Chapter 8:Electron Configurations

and Periodicity

Electron Spin & the Pauli Exclusion Principle

3 quantum numbers (n, l, ml) define the energy, size, shape, and spatial orientation of each atomic orbital.

To explain how electrons populate atomic orbitals in an atom, we need a 4th quantum number.

4. spin quantum number, ms

◆ electrons behave like they are spinning around an axis

◆ spinning of a charged particle creates a magnetic field

magnetic field created has a direction

if e– spins clockwise, magnetic field is one direction (ms = +!)

if e– spins counter-clockwise, magnetic field is opposite direction (ms = –!)

Experimental Evidence of Electron Spin:Stern & Gerlach (1921)

How Do Electrons Populate Atomic Orbitals?Pauli Exclusion Principle (1925)

No 2 electrons in an atom can have the same set of 4 quantum numbers.

◆ n, l, ml define the atomic orbital

◆ ms will define the electrons in the orbital

If there are only 2 possible ms values, then each atomic orbital can hold no more than 2 electrons;

specifically, one e– must have ms = +!and the other e– must have ms = –!

◆ These 2 e–’s in an atomic orbital are said to be spin-paired.

Effective Nuclear Charge (Zeff)What is the charge felt by an electron in an atom?

◆ depend on n and l of the orbital where the e– lives

◆ the farther the electron is from the nucleus:the less the force of attraction to the nucleusthe greater the e– - e– repulsion

◆ an outer shell electron is “shielded” by inner shell e–’s

Effective Nuclear Charge (Zeff)

Zeff = Zactual – shielding factor

Zeff and Atomic Orbitals

◆ relationship between Zeff and n

probability of an e– being close to the nucleus:

n = 1 > n = 2 > n = 3

Zeff felt by an e– in an orbital:

n = 1 > n = 2 > n = 3

energy of orbital:

n = 1 < n = 2 < n = 3

Zeff and Atomic Orbitals

◆ relationship between Zeff and l (within a same shell)

probability of an e– being close to the nucleus:l = 0 > l = 1 > l = 2

or: s > p > d

Zeff felt by an e– in an orbital:l = 0 > l = 1 > l = 2

or: s > p > d

energy of orbital:s < p < d

Electron Configurations

◆ give complete electronic description for every element

◊ predict orbitals occupied by electrons

◊ write electron configurations

◊ draw orbital diagrams

◆ follow set of 3 rules: Aufbau (“building up”) Principle

◊ each successive electron will go into the lowest energy orbital available

◊ this results in the lowest energy, ground state configuration

The Aufbau Principle1. Lower energy orbitals fill before higher energy orbitals.

◆ use the Relative Energies of Atomic Orbitals diagram

2. An orbital can accommodate a maximum of 2 e–’s which must be spin-paired.

◆ Pauli Exclusion Principle

3. Hund’s Rule:If 2 or more degenerate orbitals are available, one e– will go into each orbital until all are half-full.

◆ the e–’s in the singularly populated orbitals must have the same ms

After all degenerate orbitals are half-full, then a 2nd e– may be added to fill the orbitals.

In What Order Do Atomic Orbitals Populate?Lower Energy to Higher Energy

examples:

Write the ground state electron configurations, and complete an orbital diagram for neutral atoms of the following elements.

N (7 e–) : 1s2 2s2 2p3

Al (13 e–) : 1s2 2s2 2p6 3s2 3p1

1s 2s 2p

1s 2s 2p 3s 3p

↑↓ ↑↓ ↑ ↑ ↑

↑↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

Closed Shells and Subshells & Using Noble Gas Core Symbolism in Electron Configurations

Sc (21 electrons): 1s2 2s2 2p6 3s2 3p6 4s2 3d1

1s 2s 2p 3s 3p 4s 3d

Ga (31 electrons): [Ar] 4s2 3d10 4p1

4s 3d 4p

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑↓↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑

↑

Some Terminology:

inner shell electrons outer shell electrons

core electrons valence electrons

paramagnetic diamagnetic

Some Anomalies in Electron Configurations:

◆ result from unusual stability of half-filled or completely filled shells or subshells

◆ heavy elements (above atomic # 40) ∆E between orbitals is smaller, so anomalies are common

4s 3d 4s 3d

4s 3d 4s 3d

!

!

ex: Cr predict: [Ar] 4s2 3d4 actual: [Ar] 4s1 3d5

ex: Cu predict: [Ar] 4s2 3d9 actual: [Ar] 4s1 3d10

↑↓

↑↓ ↑↓ ↑↓↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑

Electron Configurations and the Periodic Table

Periodic Trends

The goal is to use our understanding of electron configurations and Zeff to understand trends in:

◆ atomic radius

◆ ionization energy

◆ electron affinity

How does a given property change from left to right across periodic table?

How does a given property change from

top to bottom of periodic table?

Periodic Trend in Zeff

Effective Nuclear Charge,Zeff

increase

decrease

Na Mg Al Si P S Cl Are–

configuration[Ne]3s1 [Ne]3s2 [Ne]3s2 3p1 [Ne]3s2 3p2 [Ne]3s2 3p3 [Ne]3s2 3p4 [Ne]3s2 3p5 [Ne]3s2 3p6

actual nuclear charge 11 12 13 14 15 16 17 18

# core e–’s 10 10 10 10 10 10 10 10

# valence e–’s 1 2 3 4 5 6 7 8

Zeff +1 +2 +3 +4 +5 +6 +7 +8

Atomic Radius

radius (typically in pm or Å) of neutral atoms of elements

trend:atomic radius decreases left to right across the periodic table

atomic radius increases top to bottom of the periodic table

Atomic Radius

decrease

increase

Periodic Trend in Atomic Radius

Periodic Trend in Atomic Radius

Ionization Energy

increasedecrease

Ionization Energy

ionization energy – the energy required to remove an electron from a gas phase atom or ion in its ground state

X (g) " X+ (g) + e– ; endothermic

Periodic Trend in Ionization Energy

◆ Note the unexpected changes between groups IIA & IIIA, and groups VA & VIA. Why? Think about e– configurations.

Periodic Trend in Ionization Energyconsider successive ionization energies:

M (g) ! M+ (g) + e– 1st ionization energyM+ (g) ! M2+ (g) + e– 2nd ionization energyM2+ (g) ! M3+ (g) + e– 3rd ionization energy

◆ It becomes successively harder to remove an e– from a positively charged species because of forces of electrostatic attraction.

Periodic Trend in Ionization Energy

◆ removing a core e– costs MUCH more energy than removing a valence e–

◆ Valence electrons are most easily lost during ionization, and are gained, lost, or shared during chemical reactions.

Electron Affinity

Electron Affinity

* increase*decrease

electron affinity – change in energy that occurs when an electron is added to an isolated gas phase atom.

X (g) + e– ! X– (g)

* increase means becomes larger, negative value ∴ more favorable for anion formation;

decrease means becomes smaller, negative value ∴ less energy released and less favorable for anion formation

Periodic Trend in Electron Affinity

note: where electron affinity values are > 0, anion formation is very unfavorable; alkaline earth metals & the noble gases

Periodic Trend in Electron Affinity