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)/(2 sqrt(2))`
C. `(1)/(sqrt(2))`
D. `sqrt(2 ) - 1`

Answer

c

Explanation

`(0.693)/(t_(1//2)) = (2.303)/(t) log ((N_(0))/(N))`
`(2.303 xx log 2)/(t_(1//2)) = (2.303)/((t_(1//2)//2)) log_(10) ((N_(0))/(N))`
`log_(10) (2^(1//2)) = log_(10) ((N_(0))/(N))`
`((N)/(N_(0))) = (1)/(sqrt(2))`