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`
Text Solution
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The correct Answer is:
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
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