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Half lives of two radioactive nuclei A a...

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:

A

`1:8`

B

`3:8`

C

`8:1`

D

`9:8`

Text Solution

Verified by Experts

The correct Answer is:
D
Let initially, there are n nuclei of each type.
`n_(A)=n e^(-(t/(t_(1//2)))ln2)= n e^(-(tln2)/10),n_(B)=n e^((-tln2)/20)`
At `t=60` minutes, `n_(A)=n/(2^(6))` and `n_(B)=2/(2^(3))`
Ratio of decayed numbers `=(n-n_(A))/(n-n_(B))=(n-n/(2^(6)))/(n-n/(2^(3)))=(9/8)`
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