Atomic Orbitals

The shapes of the atomic orbitals are determined be graphing the appropriate wave functions. Each wave function is controlled by a set of three numbers called the Quantum Numbers. The combination of the three Quantum Numbers determines the act ual size, shape and direction of the individual orbitals that appear on an atom. The individual interpretations of the numbers are:

  • The n quantum number, known as the Principle Quantum Number, will determine the size of the orbital.
  • The l quantum number, known as the Azimuthal Quantum Number, will determine the shape of the orbital.
  • The m quantum number, known as the Magnetic Quantum Number, will determine the direction of the orbital, oriented in three dimensional space.

The shape of an orbital is determined by the value of the Azimuthal Quantum Number, symbolized "l".

  • When l = 0, the orbital is a sphere. It is known as an "s orbital".
  • When l = 1, the orbital is a dumbell shaped structure. It is known as a "p orbital".
  • When l = 2, the orbital can exist in either of two forms. It can be a cloverleaf pattern or a dumbbell with a donut. In both cases, the orbital is called a "d orbital".
  • When l = 3, the orbital can exist in three different shapes. The shapes are quite elaborate and are not associated with a particular name. However, the orbital type is called an "f orbital".
  • When the value of l exceeds 3, the orbitals become increasingly complex to draw. None of them are presently used by any existing atom under normal conditions. The names for these orbitals will appear in alphabetical order, starting with "g orbitals" .

 

 
   

 The m quantum number will determine the orientation of the orbital in three dimensional space. In this case, the value of m is not important. The number of values of m that are possible for a given l value will determine the number of ways of draw ing a particular type of orbital.

As an example, when l = 0, then the only possible value of m is 0, or m = 0. Because there is only one answer for m, that means that the s orbital, at l = 0, will only be oriented one way on the x, y, z coordinates. In other words, there will only be one drawing necessary for s orbitals.

When l = 1, then the values of m will be -1, 0, +1, or m = -1, 0, +1. The three answers indicate that there will be three orbitals of the type known as p. Each one of these orbitals will be aligned on one of the three axis systems, x, y or z.

When l = 2, then the values of m will be -2, -1, 0, +1, +2. The five answers indicate that there will be five orbitals of the type known a d. Various combinations of orientation factors will draw this set of five orbitals in terms of x, y, and z.

From here on, the number of orbitals in a given set will increase by two each time l increases by one. In other words,

  1. l = 3: The f orbitals will be a set of seven.
  2. l = 4: The g orbitals will be a set of nine.
  3. l = 5: The h orbitals will be a set of eleven.
  4. And so on ...

As a result the Energy Level Diagram available to a basic atom becomes more complex.

After taking into consideration the problems associated with orbital overlap, the Energy Level Diagram changes one final time. The resulting diagram is used by all atoms.

 Questions and comments should be sent to :
   kdrews@bcpl.net  

Updated September 1, 2000