Question

Two radioactive substances `A` and `B` have half lives of `T` and `2T` respectively. Samples of `a` and `b` contain equal number of nuclei initially. After a time `4T`, the ratio of the number of undecayed nuclei of `A` to the number of undeacyed nuclei of `B` is
A. `(1)/(10lambda)`
B. `(1)/(11lambda)`
C. `(11)/(10lambda)`
D. `(1)/(9lambda)`

Answer 1

Correct Answer - D
`N = N_(0)e^(-lambdat)`
`X_(1): N_(X_(1)) = N_(0)e^(-10 lambdat), X_(2): N_(X_(2)) = N_(0)e^(-lambdat)`
`(N_(X_(1)))/(N_(X_(2))) =e^(-9lambdat) rArr (1)/(9) = e^(-9lambda t) rArr e^(-1) = e^(-9lambdat)`
`9lambdat = 1 rArr t = (1)/(9lambda)`