The radioactivity of a certain radioactive element drops to `1//64` of its initial value in `30` seconds. Its half-life is.

Options

A. 2 seconds
B. 4 seconds
C. 5 seconds
D. 6 seconds

Answer

C

Explanation

Since, `N = N_(0) ((1)/(2))^((t)/(T))`
`rArr (N_(0))/(64) = N_(0) ((1)/(2))^((30)/(T))`
`rArr ((1)/(2))^(6) = ((1)/(2))^((30)/(T)) rArr (30)/(T)= 6`
`rArr T=5` sec