Compare the energies of the following orbitals in a multi-electronic atom:
| Orbital | n | l | m |
|---|---|---|---|
| A | 3 | 0 | 0 |
| B | 3 | 1 | -1 |
| C | 4 | 2 | 0 |
| D | 3 | 2 | 1 |
In multi-electron atoms, orbital energy depends primarily on the value of (n + l), where n is the principal quantum number and l is the azimuthal quantum number. This is known as the (n + l) rule or Madelung rule.
The orbital with higher (n + l) value has higher energy. If two orbitals have the same (n + l) value, then the orbital with larger n has higher energy.
Let us calculate (n + l) for each orbital:
| Orbital | n | l | n+l |
|---|---|---|---|
| A (3s) | 3 | 0 | 3 |
| B (3p) | 3 | 1 | 4 |
| C (4d) | 4 | 2 | 6 |
| D (3d) | 3 | 2 | 5 |
Now arrange according to increasing energy:
3s < 3p < 3d < 4d
Therefore:
C > D > B > A
The magnetic quantum number m has no effect on energy in the absence of an external magnetic field. Only n and l determine the relative energies in multi-electron systems. Understanding orbital energy order is important for writing electronic configurations, predicting chemical properties, and explaining periodic trends.
C > D > B > A