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					Wave Functions:

Schrödinger hypothesized that energy changes of the electrons in an atom are simply the result of
an electron changing wave functions (orbits) . His wave functions indicate areas within an atom
where one has the greatest probability of finding an electron at any given time. These areas of
probability of finding an electron have different shapes for the different quantum numbers.

The key points of Schrödinger’s theories :

Quantum numbers are used to describe an electron in an orbital. “n” is the principle quantum
number and indicates the energy level of the electrons. The value n2 determines the number of
possible orbitals for each energy level.

“l” is the second (azimithal) quantum number and designates the shape of an orbital. The letters
s, p, d, f can be used to specify the second quantum number. s orbitals are spherical, p orbitals
are double lobed, and the d and f orbitals are also composed of lobes but are more complex.

“m” is the third (magnetic) quantum number and describes the orbital’s orientation about the x,
y, and z axis. It’s value is dependent on the value of “l”. In order to define a given orbital 3
quantum numbers must be used.

The spectral analysis of multi-electron atoms suggests that only 2 electrons can occupy the same
orbital. The electrons behave as if they spin about their own axis. One electron is arbitrarily
assigned a spin of +½ and the other a spin of -½. This spin characteristic of electrons is the 4th
quantum number and is designated by the letter “ms”

1st energy level – n=1
has only 1 orbital called the s orbital
(s stands for sharp)

2nd energy level n=2
has 4 orbitals, the s orbital and the 3 p orbitals.
(p stands for principle)

3rd energy level n=3
has 9 orbitals, the s orbital, the 3 p orbitals and the 5 d orbitals
(d stands for diffuse)

4th energy level n=4
has 16 orbitals, the s orbital, the 3 p orbitals, the 5 d orbitals, and the 7 f orbitals
The quantum #’s can have only certain values.

       n = 1, 2, 3, 4, … (integer values)

       l = 0 to n

       ml = -l to l

       ms = ½

The first 3 quantum numbers define the orbitals that are filled for a particular atom in the ground
state. The 4th quantum number allows for two electrons to occupy each sub-orbital.

The Pauli Exclusion Principle says that if two electrons occupy the same orbital they must have
opposite spins. In other words, no two electrons can have the same set of 4 identical quantum

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