Wave–particle duality

Overview

De Broglie's hypothesis that matter has wave properties, the equations λ = h/p and λ = h/√(2meV), and how low-energy electron diffraction confirmed it, including how electron speed changes the rings.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State de Broglie's hypothesis about matter.

   Model answer

   All matter exhibits wave-like properties, with wavelength inversely proportional to momentum.

2. 2

   Write the equation for the de Broglie wavelength of a particle.

   Model answer

   λ = h/p, where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.

3. 3

   Write the equation for the de Broglie wavelength of an electron accelerated through a potential difference V.

   Model answer

   λ = h/√(2meV), where h is Planck's constant, m is the electron mass, e is the electron charge, and V is the accelerating voltage.

4. 4

   In the equation λ = h/√(2meV), identify what each symbol represents.

   Model answer

   λ is the de Broglie wavelength, h is Planck's constant, m is the electron mass, e is the electron charge, and V is the accelerating potential difference.

5. 5

   When is the equation λ = h/√(2meV) used?

   Model answer

   When calculating the de Broglie wavelength of an electron that has been accelerated from rest through a potential difference V.

6. 6

   Calculate the de Broglie wavelength when Planck constant = 6.63 × 10⁻³⁴ J s, electron mass = 9.11 × 10⁻³¹ kg, elementary charge = 1.60 × 10⁻¹⁹ C, accelerating voltage = 50 V.

   Model answer

   De Broglie wavelength = 6.63 × 10⁻³⁴ ÷ √(2 × 9.11 × 10⁻³¹ × 1.60 × 10⁻¹⁹ × 50) = 1.74 × 10⁻¹⁰ m.

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