Q 12-11-165JEE MainJEE Main 2019 (9 Apr, Shift 2)Easy
A particle P is formed due to a completely inelastic collision of particles x and y having de Broglie wavelengths $\lambda_x$ and $\lambda_y$ respectively. If x and y were moving in opposite directions, then the de Broglie wavelength of P is
Answer: (C) $\dfrac{\lambda_x\lambda_y}{|\lambda_x - \lambda_y|}$
The momenta are opposite, so the combined particle has
$$p = \left|\frac h{\lambda_x} - \frac h{\lambda_y}\right| = h\frac{|\lambda_y - \lambda_x|}{\lambda_x\lambda_y}$$
$$\lambda = \frac hp = \frac{\lambda_x\lambda_y}{|\lambda_x - \lambda_y|}$$
Solution by Sreeraj P, M.Sc Physics