Question

# Two radioactive sources A and B initially contain equal number of radioactive atoms. Source A has a half-life of 1 hour and source B has a half-life of 2 hours. At the end of 2 hours, the ratio of the rate of disintegration of A to that of B is :

A
1:2
B
2:1
C
1:1
D
1:4
Solution
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#### Two radioactive nuclei X and Y initially contain equal number of atoms. The half life is 1 hour and 2 hours respectively. Calculate the radio of their rates of disintegration after two hours.Given, nucleii X and Y contain equal number of atoms.Half-life of X, T1=1hrHalf-life of Y, T2=2hrRadio of radioactive sample of X left after 2 hours,N1=(12)2/1N0=14N0Radio of radioactive sample of Y left after 2 hours,N2=(12)2/2N0=12N0Now, decay rate is given by,R=λN=0.693NT1/2⇒R∝NT1/2R1R2=(T1/2)2(T1/2)1×N1N2i.e., =21×N04N02=1

2
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