5.2. The Quantum Mechanical Model http://www.ck12.org
FIGURE 5.14
An electron cloud: the darker region near
the nucleus indicates a high probability
of finding the electron, while the lighter
region farther from the nucleus indicates
a lower probability of finding the electron.will describe each of these quantum numbers separately.
Principal Quantum Number
Theprincipal quantum numberis symbolized by the letter n and designates the principal or main energy level
occupied by the electron.The possible values ofnbegin withn= 1, which is the lowest energy level and is located
closest to the nucleus. As the value ofnincreases ton= 2, 3, and so on, the distance from the nucleus increases.
The principal quantum number is essentially the same as the energy levels in the Bohr model of the atom that were
used to explain atomic emission spectra. More than one electron may occupy a given principal energy level, but the
specific number of electrons that can be held by each energy level varies depending on the value ofn.
Angular Momentum Quantum Number
Theangular momentum quantum numberis symbolized by the letter l and indicates the shape of the orbital.
Orbitals of different shapes exist for most principal energy levels, and for atoms that contain more than one electron,
the different shapes result in slightly different energies for the electrons in each orbital. The various orbital shapes
split each principal energy level into one or more energy sublevels. The number of possible sublevels in a given
principal energy level is equal to the value ofn. For example, whenn= 1, there is only one sublevel, but whenn=
2, there are two sublevels. The quantum numberlis an integer that varies from 0 up to a value equal ton- 1. Ifn=
1, the only possible value oflis 0, whereas ifn= 4,lcan have a value of 0, 1, 2, or 3. The orbitals of each sublevel
are also designated by a particular letter, such ass,p,d, orf. Ifl= 0, the orbital is called ansorbital, and ifl= 1, the
orbital is aporbital. A summary is shown below (Table5.1).