The half-life of a certain radioactive isotope is `32 h`. What fraction of a sample would remain after `16h`?

Options

A. `0.25`
B. `0.71`
C. `0.29`
D. `0.75`

Answer

B

Explanation

The radioactive decay constant `lambda` is given by
`lambda =In(2)/(T_(1//2)) =(0.693)/(32 h^(-1))`
From the equation `N=N_(0) e^(-lambda t)` , the fraction of a sample reamaining after `16 h` is given by
`(N)/(N_(0)) =e^(- lambda t)=e^(-((0.693)/(32)) =e^(-0.3465)=0.71`.