M

Magnetic Quantum Number

m_l quantum number: −l to +l integers; e.g., p: m_l = −1, 0, +1
Quick Reference
Formula / Notationm_l quantum number: −l to +l integers; e.g., p: m_l = −1, 0, +1
Also Known Asm_l, orbital magnetic quantum number, azimuthal quantum number component

What is Magnetic Quantum Number?

The quantum number (mₗ) that specifies the orientation of an atomic orbital in space relative to a magnetic field. For a subshell with angular momentum quantum number l, mₗ takes integer values from -l to +l, giving (2l+1) possible orientations. It determines the number of orbitals in each subshell.

Formula & Notation

m_l quantum number: −l to +l integers; e.g., p: m_l = −1, 0, +1

Other Names / Synonyms: m_l, orbital magnetic quantum number, azimuthal quantum number component

Properties & Characteristics

The magnetic quantum number (m_l) is one of four quantum numbers used to describe the quantum state of an electron in an atom. It specifies the spatial orientation of an orbital within a subshell and takes integer values from −l to +l (2l+1 values total). For l = 0 (s orbital): m_l = 0 (1 orbital); l = 1 (p): m_l = −1, 0, +1 (3 orbitals); l = 2 (d): m_l = −2, −1, 0, +1, +2 (5 orbitals). In a magnetic field, orbitals of the same l but different m_l have slightly different energies (Zeeman effect).

Uses & Applications

Magnetic quantum numbers explain the number of orbitals in each subshell, the structure of the periodic table, the Zeeman splitting of spectral lines in a magnetic field, the basis of NMR spectroscopy (nuclear spin quantum numbers parallel the concept), and the degeneracy lifting in crystal field theory.

Safety Information

No direct safety concern. The magnetic quantum number determines orbital orientation, which is relevant to understanding the directional nature of covalent bonds and why some coordination geometries (octahedral, tetrahedral) are favoured — information used in rational catalyst design.

Always consult the SDS/MSDS before handling any chemical. This information is for educational purposes only.

Key Facts

Term Magnetic Quantum Number
Formula m_l quantum number: −l to +l integers; e.g., p: m_l = −1, 0, +1
Synonyms m_l, orbital magnetic quantum number, azimuthal quantum number component

Frequently Asked Questions

The quantum number (mₗ) that specifies the orientation of an atomic orbital in space relative to a magnetic field. For a subshell with angular momentum quantum number l, mₗ takes integer values from -l to +l, giving (2l+1) possible orientations. It determines the number of orbitals in each subshell.

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