The fraction of the initial number of radioactive nuclei which remain undercayed after half of a half-life of the radioactive sample is

Options

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

Answer

D

Explanation

`N_(0)` is the initial number of radioactive nuclei and N is the number of nuclei remain undecayed.
Thus,`(N)/(N_(0))=((1)/(2))^(n)`
Where n is the number of half lives
As `n=(t)/(T_(1//2))=((1)/(2)T_(1//2))/(T_(1//2))=(1)/(2)`
`therefore (N)/(N_(0))=((1)/(2))^(1//2)=(1)/(sqrt(2))`