Download Pauli Exclusion Principle

Pauli Exclusion Principle
Otto Stern and Walther first observed electron spin magnetism when they directed a
beam of silver atoms into the field of a specially designed magnet. The beam of atoms is
split in half by the magnetic field. The beam of atoms is split into two because the
electron in each atom behaves as a tiny magnet with only two possible orientations. Not
all of the many arrangements of electrons among the orbitals of an atom are physically
possible. The Pauli exclusion principle states that no two electrons in the same atom can
have have all four quantum numbers the same. Because electrons in a given orbital must
have the same values of n, l, and ml (for example n = 4, l = 0, ml = 0 in the 4s orbital) they
must have different values of ms, Only two values of ms are possible: +1/2 and -1/2. That
means that an atomic orbital can accommodate only two electrons and these electrons
must have opposing spins.
The Aufbau Principle
The electron configuration of an atom gives the distribution of electrons among atomic
orbitals in the atom. Two general methods are used to show electron configurations. The
subshell notation uses numbers to designate the principal shells and the letters s, p, d, and
f to identify the subshells. A superscript following the letter indicates the number of
electrons in the designated subshell. The ground state electron configuration for nitrogen
would be 1s22s22p3. A drawback to this method of showing the electron configuration
is that it does not tell us how the three 2p electrons are distributed among the three 2p
orbitals. We can show this by using an orbital diagram in which boxes are used to
indicate orbitals within subshells and arrows to represent electrons in these orbitals. The
direction of the arrows represent the directions of the electron spins. The orbital diagram
for nitrogen is
1s
2s
2p
The way we arrive at electron configurations such as the one for nitrogen above is to use
a set of rules collectively called the aufbau principle.
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Electrons occupy orbitals of the lowest energy available
No two electrons in the same atom may have all four quantum numbers alike
When entering orbitals of the same energy, electrons initially occupy them singly
ant with the same spin
Electrons fill orbitals in order of the quantum number sum (n + l). For equal (n +
l) sums, fill levels in order of increasing n.
A mnemonic diagram for the aufbau principle known as the diagonal rule is shown here
The aufbau principle is really a thought process in which we think about building up an
atom from the one that preceeds it in atomic number, by adding a proton and neutrons to
the nucleus and one electron to the appropriate atomic orbital.
There are some exceptions to the to the aufbau principle. The first is chromium (Z = 24),
the aufbau principle predicts the an electron configuration of [Ar]3d44s2 but
experimentally we find it to be [Ar]3d54s1. The next exception found is that of copper (Z
= 29), the predicted electron configuration is [Ar]3d94s2 but experimentally we find it to
be [Ar]3d104s1. The reason for these and other exceptions are not completely
understood, but it seems that a half-filled 3d subshell in the case of chromium or a
completely-filled 3d subshell in the case of copper lend a special stabilty to the observed
electron configurations. There is no need to dwell on these exceptions, the point to
remember is that the aufbau principle predicts the correct electron configuration most of
the time and that the energy of the predicted electron configuration is very close to the
ground state energy.