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Half-lives of two radioactive elements A...

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

A

`4:1`

B

`1:4`

C

`5:4`

D

`1:16`

Text Solution

Verified by Experts

The correct Answer is:
C
Number of decayed sample = `1 - N/(N_(0))`
Now , `(1-(N/(N_(0)))_(A))/(1-(N/(N_(0)))_(B))=(1-(1/2)^(t(T_(1//2))_(A)))/(1-(1/2)^(t//(T_(1//2))_(B)))`
`=(1-(1/2)^(80/20))/(1-(1/2)^(80/40))=(1-1/16)/(1-1/4)=5/4`
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