Electronic Structure
Sections 7.5-7.6, 8.2-8.4
RW Session ID = MSTCHEM1
Quantum Mechanical Theory
• Describes the behavior of electrons in atoms
• Electrons in atoms exist within orbitals
• Quantum numbers
– Principal quantum number
• Energy level or shell – relates to size and overall energy
• n = 1, 2, 3, 4, …
– Angular momentum quantum number (azimuthal QN)
• Sublevel or subshell – relates to the shape of the orbitals
• l = 0, …, n -1
(s,p,d,f,…)
– Magnetic quantum number
• Orbital – relates to the orientation of the orbitals
• ml = -l, …, +l
– Spin quantum number
• Electron – relates to the interaction of an electron with a magnetic field
• ms = - ½ , + ½
Principal Quantum Number
n = 1, 2, 3, …
– Shell (principal shell, principal level, energy level)
• Relates to the overall size and energy of an orbital
• Energy is lower for lower values of n
(due to interaction with the nucleus)
• Energy level spacing decreases as n increases
Principle Quantum Number
Three-dimensional solution of
Schrödinger's wave equation
Born’s probability
interpretation
Angular Momentum Quantum Number
(Azimuthal Quantum Number)
l = 0, 1, 2, … (n-1)
– Subshell (sublevel)
• Relates to the shape of the orbital
l=0
l=1
l=2
l=3
s
p
d
f
s orbitals are spherical
p orbitals are like two balloons tied at the knots
d orbitals are mainly like four balloons tied at the knot
f orbitals are mainly like eight balloons tied at the knot
Indeterminacy and Probability Distribution
• Newton’s laws of motion are deterministic
– The present determines the future
– Particles move in a trajectory that is determined by
velocity, position, and force
• The motion of an electron is indeterminate
– The future path can only be described statistically
– A probability distribution map shows where an electron is
likely to be found
Complementary properties
• Position & velocity
(Heisenberg’s uncertainty principle)
• Position & energy
(KE=½mv2 - energy & velocity are directly related)
Probability distribution map (orbital)
–
–
–
–
Location where electron is likely to be found
Energy is well-defined
Position is not well defined
Specified by three interrelated quantum numbers
p orbitals
d orbitals
f orbitals
Magnetic Quantum Number
ml = -l to +l
– orbital
• Relates to the orientation of the orbital
Electron Spin
A fundamental property of all electrons that
affects the number of electrons allowed in one
orbital
– All electrons have the same amount of spin
– The orientation of the electron spin is quantized
– There are only two possibilities, spin up and spin
down
Spin quantum number, ms = +1/2, -1/2
Electron Spin Experiment
Identify whether each of the following sets of quantum
numbers is valid.
n=0
not valid, n cannot equal 0
n=2
valid
n=3, l=1
valid
n=4, l=4
not valid, l cannot equal n
n=3, l=2, ml=+2
valid
n=1, l=0, ml=-1
not valid, ml cannot be > l
n=4, l=4, ml=-3, ms=+1/2
not valid, l cannot equal n
n=2, l=1, ml=-1, ms=-1/2
valid
Electron Configuration
Shows the particular subshells that are occupied
for an atom, including the number of electrons
in each subshell
N
1s22s22p3
Mg 1s22s22p63s2
• Ground state – lowest energy state
– Electrons generally occupy the lowest energy
orbitals available
Pauli exclusion principle
No two electrons in an atom can have the same
four quantum numbers
– Electrons in the same orbital have three identical
quantum numbers (n, l, and ml )
– Electrons in the same orbital must have different
spin quantum numbers (ms )
– Each orbital can have a maximum of only two
electrons with opposing spins
Electron Configurations
• Aufbau principle (“building up” principle)
– Electrons occupy the lowest energy orbitals available
in the ground state
– Electrons fill orbitals in the order: 1s, 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, …
• Hund’s rule – when filling degenerate orbitals,
electrons fill them singly first, with parallel spins
– No more than two electrons can occupy one orbital
(Pauli exclusion principle)
– First fill singly with parallel spins rather than paired
Sublevel Energy Splitting
E2s < E2p
E3s < E3p < E3d
E4s < E4p < E4d < E4f
• Coulomb’s law – the potential energy of two charge
particles depends on their charges and their separation
=
• Shielding – repulsion of one electron by others that
reduce the attraction to the nucleus
7s
6p
6s
6
d
5d
4f
5p
Energy
5s
4d
4p
3d
4s
3p
3s
2p
2s
1s
5f
1s2
2s2 2p6
3s2 3p6 3d10
4s2 4p6 4d10 4f14
5s2 5p6 5d10
6s2 6p6
7s2
Notice the following:
1. sublevels within an energy level are not degenerate
2. penetration of the 4th and higher energy levels is so strong that their s sublevel
is lower in energy than the d sublevel of the previous energy level
3. the energy difference between levels becomes smaller for higher energy levels
(and can cause anomalous electron configurations for certain elements)
Orbital Diagrams
• We often represent an orbital as a square and the
electrons in that orbital as arrows
– the direction of the arrow represents the spin of the
electron
unoccupied
orbital
orbital with
one electron
orbital with
two electrons
Electron Configurations
Orbital Blocks in the Periodic Table
Core Notation
Shorthand electron configuration
• Inner electron configuration is abbreviated using the
previous noble gas electron configuration by writing
the noble gas element symbol in square brackets
Mg
Fe
Te
[Ne]3s2
[Ar]4s23d6
[Kr]5s24d105p4
• Electron configurations abbreviated using the noble
gas for the inner electrons are referred to as core
notation
Write the ground state electron
configuration for the following elements.
Ti 1s22s22p63s23p64s23d2
core notation: [Ar]4s23d2
F 1s22s22p5
core notation: [He]2s22p5
I 1s22s22p63s23p64s23d104p65s24d105p5
core notation: [Kr]5s24d105p5
W 1s22s22p63s23p64s23d104p65s24d105p66s24f145d4
core notation: [Xe]6s24f145d4
Valence Electrons
• Chemical properties of an element depend on its valence
electrons, because they are held most loosely
• Elements in the same column have the same number of
valence electrons
• For main group elements
– The electrons in the outermost principal energy level (highest n)
• For transition elements
– The electrons in the outermost principal energy level and the
outermost d or f electrons (if the d or f subshell is not full)
– Core electrons
• Electrons in complete principal energy levels
• Electrons in complete d and f sublevels