7.1: The Pauli Exclusion Principle
- Page ID
- 158448
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Learning Objectives
- Determine the four quantum numbers associated with an electron in orbital
- Summarize the Pauli Exclusion Principle
- Identify the number of electrons in a shell, subshell, or orbital
Pauli Exclusion Principle
The Pauli exclusion principle states that no two electrons can have the same four quantum numbers. The first three (n, l, and ml) may be the same, but the fourth quantum number must be different. A single orbital can hold a maximum of two electrons, which must have opposing spins; otherwise they would have the same four quantum numbers, which is forbidden. One electron is spin up (ms = +1/2) and the other would spin down (ms = -1/2).
In the first example, the 2 electrons would have the same ms quantum number, and therefore, will be incorrect, since no two electrons are exactly alike. To correct this, we represent one electron as pointing up and the other is pointing down. In both cases, n=2, l=0, ml=0, but the orange electron has an ms= +1/2 and the blue electron has an ms=-1/2.
So, this tells us that each subshell has double the electrons per orbital. The s subshell has 1 orbital that can hold up to 2 electrons, the p subshell has 3 orbitals that can hold up to 6 electrons, the d subshell has 5 orbitals that hold up to 10 electrons, and the f subshell has 7 orbitals with 14 electrons. Let's summarize the number of electrons held in Shells and Subshells of n= 1 to n=5.
| Shell (n) | Subshell | Number of Orbitals (2l+1) | Number of Electrons in each Subshell [2(number of orbitals)] | Total Number of Electrons in the nth shell (2n2) or 2(total number of orbitals in the shell) |
| 1 | s | 1 | 2 | 2 |
| 2 |
s p |
1 3 |
2 6 |
8 |
| 3 |
s p d |
1 3 5 |
2 6 10 |
18 |
| 4 |
s p d f |
1 3 5 7 |
2 6 10 14 |
32 |
| 5 |
s p d f g* |
1 3 5 7 9 |
2 6 10 14 18 |
50 |
*Note: there is currently no known element whose electrons occupy the g subshell.
Example 1: Hydrogen and Helium
The first three quantum numbers of an electron are n=1, l=0, ml=0. Only two electrons can correspond to these, which would be either ms = -1/2 or ms = +1/2. As we already know from our studies of quantum numbers and electron orbitals, we can conclude that these four quantum numbers refer to the 1s subshell. If only one of the ms values are given then we would have 1s1 (denoting hydrogen) if both are given we would have 1s2 (denoting helium). Visually, this is be represented as:
As shown, the 1s subshell can hold only two electrons and, when filled, the electrons have opposite spins.
Exercise \(\PageIndex{1}\)
How many electrons are found in the p subshell? In the p orbital?
- Answer
-
Six electrons are in the p subshell. Two in in the p orbital. As a matter of fact, any individual orbital, not matter the shell or subshell will have two electrons.