A counter gives a count of 320 counts/minute for a radioactive source . After 75 minutes, the counter shows a count rate of 40 counts/minute . What is the half life period of the source ?

Options

A. 15 min
B. 25 min
C. 35 min
D. 40 min

Answer

B

Explanation

Initial rate = 320 counts/ min.
Rate after 75 min. = 40 counts/min.
i.e. the activity of the element has become `40/320 = 1/8` of the original activity or `N_2/N_1 = 1/8`
using `N_2/N_1 = (1/2)^n , " we get" 1/8 = (1/2)^n = (1)/(2^n)`
`therefore (1)/(2^3) = (1)/(2^n) therefore n = 3 ` = No. of half lives
`because` Half life = `("Total time")/("No. of half lives")`
`therefore T = 75/3 = 25` min.