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.
Answer & explanation
Correct answer: option 2
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
$I_{safe}=128×I_{safe}\left(\frac{1}{2}\right)^{t/T_{1/2}}$
$⇒\frac{t}{T_{1/2}}=7$
$⇒t=7×3=21h$