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Question

# Two radioactive substances X and Y initially contain an equal number of atoms. Their half-lives are 1 hour and 2 hours respectively. Then the ratio of their rates of disintegration after two hours is.

A
1:1
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B
2:1
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C
1:2
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D
2:3
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Solution

## The correct option is A 1:1Their disintegration constant will be in ratio of λ1λ2=t2t1=21=2, t1 t2 are their half lives.If their initial number of atoms are N0 then after 2 hour so for first sample is will be 2 half lives so remaining atoms N1=N022And for second sample is will be just 1 half life so remaining atoms N2=N021so their activity ratio after 2 houe will be A1A2=N1λ1N2λ2=1×22×1=11

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