Electron Configuration Energy Diagrams

We have just seen that electrons fill orbitals in shells and subshells in a regular pattern, but why does it follow this pattern? There are three principles which should be followed to properly fill electron orbital energy diagrams:

1. The Aufbau principle
2. The Pauli exclusion principle
3. Hund’s rule

The overall pattern of the electron shell filling order emerges from the Aufbau principle (German for “building up”):  electrons fill the lowest energy orbitals first. Increasing the principle quantum number, n, increases orbital energy levels, as the electron density becomes more spread out away from the nucleus. In many-electron atoms (all atoms except hydrogen), the energy levels of subshells varies due to electron-electron repulsions. The trend that emerges is that energy levels increase with value of the angular momentum quantum number, l, for orbitals sharing the same principle quantum number, n. This is demonstrated in Figure 1.1, where each line represents an orbital, and each set of lines at the same energy represents a subshell of orbitals.

Figure 1.1. Generic energy diagram of orbitals in a multi-electron atom.

As previously discussed, the Pauli exclusion principle states that we can only fill each orbital with a maximum of two electrons of opposite spin. But how should we fill multiple orbitals of the same energy level within a subshell (eg. The three orbitals in the 2p subshell)? Orbitals of the same energy level are known as degenerate orbitals, and we fill them using Hund’s rule: place one electron into each degenerate orbital first, before pairing them in the same orbital.

Let’s examine a few examples to demonstrate the use of the three principles.

Boron is atomic number 5, and therefore has 5 electrons. First fill the lowest energy 1s orbital with two electrons of opposite spin, then the 2s orbital with 2 electrons of opposite spin and finally place the last electron into any of the three degenerate 2p orbitals (Figure 1.2).

Figure 1.2. Boron electron configuration energy diagram

Moving across the periodic table, we follow Hund’s rule and add an additional electron to each degenerate 2p orbital for each subsequent element (Figure 1.3). At oxygen we can finally pair up and fill one of the degenerate 2p orbitals.

Figure 1.3. Electron configuration energy diagrams for carbon, nitrogen and oxygen.

Exercises

1. Give two possible sets of four quantum numbers for the electron in an H atom.

2. Give the possible sets of four quantum numbers for the electrons in a Li atom.

3. How many subshells are completely filled with electrons for Na? How many subshells are unfilled?

4. How many subshells are completely filled with electrons for Mg? How many subshells are unfilled?

5. What is the maximum number of electrons in the entire n = 2 shell?

6. What is the maximum number of electrons in the entire n = 4 shell?

7. Write the complete electron configuration for each atom.

a)  Si, 14 electrons

b)  Sc, 21 electrons

8.  Write the complete electron configuration for each atom.

a)  Br, 35 electrons

b)  Be, 4 electrons

9.  Write the complete electron configuration for each atom.

a)  Cd, 48 electrons

b)  Mg, 12 electrons

10.  Write the complete electron configuration for each atom.

a)  Cs, 55 electrons

b)  Ar, 18 electrons

11.  Write the abbreviated electron configuration for each atom in Exercise 7.

12.  Write the abbreviated electron configuration for each atom in Exercise 8.

13.  Write the abbreviated electron configuration for each atom in Exercise 9.

14.  Write the abbreviated electron configuration for each atom in Exercise 10.

15.   Draw electron configuration energy diagrams for potassium, and bromine.

Answers

1.

{1, 0, 0, 1/2} and [1, 0, 0, −1/2}

3.

Three subshells (1s, 2s, 2p) are completely filled, and one shell (3s) is partially filled.

5.

8 electrons

7.

a)  1s²2s²2p⁶3s²3p²

b)  1s²2s²2p⁶3s²3p⁶4s²3d¹

9.

a)  1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰

b)  1s²2s²2p⁶3s²

11.

a)  [Ne]3s²3p²

b)  [Ar]4s²3d¹

13.

a)  [Kr]5s²4d¹⁰

b)  [Ne]3s²

15.