# What is the reason for the electrons in a given subshell to orient in certain preferred regions?

My text book says: "Magnetic quantum number describes the behavior of electron in a magnetic field. We know that the movement of electrical charge is always associated with magnetic field. Since the revolving electron possesses angular momentum, it will give rise to a very small magnetic field which interact with the external magnetic field of the earth. Under the influence of external magnetic field, the electrons in a given subshell orient themselves in certain preferred regions of space around the nucleus. These are called orbitals".

I got a question here. If external magnetic field of the earth is the reason for the electrons in a given subshell orient themselves in certain preferred regions of space, then

• would there be no particular orientations of electrons when there is no earths magnetic field? If this is the case, won't geometry of the compounds change (because of varied angle between the orbitals) without earth's magnetic field?

• And won't it also cause crashing of orbitals in the absence of particular orientation? But this never happens, I hope. Then what could be the possible explanation that can be given for the above cases.

Even I am not convinced with my text book explanation regarding orientation of electron in the subshell. How could the $p$ orbitals be oriented exactly perpendicular to each other, only because of the earth's magnetic field? We can even consider other orbitals too. Is there any other factor which is responsible for the orientations?

I don't know whether I have misunderstood anywhere, if so please explain and pardon me.

• Ye, gads! That text is bad. Run, don't walk away from that book. Do not take it seriously. The definition of orbitals is wrong. The suggestion that the Earth's magnetic field can generate any significant degree of polarization is wrong (experimentally we use multi-Tesla fields to get enough polarization to be useful). And while it is true that there is an interaction between the orbital magnetic moment and that of the nucleus the text has not told you how that is observable. – dmckee Jan 14 '14 at 18:10

I think you are correct in being confused. The earth's magnetic field, or any external to the atom magnetic field , can distort orbitals but is not the creators of them.

Orbitals are the locus in space where the probability of finding an electron is large enough to be measurable. In the quantum mechanical framework orbitals play the role orbits have in classical central potentials, for example gravity.

The five d orbitals in ψ(x, y, z)2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus.

The wave functions, i.e. the quantum mechanical solutions of the Schrodinger equation for the atom, have complicated functions of space. Their square describes the probability of finding an electron which is symmetric but does not fill all space. The solution giving the figure depends on the n,l,m quantum numbers . The n quantum number defines the main energy level, the angular momentum l (=2 in the figure) gives the shapes we see in the figure and the m is degenerate and can split in magnetic fields, each triplet defining a specific orbital. If there are no external magnetic fields the m states are degenerate as far as energy goes. An external magnetic field would split the degeneracy and create a difference in the pattern above in space, but it is not the creator of the orbitals.

To start answering this question let us talk about a diatomic molecule. In that case we can define the internuclear axis as the z axis in the molecular frame, and talk about the orientation of the various atomic orbitals with respect to that. There is a natural choice of orientation along the bond.

For an isolated atom there is no preferred z axis to refer the orbital orientation to but what we can do is to choose the z axis so that if the atom were in a magnetic field, the z axis would be along the direction of the field. The projection of the orbital angular momentum along the z (magnetic) axis is then m hbar.

The book is badly confused/confusing