The n+l rule, or (n+l) rule, is a guideline used to predict the order in which electrons fill atomic orbitals within a neutral isolated atom.
Understanding the (n+l) Rule
The rule states that the energy of an atomic orbital is determined by the sum of its principal quantum number (n) and azimuthal quantum number (l), as indicated in the reference.
- Principal Quantum Number (n): This number corresponds to the energy level or shell of the electron, with higher numbers indicating higher energy levels (n = 1, 2, 3, etc.).
- Azimuthal Quantum Number (l): Also known as the angular momentum quantum number, this number describes the shape of the orbital and has values ranging from 0 to n-1. The values for l correlate to specific subshells: l=0 is an s subshell, l=1 is a p subshell, l=2 is a d subshell, and l=3 is an f subshell.
Core Principle
The (n+l) rule has a simple core principle:
- Lower (n+l) value means lower energy. In a neutral isolated atom, if an orbital has a lower sum of (n+l), it will have a lower energy and will be filled before an orbital with a higher (n+l) value.
How to Apply the n+l Rule
Here’s how the n+l rule is applied:
- Calculate the (n+l) value: For each orbital, add its principal quantum number (n) and azimuthal quantum number (l).
- Compare the values: The orbital with the lowest (n+l) value will have the lowest energy and fill first.
- If (n+l) values are equal: If two orbitals have the same (n+l) value, the orbital with the lower n value will be filled first.
Example:
Let's compare 3d and 4s orbitals:
| Orbital | n | l | n + l |
|---|---|---|---|
| 3d | 3 | 2 | 5 |
| 4s | 4 | 0 | 4 |
According to the (n+l) rule, 4s (n+l=4) has a lower energy than 3d (n+l=5), therefore 4s will be filled first.
Practical Insight
- The (n+l) rule provides an excellent way of remembering the order of filling atomic orbitals in atoms.
- The rule breaks down when considering ions or heavier atoms, where other effects become important. However, it is reliable for neutral atoms and up to a reasonable atomic number.
Summary of (n+l) Rule
The (n+l) rule is based on the sum of principal (n) and azimuthal (l) quantum numbers. The lower the sum of (n+l), the lower the energy level in a neutral atom and the sooner that orbital will be filled. If two orbitals have the same (n+l) sum, the one with the lower n value will be filled first.
