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Quantum numbers
Intermediate
n, l, m, s specify electron states.
n (principal), l (orbital, 0 to n−1), m_l (−l to +l) and m_s (±½) specify an electron's state in an atom. They determine energy, shape, orientation and spin.
n = 3 has l = 0, 1, 2 subshells: 9 orbitals.
Each state holds one electron (Pauli).
In more detail
Quantum numbers label the states of an atom: n for energy, l for orbital angular momentum, m_l for its orientation, and m_s for spin. They determine the allowed states of electrons.
Real-world uses
- Chemists use quantum numbers to predict electron configurations.
- Spectroscopy assigns transitions using quantum numbers.
- Chemists use quantum numbers to describe the electrons in an atom and to predict how they fill shells.
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Frequently asked questions
How many values can l take?
For a given n, l runs from 0 to n minus 1.
What is m_l?
The magnetic quantum number, which gives the orientation of the orbital.
What do the four quantum numbers describe?
The principal shell, the orbital shape, the orientation and the electron spin.
Related topics in Quantum Mechanics
Quantum harmonic oscillator · Zero point energy · Hydrogen atom in quantum mechanics · Atomic orbitals · Electron spin · Stern–Gerlach experiment