Two particles are moving perpendicular to each other with de-Broglie wavelengths and if they collide and stick then the de-Broglie wavelength of the system after the collision is,
Step 1: Given
The de-Broglie wavelengths of the given particles are and .
Step 2: Calculating de-Broglie wavelength
Let the wavelength of the particle after collision be .
Let the momentum of the first and second particles be and and momentum of the particle after collision be .
From the conservation of momentum,
Hence, the de-Broglie wavelength of the system after the collision is .
Therefore, option (A) is the correct answer.