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5.ATOMIC STRUCTURE eLearn.Punjab

when  = 0 s-subshell m=0
 = 1 p-subshell m=0, ±1(p-subshell has three degenerate orbitals)
 = 2 d-subshell m=0,±1, ±2(d-subshell has five degenerate orbitals)
 = 3 f-subshell m=0,±1, ±2, ±3(f-subshell has seven degenerate orbitals)
This above description shows that for a given value of ‘  ’ the total values of’m’ are (2  +1).
Actually, the value of m gives us the information of degeneracy of orbitals in space. It tells
us the number of different ways in which a given s, p, d or f-subshell can be arranged along x, y
and z-axes in the presence of a magnetic field. Thus, different values of’m’ for a given value of ‘  ‘,
represent the total number of different space orientations for a subshell.
In case of s-subshell  = 0, so, m = 0. It implies that s-subshell of any energy level has only one
space orientation and can be arranged in space only in one way along x, y and z-axes. So s-subshell
is not sub-divided into any other orbital. The shape of’s’ orbital is such that the probability of finding
the electron in all the directions from the nucleus is the same. It is a spherical and symmetrical
orbital. Fig (5.20).
For p-subshell,  = 1 and m = 0, ±1. These values of’m’ imply that p-subshell of any energy
level has three space orientations and can be arranged in space along x, y, and z axes Fig. (5.21).
These three orbitals are perpendicular to each other and named as px, py, and pz. They have egg
shaped lobes which touch each other at the origin. They are disposed symmetrically along one of
the three axes called orbital axis. In the absence of the magnetic field, all the three p-orbitals have
the same energy and are called degenerate orbitals. Since, they are three in number, so these
orbitals are said to be 3-fold degenerate or triply degenerate.
For d-subshell  = 2 m = 0, ±1, ±2. It implies that it has five space orientations and are
designated as dxy (m = -2), dyz (m = -1), dzx(m = +1), dx2-y2(m = +2) and dz2(m - 0) Fig. (5.22).
All these five d-orbitals are not identical in shape. In the absence of a magnetic field, all five
d-orbitals have the same energy and they are said to be five fold degenerate orbitals.

For f-subshell,  = 3 and m = 0, ±1, ±2, ±3. They have complicated shapes.

The whole discussion shows that magnetic quantum number determines the orientation of
orbitals, so it is also called orbital orientation quantum number.

Spin Quantum Number (s)

Alkali metals have one electron in their outermost shell. We can record their emission spectra,
when the outermost electron jumps from an excited state to a ground state. When the spectra are
observed by means of high resolving power spectrometer, each line in the spectrum is found to
consist of pair of lines, this is called doublet line structure. We should keep it in mind, that doublet
line structure is different from the fine spectrum of hydrogen (as we have discussed in azimuthal
quantum number).

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