Dual Nature of Radiation and Matter
Watch a 3D electron wave wrap around a nucleus. Rotate it with your finger. At integer wavelengths the wave closes cleanly — at fractions it fails. The same standing-wave principle that explains why orbits are quantized, in 3D.
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An s-orbital is the lowest-energy 3D standing wave around a nucleus, with no angular nodes. Since the only solution with this symmetry is one that depends solely on distance from the nucleus, the electron probability is the same in every direction — making the orbital perfectly spherical.
Bohr drew electrons in flat circular orbits, which was a useful first approximation but physically incomplete. This lab shows the upgrade: the electron is really a 3D standing wave wrapped around the nucleus. The quantization that Bohr postulated emerges naturally from the wave fitting condition.
If a fractional number of wavelengths tries to fit around the nucleus, the wave overlaps itself out of phase on each loop and cancels by destructive interference. Only wavelengths that close cleanly survive. This is why electron energies in atoms come in discrete levels.