1 mg of a radioactive substance starts decaying . How much substance will be left after 24 hours ? Half life is 8 hours.

Options

A. `(1)/(2)` mg
B. `(1)/(4)` mg
C. `(1)/(8)` mg
D. `(1)/(16)` mg

Answer

C

Explanation

`N_(t)=n_(0)((1)/(2))^(n)`
`[because t_(1//2)=8` hours, T=24 hours , `N_(0)` =1, `N_(t)implies]`
`T=t_(1//2)xxn`
`24=8xxn` or `n=(24)/(8)=3`
`therefore N_(t)=N_(0)((1)/(2))^(3)=1 ` mg `xx((1)/(2))^(3)=(1)/(8)` mg