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

Question

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

MARKS App · Accepted Answer

Momentum of each electron h λ 1 i ^ a n d h λ 2 j ^ Velocity of centre of mass V c m = h 2 m λ 1 i ^ + h 2 m λ 2 j ^ Velocity of 1 s t particle about centre of mass V c m = h 2 m λ 1 i ^ - h 2 m λ 2 j ^ λ c m = h h 2 4 λ 1 2 + h 2 4 λ 2 2 = 2 λ 1 λ 2 λ 1 2 + λ 2 2

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