/2))+(1)/(T_(3 1//3))+...`
Where, `T_(n 1/2)=` half life of `n^(th)` material.
Here, effective half life of the net material,
`T_("eff" 1/2)=(0.7xx0.3)/(0.7+0.3)=0.21 hr` `( :. T_(1 1/2)+0.7 hr, T_(2 1/2)=0.3 hr)`
As we know, `T_(1//2)=0.693 tau_("aveg. mean life")`
`rArr tau_("aveg. mean life")=(T_("eff" 1/2))/(0.693)`
`=(0.21)/(0.693)=0.3 hr`.
`rArr tau_("aveg. mean life")=0.3xx60=18` min.
Hence, the correct option is (b).