The mean lives of a radioactive substance are 1620 years and 405 years of `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.

Explanation

For succiessive `alpha, beta`-emission
`K_("avg") = K_(alpha) + K_(beta) = (1)/(1620) + (1)/(405) = (5)/(1620) "years"^(-1)`
Given at `t = t`, `N = 1//4 N_(0)` (since `3//4` part decays)
`t = (2.303)/(K_("avg")) "log" (N_(0))/(N)`
`= (2.303 xx 1620)/(5) "log" 4 = 449.24` years