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Question
Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the nucleus.
Solution
According to the de Broglie concept, the electron that revolves around the nucleus exhibits both particle and wave character. In order for the electron wave to exist in phase, the circumference of the orbit should be an integral multiple of the wavelength of the electron wave, Otherwise, the electron wave is out of phase.
Circumference of the orbit = nλ
2πr = nλ
2πr = `"nh"/"mv"`
Rearranging, mvr = `"nh"/"mv"`
Angular momentum = `"nh"/(2π)`
The above equation was already predicted by Bohr.
Hence, de Broglie and Bohr’s concepts are in agreement with each other.
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