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Textbook-model calculations for quantum numbers, hydrogen spectra, de Broglie wavelength, photon energy, and the Bohr model, with symbolic diagrams.
Verify if a set of quantum numbers (n, l, mₗ, mₛ) is valid for an electron in an atom.
Shell number (1, 2, 3, ...)
0 to n-1 (s, p, d, f)
-l to +l
+1/2 or -1/2
Key concepts in quantum mechanics and atomic structure.
Four quantum numbers (n, l, mₗ, mₛ) uniquely describe each electron in an atom. No two electrons can share all four (Pauli Exclusion Principle).
All matter exhibits both wave and particle properties. The de Broglie wavelength λ = h/mv is significant only for subatomic particles.
The Bohr model uses quantized energy levels. Eₙ = -13.6/n² eV applies to hydrogen; the Z² form applies to one-electron hydrogen-like ions. It is not a general many-electron atomic model.
Light consists of photons with energy E = hf = hc/λ. Higher frequency (shorter wavelength) means higher energy.
Atomic orbitals are wavefunctions whose squared magnitude gives a probability density. The s, p, d, and f icons shown here are symbolic teaching diagrams, not computed isosurfaces.
When electrons drop to lower energy levels, they emit photons. The Balmer series (n→2) produces visible hydrogen lines.
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