A radioactive isotope has h half-life of 2 yr. how long will itt take the activity to reduce to 3.125% of its original value

Options

A. 4.8 years
B. 7 years
C. 10 years
D. 9.6 years

Answer

C

Explanation

Here, `T_(1//2)="2 years"`
Activity law, A=A_(0)e^(-lambdat)`
`or t=(1)/(lambda)ln((A_(0))/(A))=(T_(1//2))/(0.693)ln((100)/(3))" "(because lambda=(0.693)/(T_(1//2)))`
`=(2)/(0.693)ln((100)/(3))~~"10 years"`