Inorganic and Applied Chemistry

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Inorganic and Applied Chemistry

Example 1- H:

Quantum numbers and designations for different orbitals

We are going to list the different possible quantum numbers when the primary quantum number n has the

value of 4. We are also going to assign the orbitals with letter symbols.

When n = 4, the angular momentum quantum number l can assume the values of 0, 1, 2 or 3. For each

value of l the magnetic quantum number ml can attain the values from -l to +l. This is sketched in Figure

1- 5.

Figure 1- 5: Listing of orbitals

The individual orbitals for the primary quantum number n = 4.

It is thus seen that when the primary quantum number has the value of 4 it gives a total of 16 “4-orbitals”

which are the one 4s-orbital, the three 4p-orbitals, the five 4d-orbitals and the seven 4f-orbitals.

The Schrödingers wave equation has thus resulted in a theory about orbitals that host electrons. This model is,

contradictory to the atomic model of Niels Bohr, also applicable for atoms with more than one electron

(elements other than hydrogen). The lines in the line spectrums are explained by postulating that an electron

in excited state have one or more electrons that have “jumped” out in an outer atomic orbital with larger

energy. When this or these electrons then “jump” back into the orbitals of lower energy, energy is emitted in

the form of photons. The energy (wavelength) of these photons then corresponds to the energy difference

between the two affected orbitals and hence only light with certain wavelengths can be emitted when for

example element samples are burned off. This is pretty much the same principle as explained by Niels Bohr,

the difference is just that the electrons are “now” hosted in orbitals instead of circular orbits.

It is important to emphasize that orbitals are areas/volumes in which the electrons with a certain probability

can be found. Orbitals are derived from mathematical models and the concept of orbitals is developed in

order to be able to explain certain characteristics of the element such as the line spectra. Thus we are talking

about theoretical and mathematical description of probabilities of finding electrons in certain areas and this

Atoms