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Half-life of a radioactive substance A a...

Half-life of a radioactive substance` A` and `B` are, respectively, `20 min` and `40min`. Initially, the samples of `A` and `B` have equal number of nuclei. After `80 min`, the ratio of the ramaining number of `A` and `B` nuclei is

A

`1:16`

B

`4:1`

C

`1:4`

D

`1:1`

Text Solution

Verified by Experts

The correct Answer is:
C
According to question,
`(N_(0))_(A)=(N_(0))_(B)=N_(0)`
`(t_(1//2))_(A)=20` min
`(t_(1//2))_(B)=40` min
`T=80` min
`n to `no. of half lives
`T=n xx t_(1//2)`
`n_(A) = (80)/(20) =4`
`n_(B) = (80)/(40) =2`
`N=(N_(0))/(2^(n))`
`(N_(A))/(N_(B)) = (N_(0))/(2^(4)) xx (2^(2))/(N_(0)) =(1)/(4)`
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