A radioactive source is freshly prepared. It is found that it emits radiation of intensity which is 128 times the premissible safe level. The half life of this sample is 3 hours. Find the minimum time after which it would be possible to work safely with this radioactive source.

21 h

The correct answer is Option (2) - 21 h

The intensity of radiation emitted by a radioactive source -

$I_t=I_0\left(\frac{1}{2}\right)^{t/T_{1/2}}$

where,

$I_t$ = Intensity after time $t$

$I_0$ = Initial intensity

$T_{1/2}$ = half life of radioactive.

Given,

$I_0=128×I_{safe}$

$I_t=I_{safe}$ (Permissible safe level)

$T_{1/2}=3$ hours

$I_{safe}=128×I_{safe}\left(\frac{1}{2}\right)^{t/T_{1/2}}$

$⇒\frac{t}{T_{1/2}}=7$

$⇒t=7×3=21h$