Question

A radioactive substance X decays into another radioactive substance Y. Initially, only X was present. ${\lambda }_x$ and ${\lambda }_y$ are the disintegration constants of X and Y. $N_y$ will be maximum when($N_y$ is atoms of $Y$)

• A. $\frac{N_y}{N_x-N_y}=\frac{{\lambda }_y}{{\lambda }_x-{\lambda }_y}$
• B. $\frac{N_x}{N_x-N_y}=\frac{{\lambda }_x}{{\lambda }_x-{\lambda }_y}$
• C. ${\lambda }_y{N}_y={\lambda }_x{N}_x$
• D. ${\lambda }_y{N}_x={\lambda }_x{N}_y$

Answer 1

Answer: (C)

${\lambda }_y{N}_y={\lambda }_x{N}_x$

Considering first order decay:
$\frac{d{N}_x}{dt}=-{\lambda }_x{N}_x$
$\frac{d{N}_y}{dt}=-\frac{d{N}_x}{dt}-{\lambda }_y{N}_y$

$N_y$ becomes const.

Hence $\frac{d{N}_y}{dt}=0$
${\lambda }_x{N}_x-{\lambda }_y{N}_y=0$
${\lambda }_x{N}_x={\lambda }_y{N}_y$