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 disintergration after two hours is

Explanation

Let the samples P and Q have N radioactive nuclei initially.
Number of nuclei of P left undecayed after 1 hour `=N/2`
Number of nuclei of Q left undecayed after 2 hours.
`N/4`
Rate of decay of `R_(1) =0.693/1 xx N/4 = (0.693 N)/4`
Rate of decay of Q, `R_(2) = 0.693/2 xx N/2 = (0.693 N)/4`
Let `R_(1)` and `R_(2)` be rates of disintegration
`rArr R_(1)/R_(2)=1`