Calculating the radius of atomic orbits for hydrogen

Let us assume that the electron moves in a circular orbit around a proton which is at rest.

Classical angular momentum mvr = —, n = 1, 2, 3..

The quantum condition

Centripetal force -=-2 Coulomb attraction r 4pe0 r r nhj 2p ^ 2 v mr j

n = 1 for the stable hydrogen atom ^ r = 0.529 x 10-10 m.

Planck's constant, in combination with previously known physical constants, enabled Bohr to calculate the size of electron orbits, which can be considered as defining the size of an atom. We have detailed information about something that is small almost beyond imagination.

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