A radioactive element emits `200` particle per second. After three hours `25` particle per second are emitted. The half-life period of element will be

Options

A. 50 minutes
B. 60 minutes
C. 70 minutes
D. 80 minutes

Answer

B

Explanation

(b) `R = (dN)/(dt) prop N rArr (R_2)/(R_1) = (N_2)/(N_1)`
But `(N_2)/(N_1) = ((1)/(2))^(t_1//2) rArr (25)/(200) = (1)/(8) = ((1)/(2))^3 rArr (t)/(t_(1//2)) = 3`
`:. t_(1//2) = (t)/(3) = (3)/(3) = 1 hour = 60` minutes.