〰️ de Broglie's condition — a whole number of electron wavelengths fits the orbit

Bohr's rule is really a standing wave: an allowed orbit is one whose circumference holds a whole number of electron wavelengths, 2πr = nλ. A non-integer number cannot close on itself and is not allowed.

Walkthrough 1 / 3

Step 1 — the nucleus and a circular orbit, the path the electron is confined to.

Wave count n 3

Nuclear charge Z 1

Amplitude 0.60

n = 3 wavelengths · r_n = 4.76 Å
2πr = 29.9 Å · λ = 9.97 Å

whole n → wave closes on itself (allowed)
2πr = nλ is Bohr's quantum condition

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