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Question

# The radioactive sources A and B with half lives of t hr and 2t hr respectively, initially contains the same number of radioactive atoms. At the end of t hours, their rates of disintegration are in the ratio :

A
4:1
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B
2:1
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C
2:1
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D
1:1
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Solution

## The correct option is C √2:1A=t1/2=t hourλ1B=t1/2=2t hourλ2At t=0 number of nuclei=NoAt t=0number of nuclei=Nonuclei of A left after time tNuclei of B left after time t(t=t1/2)=N02=N0e−λ2tRate of disintegration of =N0e−ln22tA=λ1N02=N0eln⎛⎝12⎞⎠12=ln 2tN02=N0√2Rate of disintegration of B=λ2N0√2=ln 22tN0√2 Ratio of rate of disintegration of A & B =ln 2tN02ln22lN0√2=√21

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