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

(d) `A = A_0 ((1)/(2))^n rArr 30 = 240 ((1)/(2))^n rArr ((1)/(2))^3 = ((1)/(2))^n`
`rArr n = 3`
`:. (t)/(T_(1//2)) = 3 rArr T_(1//2) = (t)/(3) = (1)/(3) hr = 30 min`.