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Magnetic Quantum Number

Each subshell is comprised to one or more orbital’s (regions of space with maximum probability of finding the electron) whose number is equal to the number of ways the electrons in subshell can orient themselves in space. The number of orientations is given by 2/+1 . That means, the number of orientations or orbitals is one when =0 (s-subshell). theree for =1 (p-subshell),five for =2 (d-subshell and seven for =3 (f-subshell). In other words, s-sushell has one s-orbital, p-subshell has three p-orbital’s, d-subshell has five d-orbital’s and so on. In the absence of electric or magnetic field, these or titrations or orbital’s in subshell are degenerate , that is , they have identical values of energy . For example, for=1m the three orbitals, px’ py and pz  are degenerate but this degeneracy is split in the presence of a magnetic field as shown in . In this way three p-orbital’s of different energies with the lowest energy orbital aligne with magnetic field (m = + 1) and five d-orbital’s of different energies with the lowest aligned with H(m = +2) are obtained . Each orbital within a subshell is identified in term of the component

of the angular momentum where m = magnetic quantum number. In other words, m is associated with different orientations or the orbital with reference to some defined directions.

For given subshell, m can have values :

Thus for = 0, m = 0, we get an s-orbital.
For = 1,m can have three values m = 1,0, corresponding to three p-orbitals; px, py,pz
For = 2, m can have five values m = 2, 1,0, corresponding to five d-orbitals; .

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