1931, Niels Bohr proposed a model of the hydrogen atom in which the wlwctron cou

Question

1931, Niels Bohr proposed a model of the hydrogen atom in which the wlwctron could exist only in specific circular orbits. He did not offer any explanation as to why only those particular orbits would be allowed in 1924, Louis de Brogile suggested that the electron could only exist in orbit corresponding to certain kinds of wave patterns. In the diagram at right is shown an electron orbit that has been "cut and unwrapped" to better show the electron wave. Sort the wave patterns below by whether or not they are compatible with de Broglie's description of the allowed Bohr orbits of the hydrogen atom.

Explanation / Answer

By De-Brogglie Theory,

the electron can occupy the orbit if the circumference of the orbit is an integral multiple of the wavelength

From the cut out figures , only the figures which have integral multiple of wavelengths are allowed(compatible)

From the left-top figure, we see that there are 2 full wavelengths but we see that there are 2 frequencies in the wave(not a perfect sinusoid) , so it is incompatible

For the left middle one, same case as before, so not compatible

For the left lowest, we see that there are 2 wavelengths. and perfectly sinusoid, so compatibe;

For the right-top, 4 wavelengths, so compatible

For the right-middle, 4.5 wavelengths , so not compatible

For the right-lowest, 3.5 wavelengths, so not compatible

So, only left lowest and right-top are compatible <------answer

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