General Chemistry/The Quantum Atom
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[edit] The Quantum Numbers
These four numbers are used to describe the location of an electron in an atom.
| Number | Symbol | Possible Values |
|---|---|---|
| Principal Quantum Number | n | 1, 2, 3, 4 ... |
| Angular Momentum Quantum Number | l | 0, 1, 2, 3 ... (n - 1) |
| Magnetic Quantum Number | ml | -l ... -1, 0, +1 ... +l) |
| Spin Quantum Number | ms | +½, -½ |
[edit] Principal Quantum Number (n)
Determines the shell the electron is in. The shell is the main component that determines the energy of the electron (higher n corresponds to higher energy), as well as nuclear distance (higher n means further from the nucleus). The row that an element is placed on the periodic table tells how many shells there will be. Helium (n=1), neon (n=2), argon (n=3), etc.
[edit] Angular Momentum Quantum Number (l)
Determines the subshell the electron is in. Each subshell has a unique shape and a letter name. The s orbital is shaped like a sphere and occurs when l=0. The p orbitals (there are three) are shaped like teardrops and occur when l=1. The d orbitals (there are five) occur when l=2. The f orbitals (there are seven) occur when l=3. (By the way, when l=4, the orbitals are "g orbitals", but they (and the l=5 "h orbitals") can safely be ignored in general chemistry.)
Here are pictures of the orbitals. Keep in mind that they do not show the actual path of the electrons, due to the Heisenberg Uncertainty Principle. Instead, they show the area where the electron is most likely to occur (say, 90% of the probability).
| S orbital → |  |
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| P orbitals → |  |
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| D orbitals → |  |
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| F orbitals → |  |
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[edit] Magnetic Quantum Number (ml)
Determines the orbital in which the electron lies. E.g. there are three p orbitals in shell n=2; the magnetic quantum number determines which one of these orbitals the electrons reside in. The different orbitals are oriented at different angles around the nucleus. See how each p orbital has the same general shape, but they point in different directions around the nucleus.
[edit] Spin Quantum Number (ms)
Determines the "spin" on the electron.
[edit] Some Examples
Let's examine the quantum numbers of electrons from a magnesium atom. Remember that each list of numbers corresponds to (n, l, ml, ms).
| Two s electrons: | (1, 0, 0, +½) | (1, 0, 0, -½) | ||||
| Two s electrons: | (2, 0, 0, +½) | (2, 0, 0, -½) | ||||
| Six p electrons: | (2, 1, -1, +½) | (2, 1, -1, -½) | (2, 1, 0, +½) | (2, 1, 0, -½) | (2, 1, 1, +½) | (2, 1, 1, -½) |
| Two s electrons: | (3, 0, 0, +½) | (3, 0, 0, -½) |
[edit] The Periodic Table
Notice a pattern on the periodic table. Different areas, or blocks, have different types of electrons. The two columns on the left make the s-block. The six columns on the right make the p-block. The large area in the middle (transition metals) makes the d-block. The bottom portion makes the f-block. Each row introduces a new shell (aka energy level). Basically, the row tells you the how many shells of electrons there will be, and the column tells you which subshells will occur (and which shells they occur in). The value of ml can be determined by some of the rules we will learn in the next chapter. The value of ms doesn't really matter as long as there are no repeating values in the same orbital.
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To see the pattern better, take a look at this periodic table. |
