Question

An accident occurs in a laboratory in which a large amount of radioactive material with a known half life of 30 day becomes embedded on the floor walls etc. Tests show that the level of radiation is 32 times the permissible level of normal occupancy of the room. Assuming that the last statement is correct, after how many days the laboratory can be safety occupied after.

(1) 32 days 

(2) 100 days 

(3) 20 days 

(4) Lab can safety be reoccupied after an infinite time

Answer 1

Correct option : (2) 100 days

Explanation: 

Since the initial value of radiation is 32 times the permissible level we have to find t after which the activity drops to 1/32 of its initial value which implies that we must have

Since the half life is 20 days, the lab will be safe for use after 5 half–lives i.e., t = 20×5 = 100 days