b

$\text{Momentum of Particle X }P_x = \frac{h}{\lambda_x}$

$\text{Momentum of Particle Y }P_y = \frac{h}{\lambda_y}$

$\text{Momentum after collision }P = \frac{h}{\lambda} =P_x - P_y = \frac{h}{\lambda_x} - \frac{h}{\lambda_y}$

$\Rightarrow \frac{1}{\lambda} = \frac{1}{\lambda_x} - \frac{1}{\lambda_y}$

$\Rightarrow \lambda = \frac{\lambda_x \lambda_y}{|\lambda_x - \lambda_y|}$