The fraction of a radioactive material which reamins active after time t is `9//16`. The fraction which remains active after time `t//2` will be .

Options

A. `3/4`
B. `7/8`
C. `4/5`
D. `3/5`

Answer

A

Explanation

`N=N_0 e^(- lamda t)`
` ((N)/(N_0))=e^(-lamda t)`
`(9)/(16 ) = e ^(-lamda t)`
` (N )/(N_0 )= e^(- lamda t //2 )`
` (N )/(N_0 ) =e^(-lamda t //2)`
`(N )/(N_0 ) =((9 )/(16 ))^(1/2) =3/4`