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Quantum numbers, orbital explorer, hydrogen atom spectra, de Broglie wavelength, photon energy, and Bohr model.
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.
Electrons orbit the nucleus at quantized energy levels. Eₙ = -13.6/n² eV for hydrogen. Predicts spectral lines accurately.
Light consists of photons with energy E = hf = hc/λ. Higher frequency (shorter wavelength) means higher energy.
Orbitals are probability distributions for finding electrons. s(sphere), p(dumbbell), d(clover), f(complex) shapes.
When electrons drop to lower energy levels, they emit photons. The Balmer series (n→2) produces visible hydrogen lines.
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