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Question

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

A
λCM=2λ1λ2λ12+λ22
B
λCM=λ1=λ2
C
1λCM=1λ1+1λ2
D
λCM=(λ1+λ22)
Solution
Verified by Toppr

Since λ=hmv
v=hmλ

Let v1 and v2 are the speeds of electrons

vcm=v1+v22
h2mλcm=12(hmλ1+hmλ2)

1λcm=1λ1+1λ2

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