The number m_l, from -l to +l, defining the orientation of an orbital in space.
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The magnetic quantum number, m_l, takes 2l + 1 integer values from -l to +l, and it labels the orientation of an orbital in space. Its values give the number of orbitals within a subshell: one for s, three for p, five for d and seven for f. In the absence of an external magnetic field, orbitals with different m_l in the same subshell have the same energy, a condition called degeneracy. A magnetic field lifts this degeneracy, which is the basis of the Zeeman effect. It describes the projection of orbital angular momentum on a chosen axis.
Key ideas: ml takes integer values from -l to +l, including 0, giving 2 l + 1 orientations: p has -1, 0, +1; d has -2 to +2. Orbitals with the same n and l but different ml are degenerate (equal energy) unless a magnetic field is applied (Zeeman effect). Lz = ml x h / (2 pi).
Common mistakes and connections: Students think ml differs in energy in an isolated atom, or that it determines orbital shape (that is l). It indicates the orientation in space, such as px, py, pz which are real combinations of ml = +1 and -1. It links to the Zeeman effect and to spectral line splitting.
In a 1 T magnetic field a p subshell splits into three levels (ml = -1, 0, +1) about 0.058 meV apart. The interactive lesson shows this as a live animation or chart.
A p subshell has m_l values of -1, 0 and +1, giving three distinct p orbitals.
The number m_l, from -l to +l, defining the orientation of an orbital in space.
Magnetic Quantum Number is a intermediate topic in Atomic Structure & Periodicity. It builds on the vocabulary of beginner topics in this area.
Study these earlier topics in Atomic Structure & Periodicity first: Atomic Orbital, Principal Quantum Number, Azimuthal Quantum Number.
The next topics in Atomic Structure & Periodicity are Spin Quantum Number and Shapes of s and p Orbitals.
Yes. The interactive lesson includes a self-check question on Magnetic Quantum Number, and the Atomic Structure & Periodicity quiz draws on every topic in this area.
Magnetic Quantum Number is topic 55 of 115 in Atomic Structure & Periodicity.