Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de…

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de brogile wavelengths are λ1 and λ2, their de brogile wavelength in the frame of reference attached to their centre of mass is:
  1. 1λCM=1λ1+1λ2
  2. λCM=2λ1λ2λ12+λ22
  3. λCM=λ1=λ2
  4. λCM=λ1+λ22

Solution

Momentum of each electron hλ1 i^ and hλ2j^

Velocity of centre of mass

Vcm=h2mλ1 i^+h2mλ2j^

Velocity of 1st particle about centre of mass

Vcm=h2mλ1 i^-h2mλ2j^

λcm=hh24λ12+h24λ22=2λ1 λ2λ12+λ22

Asked in: JEE Main 2018 (15 Apr)

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