MDCAT Physics · Physics · Dawn of modern physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Just as light can behave as particles, moving particles can behave as waves. Every particle with momentum has a de Broglie wavelength: the larger the momentum, the shorter the wavelength. Davisson and Germer proved this by diffracting an electron beam from a nickel crystal. Fast electrons have a far shorter wavelength than visible light, so an electron microscope shows finer detail.
The uncertainty principle says position and momentum (or energy and time) cannot both be known exactly at the same time.
In special relativity the speed of light in free space is the same for all observers in inertial frames. A moving clock runs slow, a moving rod is shorter along its motion, mass rises with speed, and mass and energy are equivalent.
Equal de Broglie wavelengths mean equal momentum, not equal speed or equal kinetic energy. In relativity, check your answer by sense: time and mass must come out larger, length must come out shorter.
Answer: λ = 3.3 × 10−10 m, about the size of an atom, which is why crystals can diffract electrons.
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