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Decay constant of two radioactive sample...

Decay constant of two radioactive samples is `lambda` and `3lambda` respectively. At `t = 0` they have equal number of active nuclei. Calculate ` t`, when will be the ratio of active nuclei becomes `e : 1`.

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The correct Answer is:
`1//2lambda`
`N_(1)=N_(01)e^(-lambdat)` and `N_(2)=N_(02) e^(-3lambdat)`
`N_(1)/N_(2)=(N_(01) e^(-lambdat))/(N_(02)e^(-3lambdat))=e^(2lambdat)=e^(2 lambdat) [ :' N_(01)=N_(02)` for `N_(1)/N_(2)=e/1]`
`:. 1=2 lambdatimplies t=1/(2 lambda)`
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