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

Options

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

Answer

D

Explanation

`T_(1//2)= 1600 yr, t= 4T_(1//2)= 6400 yr`
Number of nuclei remaining
`N= (N_(0))/((2)^(n)) = (N_(0))/((2)^(4)) = (N_(0))/(16)`
Fraction `= (N)/(N_(0))= (1)/(16)`