A freshly prepared radioactive source of half-life 2h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is
The intensity of radiation emitted by radioactive source also decreases with time. Half-life of the given material is 2 hours. Let the radiation starts at t=0. Initial intensity of radiation is 64 times the safe intensity level.
At t=2 hour, the intensity of radiation will be half (due to half-life) which is now 32 times the safe intensity level.
At t=4 hour, the intensity of radiation will be 16 times the safe level.
Doing this, t=6 h 
8 times; t=8 h 
4 times; t=10 h 
2 times and t=12 h 
1 times the safe intensity level. In other words, 
and thus the time will be 6*2 hour= 12 hour. Therefore, the minimum time is 12 hours after which the intensity of radiation is equal to the permissible safe level and we can work safely with the material.