Mean lives of a radioactive substance are 1620 and 405 years for `alpha and beta` -emission respectively. If `alpha and beta` decays are simultaneous, then time during which three fourth of the sample will decay is :

Options

A. 410 years
B. 442 years
C. 449 years
D. 512 years

Answer

C

Explanation

`tau=(T_(1)T_(2))/(T_(1)+T_(2))=324 years`
Also half-life period
`T=0.93 tau=0.693 xx 324"years"`
But `N/N_(0)=(1/2)^(l/T)`
`1/R=(1/2)^(t//T) rArr (1/2)^(2) =(1/2)^(t//T) therefore t/t=2`
`t=2T=2 xx 0.693 xx 324=449"years"`