Download Enthalpy

Representation of Orbitals
Thus far, we have considered the orbitals solely in terms of their energy. The wave function (ψ) also
provides information about the electron’s location in space when it is a particular allowed energy state.
Wave function
Erwin Schrödinger proposed an equation that incorporates both the wave and particle-like
behavior of the electron. The application of Schrödinger’s equation required the use of
advanced calculus; therefore, we will focus on his results qualitatively.
Solving Schrödinger’s equation mathematically leads to a series of mathematical functions
called wave functions represented by the Greek letter ψ. Although the wave function has no
direct physical meaning, ψ2 provided information about an electron’s location when it is in an
allowed energy state. The square of the wave function at a given point in space represents the
probability that an electron will be found at that location. Therefore, ψ2 is called the
probability density or electron density.
The letter subscript indicates the axis along which the orbital is oriented. Likes s orbitals,
p orbials increases in size as we move from 2p, to 3p, to 4p, and so forth.
When n = 3 or greater we encounter d orbitals. There are five 3d orbitals, five 4d orbitals,
and so forth. The different d orbitals in a given shell have different shapes and
orientations, which, although fun, are not necessary to present in this class.
When n = 4 or greater we encounter f orbitals. There are seven equivalent f orbitals. The
shapes of the different f orbitals are even more complicated than those of the d orbitals, and
will not be presented here.
You will find an understanding of the number and shapes of atomic orbitals will be helpful
in understanding chemistry at the molecular level. The following table summarizes this.