Question

There are two radio nuclei A and B. A is an alpha emitter and B a beta emitter. Their disintegration constants are in the ratio of 1 : 2. What should be the ratio of number of atoms of A and B at any time t so that probabilities of getting alpha and beta particles are same at that instant?

• A. 2 : 1
• B. 1 : 2
  
• C. e
  
• D. $e^{-1}$

Answer 1

The disintegration constants are in the ratio of 1 : 2.

So, $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{2}$

Probabilities of getting $\alpha$ and $\beta$ - particles are same. Thus, rate of disintegration are equal.

$\therefore {\lambda }_A{N}_A={\lambda }_B{N}_{B}or\frac{N_A}{N_B}=\frac{{\lambda }_B}{{\lambda }_A}=2:1$

Thus, the correct option is (A) 2:1