A count rate meter shows a count of `240` per minute from a given radioactive source. One hour later the meter shows a count rate of `30` per minute. The half-life of the source is.

Options

A. 120 min
B. 80 min
C. 30 min
D. 20 min

Answer

D

Explanation

`R= 30, R_(0)= 240`
`((R)/(R_(0)))= ((1)/(2))^(t//T_(1//2)) rArr (30)/(240) = ((1)/(2))^((1)/(T_(1//2)))`
`rArr 3= (1)/(T_(1//2)) rArr T_(1//2)= (1)/(3) hr rArr T_(1//2)= 20` min