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).`

Explanation

`lambda' = lambda_(alpha) + lambda_(beta)`
`= (1)/(bar(T_(alpha)))+(1)/(bar(T_(beta))) = (1)/(1620)+(1)/(405) = (5)/(1620)year^(-1)`
`3//4th` sample will decay i.e. remaining `1//4`th
`N = N_(0)((1)/(2))^(n)`
`(N_(0))/(4) = N_(0)((1)/(2))^(n) rArr n = 2`
`t = nT_(1//2) = n(ln2)/(lambda)`
`= 2xx(0.693)/(5//1620)`
`= 449` year