If the half lives of a radioactive element for `alpha` and `beta` decay are 4 year and 12 years respectively, then the percentage of the element that remains after 12 year will be

Options

A. `6.25%`
B. `12.5%`
C. `25%`
D. `50%`

Answer

A

Explanation

`T=(T_(alpha)T_(beta))/(T_(alpha)+T_(beta))=(4xx12)/(4+12)`
`n=(t)/(T)=(12)/(3)=4`
`(N)/(N_(0))=((1)/(2))^(n)=((1)/(2))^(4)=(1)/(16)=6.25%`