The mean lives of a radioactive substance are 1620 years and 405 years for `alpha` emission and `beta` emission respectively. Find out the time during which three fourth of a sample will decay if it is decaying both by `alpha`-emission and `beta`-emission simultaneously. `(log_e4=1.386).`

Answer

9

Explanation

Total decay constant, `lambda=lambda_(alpha)+lambda_(beta)=(1)/(324)` per year.
As `N=(N_(0))/(4)` we have `(N_(0))/(4)=N_(0)e^(-lambda t)rArr e^(-lambda t)=4`
`t=(2)/(lambda) log_(e) 2~~450= 50xx9` year.