There are two radionuclei A and B. A is an al | vedclass

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(A) The probability of getting $\alpha$ and $\beta$ particles is directly proportional to the rate of decay of the respective nuclei.The rate of decay

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$2 : 1$

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(A) The probability of getting $\alpha$ and $\beta$ particles is directly proportional to the rate of decay of the respective nuclei.The rate of decay is given by $\frac{dN}{dt} = \lambda N$.For the probabilities to be equal at $t = 0$,the rates of decay must be equal:$\lambda_A N_A = \lambda_B N_B$Rearranging the terms to find the ratio of the number of atoms:$\frac{N_A}{N_B} = \frac{\lambda_B}{\lambda_A}$Given that the ratio of disintegration constants is $\frac{\lambda_A}{\lambda_B} = \frac{1}{2}$,we have $\frac{\lambda_B}{\lambda_A} = \frac{2}{1}$.Therefore,$\frac{N_A}{N_B} = \frac{2}{1}$.

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