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Questions and Answers
What are de Broglie waves?
What are de Broglie waves?
De Broglie waves are waves associated with every moving particle.
How does the mass of a particle affect its de Broglie wavelength?
How does the mass of a particle affect its de Broglie wavelength?
A lighter particle has a greater associated wavelength.
What happens to the wavelength of a particle as its velocity decreases?
What happens to the wavelength of a particle as its velocity decreases?
The wavelength increases as the particle's velocity decreases.
Calculate the de Broglie wavelength of an electron accelerated under a potential of 100 V.
Calculate the de Broglie wavelength of an electron accelerated under a potential of 100 V.
What is the relation between the energy of a particle and its de Broglie wavelength?
What is the relation between the energy of a particle and its de Broglie wavelength?
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Study Notes
De Broglie Waves
- Every moving particle has an associated wave, called a de Broglie wave.
- Lighter particles have longer wavelengths.
- Slower particles have longer wavelengths.
- A particle at rest has an indeterminate wavelength.
- Matter waves are non-electromagnetic. Their velocity depends on the particle's velocity.
Calculating De Broglie Wavelength
-
The de Broglie wavelength (λ) is calculated using the formula: λ = h/p = h/mv = h/√(2mE)
- where:
- h = Planck's constant (6.62 x 10^-34 Js)
- p = momentum
- m = mass
- v = velocity
- E = energy
- where:
-
Example Calculation (Electron accelerated by 100V):
- Given E = 100 eV = 100 x 1.6 x 10^-19 J
- λ = (6.62 x 10^-34 Js) / √(2 * 9.1 x 10^-31 kg * 100 * 1.6 x 10^-19 J)
- λ ≈ 1.23 nm (nanometers)
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