Question

the radioactive nuclei X and Y initially contain equal number of atoms. Their half lives are 1 hour and 2 hour respectively. Compare he rate of their disintegration after two hours.

Answer 1

Half life of X = 1 hour

Half life of Y = 2 hours

Ratio of X left after 2 hr,

N1 = [ 1 / 2 ] ^ 2/1 No = 1 / 4 No

Ratio of Y left after 2 hr,

N2 = [ 1 / 2 ] ^ 2/2 No = 1 / 2 No

Then, decay rate will be :

R = N = 0.693 / T1/2

R1 / R2 = [ T1/2 ] 2 / [ T1/2 ]1   x N1 / N2

            = 2 / 1  x  No / 4  /  No / 2

               = 1

The activity will be equal after 2 hours.