If `T` is the half-life of a radioactive material, then the fraction that would remain after a time `(T)/(2)` is

Options

A. `(1)/(2)`
B. `(3)/(4)`
C. `(1)/(sqrt2)`
D. `(sqrt2 - 1)/(sqrt2)`

Answer

C

Explanation

Fraction remains after n half lives
`(N)/(N_(0)) = ((1)/(2))^(n) = ((1)/(2))^(1//T)`
`therefore (N)/(N_(0)) = ((1)/(2))^((T//2)/(T)) = ((1)/(2))^(1//2) = (1)/(sqrt2)`