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A hydrogen atom is in the n = 4 state. In the Bohr model, how many...

A hydrogen atom is in the n = 4 state. In the Bohr model, how many electron wavelengths fit around this orbit?

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Answer #1

Let the radius of orbit of electron be . Then the circumference of orbit is . According to Bohr model, this length contains an integral number of wavelengths so that the electron (acting as a wave) sets up a standing wave. This integral number is called a quantum number (later called principal quantum number).

Hence

This relation is also expressed as . This relation is called quantisation of angular momentum.

Hence for the state, four wavelengths fit on the orbit.

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