Magnetic quantum number ( m ) is a quantum number , a parameter that is introduced when solving the Schrödinger equation for an electron in a hydrogen-like atom (and generally for any movement of a charged particle). A magnetic quantum number characterizes the spatial orientation of the orbital angular momentum of an electron or the spatial arrangement of an atomic orbital . It takes integer values from -l to + l , where l is the orbital quantum number , that is, it has exactly as many values as there are orbitals on each sublevel.
History
In 1896, the Dutch physicist Peter Zeeman placed a device in a strong magnetic field similar to a hydrogen lamp, but filled with pairs of red-hot sodium ( Faraday set up a similar experiment in 1862 and failed). It was found that in a magnetic field the number of lines in the emission spectra increases. The spectra become complex, but it can be shown that each p-line splits in a magnetic field into 3 new lines, each d-line into 5, each f-line into 7 lines, and the s-lines do not change. Since the orbitals of an atom become “visible” only in a magnetic field, the next quantum number that records the “address” of the orbitals in an atom is called the magnetic quantum number .
Features
Each of 2 l + 1 possible values of the magnetic quantum number determines the projection of the vector of the orbital momentum in a given direction (usually the z axis). The projection of the orbital angular momentum onto the z axis is Since the magnetic moment is associated with the orbital moment, the magnetic quantum number, in particular, determines the projection of the orbital magnetic moment of a hydrogen-like atom on the direction of the magnetic field and causes the splitting of the spectral lines of the atom in a magnetic field.
Sometimes the magnetic quantum number is determined for the projection of any moment of the particle (orbital L , spin S , total J = L + S ). In this case, it takes 2 L +1, 2 S +1, 2 J +1 values, respectively. For projections of the spin and total moments, the magnetic quantum number can be half-integer.
The magnetic quantum number in the transitions between levels can only change by a certain value established by the selection rules for this type of transition.