Plan for Wed, 5 Nov 08• Lab Stuff

– Volumetric Analysis reports will be returned by Monday– Today’s lab (Calorimetry) will be written up as a formal report…– Your Calorimetry formal report will be due in class on Friday,

Nov 14th – No lab next week!

• Lecture: – Electron spin and the Pauli principle (7.8)– Orbital energies for polyelectronic atoms (7.9) – Aufbau (“filling-up”) principle (7.11)– Periodic trends (7.12)

• Exam 2, Quiz 4 regrades, and Quiz 5 returned

Which orbital is expected to have the greatest energy?

1s 2s

2p 3p

Electron Spin• Experiments demonstrated the

need for one more quantum number.

• Specifically, some particles (electrons in particular) demonstrated inherent angular momentum…

• Basically, this means that electrons have two ways of interacting with an applied magnetic field.

Interpretation: the electron is a bundle of “spinning” charge

“spin up”

“spin down”

Electron Spin (cont.)

• The new quantum number is ms (analagous to ml).

• For the electron, ms has two values:

+1/2 and -1/2

ms = 1/2

ms = -1/2

Pauli Exclusion PrincipleDefn: No two electrons may occupy

the same quantum state simultaneously.

In other words: electrons are very territorial. They don’t like other electrons horning in.

In practice, this means that only two electrons may occupy a given orbital, and they must have opposite spin.

Quantum Number Summary• n: principal quantum number

– index of size and energy of electron orbital– can have any integral value: 1, 2, 3, 4, …

• l: angular momentum quantum number– related to the shape of the orbitals– can have integral values 0 … n - 1

• ml: magnetic quantum number– related to orbital orientation (relative to the other l-level orbitals)– can have integral values –l … 0 … +l

• ms: electron spin quantum number– related to the “magnetic moment” of the electron– can have half-integral values –1/2 or +1/2

Polyelectronic Atoms• 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).

2 22

2 2 2 2

2

1 1sin

8 sin sin

hr

r r r

ZeE

r

No solution for polyelectronic atoms!!

Polyelectronic Atoms

+ e-

“Screening”: The presence of other electrons means a given electron does not feel the attraction of the nucleus as strongly as it would in hydrogen.

“Penetration”: Orbitals that have some probability density close to the nucleus will be energetically favored over orbitals that do not.

The Aufbau Principle• 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).

Orbital Energies

1s

2s

3s

4s

2p

3p 3d

Ene

rgy

H has only one electron, so all of the sublevels in a given principal level have the same energy...they are degenerate.

In many-electron atoms, a given electron is simultaneously attracted to the nucleus and repelled by other electrons, causing the energies of the sublevels to change relative to H.

When we put electrons in orbitals, we fill them in order of increasing energy, not n.

Let’s fill some orbitalsRULES• Orbitals are filled starting from the lowest energy.• The two electrons in an orbital must have

opposite spin.

• Example: Hydrogen (Z = 1)

1s 2s 2p

• Example: Helium (Z = 2)

1s 2s 2p

1s1

1s2

Let’s fill some more orbitals• Lithium (Z = 3)

1s 2s 2p

1s 2s 2p

• Berillium (Z = 4)

• Boron (Z = 5)

1s 2s 2p

1s22s1

1s22s2

1s22s22p1

Filling Orbitals (cont.)• Carbon (Z = 6)

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.

1s22s22p2

REVISED RULES• Orbitals are filled starting from the lowest energy.• The two electrons in an orbital must have opposite spin.• Hund’s Rule: the orbitals in degenerate series (such as 2p in the example above)

must each have an electron before any of them can have two.

Filling Orbitals (cont.)

• Carbon (Z = 6)

1s 2s 2p

1s22s22p2

• Nitrogen (Z = 7)

1s 2s 2p

1s22s22p3

Filling Orbitals (cont.)• Oxygen (Z = 8)

1s 2s 2p

1s 2s 2p

• Fluorine (Z = 9)

1s22s22p4

1s22s22p5

1s 2s 2p

• Neon (Z = 10)

1s22s22p6

full

Filling Orbitals (cont.)• Sodium (Z = 11)

3s

1s22s22p63s1Ne [Ne]3s1

1s 2s 2p

• Compare to Neon (Ne) (Z = 10)

1s22s22p6

full

1s 2s 2p 3s 3p

Filling Orbitals (cont.)• Sodium (Z = 11)

3s

1s22s22p63s1

3s 3p

• Phosphorus (P) (Z = 17)

[Ne] 3s23p3

Ne [Ne]3s1

Ne

3s 3p

• Argon (Z = 18)

[Ne] 3s23p6Ne

Filling Orbitals (cont.)• We now have the orbital configurations for the first 18 elements.

• Elements in same column have the same # of valence electrons!

Valence Electrons: The total number of s and p electrons in the highest occupied energy level.

Suppose there are four possible spin values instead of two. In this case, what would be the electron configuration of Cl?

A. 1s42s42p9

B. 1s22s22p63s23p5

C. 1s32s32p93s2

D. 1s62s62p5

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.

Back to Filling Orbitals• Elements Z=19 and Z= 20:

Z= 19, Potassium:

Z= 20, Calcium:

4s 4p

Ar

4s 4p

Ar

1s22s22p63s23p64s1 = [Ar]4s1

1s22s22p63s23p64s2 = [Ar]4s2

Filling Orbitals (cont.)

• Elements Z=21to Z=30 have occupied d orbitals:

Z= 21, Scandium:

Z= 30, Zinc:

4s

Ar

4s 4p

Ar

3d

4p 3d

1s22s22p63s23p64s23d1 = [Ar] 4s23d1

1s22s22p63s23p64s23d10 = [Ar] 4s23d10

The Aufbau Principal (cont.)• Elements Z=19 and Z= 20:

Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1

Z= 20, Calcium: 1s22s22p63s23p64s2 = [Ar]4s2

• Elements Z = 21 to Z = 30 have occupied d orbitals:

Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1

Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10

Z = 24, Chromium: [Ar] 4s13d5 exception

What if you forget the orbital-filling order?

1. Write down the orbitals for each n on separate lines.

2. Arrows drawn as shown will give you the order in which the orbitals should be filled.

Note that this scheme fills 4s before 3d, as expected.

Periodic Table This orbital filling scheme gives rise to the modern periodic table.

Periodic Table After Lanthanum ([Xe]6s25d1), we start filling 4f.

Periodic Table After Actinium ([Rn]7s26d1), we start filling 5f.

Periodic Table Row headings correspond to the highest occupied energy level for any element in that period.

“Valence” only refers to s and p electrons in the highest occupied energy level.

Periodic Table Column headings give total number of valence electrons for any element in that group.

What is the electron configuration for the indicated element?

A. 1s22s22p63s23p64s23d3

C. 1s22s22p63s23p64s23d2

B. 1s22s22p63s23p64s24d3

D. 1s22s22p73s23p64s23d2

Valence Electrons• The total number of s and p electrons in

the highest occupied energy level.• As we’ll see, all the “action” happens at

the valence electrons.• Elements in the same group (column) in

the periodic table have the same number of valence electrons.

• This means elements in the same group tend to have similar chemical properties.

Valence Electrons (cont.)Chemists use Lewis dot symbols to indicate the number of valence electrons in an atom.

The valence electrons are drawn as dots around the atomic symbol, with orbital occupancy indicated...that is, electrons that occupy the same orbital appear as paired dots.

HOWEVER, we will encounter situations where it is more convenient to spread the dots out around the element symbol.

C C