The half-life of radium is `1600 yr`. The fraction of a sample of radium that would remain after `6400 yr`

Options

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

Answer

D

Explanation

`t_(1//2)=1600 years, T=6400 years`
`:. n=(T)/(t_(1//2))=(6400)/(1600)=4`
`N=((1)/(2))^(n)N_(0)`
`=(N)/(N_(0))=((1)/(2))^(4)=(1)/(16)`