1. Lecture 19: The Aufbau Principle
Reading: Zumdahl
Outline:
Spin
The Aufbau Principle
Filling up orbitals and the Periodic Table

2. Spin
Further experiments demonstrated the need for one more quantum number.
Specifically, some particles (electrons in particular) demonstrated inherent angular momentum.

3. Spin (cont.) The new quantum number is ms (analogous to ml).
For the electron, ms has two values:
+1/2 and -1/2
ms = 1/2
ms = -1/2

4. The Aufbau Principal
For polyelectronic atoms, a direct solution of the Schrodinger Eq. is not possible.
When we construct polyelectronic atoms, we use the hydrogen-atom orbital nomenclature to discuss in which orbitals the electrons reside.
This is an approximation (and it is surprising how well it actually works).

5. The Aufbau Principal (cont.)
When placing electrons into orbitals in the construction of polyelectronic atoms, we use the Aufbau Principle.
This principle states that in addition to adding protons and neutrons to the nucleus, one simply adds electrons to the hydrogen-like atomic orbitals
Pauli exclusion principle: No two electrons may have the same quantum numbers. Therefore, only two electrons can reside in an orbital (differentiated by ms).

6. The Aufbau Principal (cont.)
Finally, orbitals are filled starting from the lowest energy.
Example: Hydrogen
1s1 1s 2s 2p
Example: Helium (Z = 2)
1s2 1s 2s 2p

7. The Aufbau Principal (cont.)
Lithium (Z = 3)
1s22s1 1s 2s 2p
Berillium (Z = 4)
1s22s2 1s 2s 2p
Boron (Z = 5)
1s22s22p1 1s 2s 2p

8. The Aufbau Principal (cont.)
Carbon (Z = 6)
1s22s22p2 1s 2s 2p
Hund’s Rule: Lowest energy configuration is
the one in which the maximum number of unpaired electrons
are distributed amongst a set of degenerate orbitals.
Nitrogen (Z = 7)
1s22s22p3 1s 2s 2p

9. The Aufbau Principal (cont.)
Oxygen (Z = 8)
1s22s22p4 1s 2s 2p
Fluorine (Z = 9)
1s22s22p5 1s 2s 2p
Neon (Z = 10)
1s22s22p6
full 1s 2s 2p

10. The Aufbau Principal (cont.)
Sodium (Z = 11) Ne
1s22s22p63s1
[Ne]3s1 3s
Argon (Z = 18)
[Ne] 3s23p6 Ne 3s 3p

11. Suppose there are four possible spin values instead of two
Suppose there are four possible spin values instead of two. In this case, what would be the electron configuration of Cl?
1s42s42p9
B. 1s22s22p63s23p5
C. 1s32s32p93s2
D. 1s62s62p5

12. Which of the following electron configuration represents an excited state of N?
A. 1s22s22p3
B. 1s22s22p23s1
C. 1s22s32p2
D. 1s22s22p2

13. The Aufbau Principal (cont.)
• We now have the orbital configurations for the first 18 elements.
• Elements in same column have the same # of valence electrons!

14. The Aufbau Principal (cont.)
• Similar to Sodium, we begin the next row of the periodic
table by adding electrons to the 4s orbital.
• Why not 3d before 4s?
• 3d is closer to the nucleus
• 4s allows for closer
approach; therefore, is
energetically preferred.

15. The Aufbau Principal (cont.)
• Elements Z=19 and Z= 20:
Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1
Z= 20, Calcuim: 1s22s22p63s23p64s2 = [Ar]4s2
• Elements Z=21to Z=30 have occupied d orbitals:
Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1
Z = 24, Chromium: [Ar] 4s13d5
exception
Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10

16. The Aufbau Principal (cont.)
• This orbital filling scheme gives rise to the modern periodic table.

17. The Aufbau Principal (cont.)
• After Lanthanum ([Xe]6s25d1), we start filling 4f.

18. The Aufbau Principal (cont.)
• After Actinium ([Rn]7s26d1), we start filling 5f.

19. What is the electron configuration for the indicated element?
A. 1s22s22p63s23p64s23d3
B. 1s22s22p63s23p64s24d3
C. 1s22s22p63s23p64s23d2
D. 1s22s22p73s23p64s23d2

20. The Aufbau Principal (cont.)
• Heading on column given total number of valence electrons.

21. The Aufbau Principal (cont.)

22. Summary
Electrons go into hydrogen-like orbitals to construct polyelectronic atoms.
Remember the adjacent “trick” for remembering how to fill orbitals.