Question

A radiacative moterial docays by simulataneous emission of two particle from the with respective half - lives `1620` and `810` year . The time , in year , after which one - fourth of the material remins is
A. `1080`
B. `2430`
C. `3240`
D. `4860`

Answer 1

Correct Answer - A
`(-dN)/(dt) = lambda_(1) N + lambda_(2) N `
`rArr log_(e) (N)/(N_(0)) = - (lambda_(1) + (lambda_(1)(lambda_(2))t`
when `N_(0) `is intial number of atoms
`Here lambda_(1) = (0.693)/(1620)` and `lambda_(2) = (0.693)/(810)`
`(N)/(N_(0)) = (1)/(4) rArr log _(e) (1)/(4) = -((0.693 )/(1620) +(03.693)/(810)) t`
`rArr t = 1.1080` year