A particle $\mathrm{\text{'}}\mathrm{P}\mathrm{\text{'}}$ is formed due to a completely inelastic collision of particles $\mathrm{\text{'}}\mathrm{x}\mathrm{\text{'}}$ and $\mathrm{\text{'}}\mathrm{y}\mathrm{\text{'}}$ having de-Broglie wavelengths $\mathrm{\text{'}}{\mathrm{\lambda }}_{\mathrm{x}}\mathrm{\text{'}}$ and $\mathrm{\text{'}}{\mathrm{\lambda }}_{\mathrm{y}}\mathrm{\text{'}}$ respectively. If $\mathrm{x}$ and $\mathrm{y}$ were moving in opposite directions, then the de-Broglie wavelength of $\mathrm{\text{'}}\mathrm{P}\mathrm{\text{'}}$ is: