Atoms And Nuclei Question 386

Question: Two radioactive substances X and Y emit $ \alpha $ and $ \beta $ particles respectively. Their disintegration constants are in the ratio 2 : 3. To have equal probabilities of getting emission of $ \alpha $ and $ \beta $ particles, the ratio of number of atoms X to that of Fat any time instant is

Options:

A) 2 : 3

B) 3 : 2

C) e : 1

D) (e-1) : 1

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ N_{1}{\lambda_{1}}=N_{2}{\lambda_{2}}\frac{{\lambda_{1}}}{{\lambda_{2}}}=\frac{2}{3}\Rightarrow \frac{N_{2}}{N_{1}}=\frac{2}{3} $
    $ \Rightarrow $ ratio of no. of nuclei of X to that of $ Y=3/2 $


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