In a sample of radioactive material, what fraction of initial number of active nuclei will remain undistintegrated after half of a half0life of the sample?

Options

A. `(1)/(4)`
B. `(1)/(2sqrt(2))`
C. `(1)/(sqrt(2))`
D. `sqrt(2)-1`

Answer

C

Explanation

`N = N_(0) ((1)/(2))^(n)`
`t = nT_(1//2) rArr T_(1//2)//2 = nT_(1//2) rArr n = (1)/(2)`
`(N)/(N_(0)) = ((1)/(2))^(n) = ((1)/(2))^((1)/(2)) = (1)/(sqrt(2))`