Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are ₁ and ₂ , their de Broglie wavelength in the frame of reference attached to their centre of mass is:

Step-by-step solution

Momentum (p) of each electron h ₁ i and h ₂ j Velocity of centre of mass V _ cm = h 2 ~m ₁ i + h 2 ~m ₂ j ( p = mv ) Velocity of 1 st particle about centre of mass V_ 1 ~cm = h 2 ~m ₁ i - h 2 ~m ₂ j _ cm = h h ^2 4 ₁^2 + h ^2 4 ₂^2 = 2 ₁ ₂ ₁^2+ ₂^2 ( = h p )