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13.Nuclei
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There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$
A
$2 : 1$
B
$1 : 2$
C
$e$
D
$e^{-1}$
Solution
Probability of getting $\alpha$ and $\beta$ particles is directly proportional to the rate of decay
$\frac{d N}{d t}=\lambda N$
$\Rightarrow \frac{P_{A}}{P_{B}}=\frac{\lambda_{A} N_{A}}{\lambda_{B} N_{B}}$
$\Rightarrow \frac{\lambda_{A} N_{A}}{\lambda_{B} N_{B}}=1$
$\Rightarrow \frac{N_{A}}{N_{B}}=\frac{\lambda_{B}}{\lambda_{A}}$
$\Rightarrow \frac{N_{A}}{N_{B}}=\frac{2}{1}$
Standard 12
Physics
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