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Two radioactive materials X1 and X2 have...

Two radioactive materials `X_1` and `X_2` have decay constants `10 lambda` and `lambda`, respectively. If initialy they have the same number of nuclei, then the ratio of the number of nuclei of `X_1` to that of `X_2` will be `1//e` after a time
(a) `1//10 lambda` (b) `1//11 lambda` (c) `11//10lambda` (d) `1//9lambda`

A

`(1)/(10 lambda)`

B

`(1)/(11 lambda)`

C

`(1)/(9 lambda)`

D

`(11)/(10 lambda)`

Text Solution

Verified by Experts

The correct Answer is:
C
`N_(1) = N_(o)e^(-10 lambda t), N_(2) = N_(o)e^(-lambdat) :. (N_(1))/(N_(2)) = (1)/(e^(9 lambdat))`
`:. (1)/(e ) = (1)/(e^(9 lambda t)) :. T = (1)/(9 lambda)`
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