The magnetic quantum number, designated by the letter ml, is the third
quantum numbers
which describe the unique quantum state of an electron. The magnetic
quantum number distinguishes the orbitals available within a subshell,
and is used to calculate the azimuthal component of the orientation of
the orbital in space. As with our discussion of rigid rotors, the
quantum number ml refers to the projection of the angular momentum in this arbitrarily chosen direction, conventionally called the z direction or quantization axis. Lz
, the magnitude of the angular momentum in the z direction, is given by the formula
Lz=mlℏ(6.6.3)
The quantum number refers, loosely, to the direction of the angular momentum vector. The magnetic quantum number ml only affects the electron's energy if it is in a magnetic field because in the absence of one, all spherical harmonics corresponding to the different arbitrary values of ml
are equivalent. The magnetic quantum number determines the energy shift
of an atomic orbital due to an external magnetic field (this is called
the Zeeman effect) - hence the name magnetic quantum number. However,
the actual magnetic dipole moment of an electron in an atomic orbital arrives not only from the electron angular momentum, but also from the electron spin, expressed in the spin quantum number, which is the fourth quantum number. and discussed in the next chapter.
Figure 6.6.3
: The orbiting electron with a non-zero l
value acts like a magnetic field with is no energetic difference for
any particular orientation (only one energy state, on the left).
However, in external magnetic field there is a high-energy state and a
low-energy state depending on the relative orientations of the magnet to
the external field. (CC SA-BY 3.0; Darekk2).
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