de Broglie Waves and Electron Diffraction
If light can behave as particles then particles can behave as waves, with wavelength h divided by momentum. Electrons fired at a thin crystal give diffraction rings, which nothing but a wave can produce.
What a learner can do afterwards
- Calculates a de Broglie wavelength from a momentum or from an accelerating voltage
- Explains why the wave nature of a cricket ball is never noticed
- Names electron diffraction rings as the evidence and says what raising the voltage does to them
1 · Read
If light can act as particles, particles can act as waves. Every moving particle carries a wavelength given by h divided by its momentum. An electron with momentum 6.63e-24 kg m/s has wavelength 1.0e-10 m, about one atom wide, since 6.63e-34 divided by 6.63e-24 equals 1.0e-10.
A 0.16 kg cricket ball rolling at 10 m/s has momentum 1.6 kg m/s, so its wavelength is about 4e-34 m. To show interference, a wave must meet an object near its own wavelength in size. Nothing that small exists, so the ball's wave nature stays hidden and it rolls in straight lines.
Electrons are light enough for the effect to show. Fired at a thin crystal of graphite, they form diffraction rings, which nothing but a wave can produce. Raise the accelerating voltage and the electrons gain momentum, so their wavelength shortens and the rings shrink toward the centre.
From a voltage, take two hops. The electron gains kinetic energy E = e V, and its momentum is p = square root of (2 m E), with m = 9.11e-31 kg. Through 150 V, E = 1.6e-19 x 150 = 2.4e-17 J, p = square root of (2 x 9.11e-31 x 2.4e-17) = 6.6e-24 kg m/s, and the wavelength is 6.63e-34 / 6.6e-24, about 1.0e-10 m. Momentum follows the square root of the voltage, so quadrupling the voltage halves the wavelength.
Matter carries wavelength h over momentum, visible only when the wavelength nears the size of the gaps it meets.
The rewritten readings were written for this dataset. Practice items x1-x4 are original to this dataset.
2 · Watch
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Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
12 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.