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Concepts Of Physics MCQ Edition [Volume 2]PhysicsPhotoelectric Effect and Wave–Particle Duality

For which of the following scenarios will the heavier of two particles have a shorter de Broglie wavelength? The two particles

Options

  1. Atravel with the same linear momentum
  2. Bpossess the same kinetic energy
  3. Chave dropped through the same height
  4. Dtravel with the same speed

Correct answer

D. travel with the same speed

Step-by-step solution

The de Broglie wavelength of a particle is given by = h p = h mv = h 2mK . For particles with the same linear momentum p , the wavelength is the same regardless of their masses. For particles with the same kinetic energy K , 1 m . Since the heavier particle has a larger mass m , it will have a shorter de Broglie wavelength. For particles dropped through the same height H , their final speeds are equal, given by v = 2gH . For particles traveling with the same speed v , 1 m . The heavier particle has a larger mass m

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