The fraction of atoms of radioactive element that decays in 6 days is 7/8. the fraction that decays in 10 days will be

Options

A. `77//80`
B. `91//80`
C. `31//32`
D. `15//16`

Answer

C

Explanation

According to radioactigve decay law `N=N_(0)e^(-lambdat)`.
or `t=(ln(N_(0)//N))/(lambda) or `t=(T_(1//2)ln(N_(0)//N))/(ln2) or (N)/(N_(0))=(1)/(32)`
`therefore" Fraction that decays "=1-(1)/(32)=(31)/(32)`