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NEETPhysicsDual Nature of Matter

An electron, a proton, and an alpha particle are accelerated such that they all have the same kinetic energy. If _e , _p , and _ are their respective de Broglie wavelengths, then which of the following represents the correct order?

Options

  1. A_ < _p < _e
  2. B_e < _p < _
  3. C_p < _ < _e
  4. D_e = _p = _

Correct answer

A. _ < _p < _e

Step-by-step solution

The de Broglie wavelength of a particle is given by the relation: = h p The momentum p can be expressed in terms of kinetic energy K as p = 2mK . Therefore, the wavelength is: = h 2mK Since the kinetic energy K is the same for all three particles, the de Broglie wavelength is inversely proportional to the square root of the mass of the particle: 1 m The masses of the given particles follow the order: m_e Hence, the order of their de Broglie wavelengths will be reversed: _ Answer: _ < _p < _e

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