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Two particles having de-Broglie wavelengths λ 1 and λ 2 , while moving along mutually perpendicular directions, undergo perfectly inelastic collision. The de-Broglie wavelength λ , of the final particle is

Options

  1. Aλ = λ 1 λ 2 λ 1 2 + λ 2 2
  2. Bλ = λ 1 λ 2
  3. Cλ = λ 1 + λ 2
  4. Dλ = λ 1 + λ 2 2

Correct answer

A. λ = λ 1 λ 2 λ 1 2 + λ 2 2

Step-by-step solution

Let us assume that one of the particles is moving along the positive x direction and the other is moving along the positive y direction. The net momentum of the system is P → net = P i ^ + P j ^ h λ = h λ 1 i ^ + h λ 2 j ^ 1 λ = 1 λ 1 2 + 1 λ 2 2 λ = λ 1 λ 2 λ 1 2 + λ 2 2

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