PhysicsTwo particles move at right angles to each other. Their de-Broglie wavelengths are and respectively. The particles are undergoing perfectly inelastic collisions. The de-Broglie wavelength , of the final particle, is found to have.

Two particles move at right angles to each other. Their de-Broglie wavelengths are {"mathml":"<math class="image_resized" style="width:15px;height:16px"><span style="font-family: and {"mathml":"<math class="image_resized" style="width:15px;height:16px"><span style="font-family: respectively. The particles are undergoing perfectly inelastic collisions. The de-Broglie wavelength{"mathml":"<math class="image_resized" style="width:8px;height:11px"><span style="font-family: , of the final particle, is found to have.


  1. A
  2. B
  3. C
  4. D
    {"mathml":"<math class="image_resized" style="width:118px;height:44px"><span style="font-family: 

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    Solution:

    Concept- Determine the momentum of both particles first. then include momentum conservation into it. We shall obtain a vector of total momentum. It is important to ascertain the outcome.
    P 1 = h A ^ λ 1  
     and  P 2 = h A ^ λ 2  
    Using momentum conservation
    P = P 1 + P 2  
    = h λ 1 λ 1 + h A j λ 2  
    | P |= h λ 1 2 + h λ 2 2  
    h λ = h λ 1 2 + h λ 2 2  
    1 λ 2 = 1 λ 1 2 + 1 λ 2 2  
     Hence, option 4 is correct.
     
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