Quantum MechanicsQuantum Mechanics

Atomic StructureAtomic Structure

Electron Cloud ModelElectron Cloud Model

““Cloud” is a Cloud” is a probability probability distribution.distribution.

Probability is the most Probability is the most information that we information that we can possibly know.can possibly know.

Schrödinger Wave EquationSchrödinger Wave Equation

)(|2

)(|)( tt

hittH

Allows you to calculate the probability of an Allows you to calculate the probability of an electron being in a given place and energy.electron being in a given place and energy.

Gives us a good idea of where the electrons are Gives us a good idea of where the electrons are in an atom.in an atom.

Quantum NumbersQuantum Numbers Address of an electron in an atomAddress of an electron in an atom

The collection of 4 quantum numbers gives you The collection of 4 quantum numbers gives you as much information as you can possibly get for as much information as you can possibly get for a particular electron.a particular electron.

Describes a hierarchical structureDescribes a hierarchical structure ShellShell SubshellSubshell OrbitalsOrbitals Electron Spin StatesElectron Spin States

Principle Quantum NumberPrinciple Quantum Number How far from the How far from the

nucleus an electron is.nucleus an electron is. Also describes most of Also describes most of

the energy.the energy. Will be integers from 1 Will be integers from 1

to 7 for our purposes.to 7 for our purposes. Call this the “shell” the Call this the “shell” the

electron is in.electron is in. n = 1 (the first shell) is n = 1 (the first shell) is

shell closest to nucleus shell closest to nucleus with lowest energywith lowest energy

nn

Angular Momentum Quantum Angular Momentum Quantum Number Number

Angular momentum Angular momentum describes movement describes movement in circles.in circles.

Describes the shape Describes the shape of the area an of the area an electron is in.electron is in.

Can be integers from Can be integers from 0 through 30 through 3

Usually called the Usually called the “sub-shell”“sub-shell”

ℓℓA cursive L

Angular Momentum Quantum Angular Momentum Quantum NumberNumber

Specific Values have specific namesSpecific Values have specific names

ℓ ℓ = 0 is called an s subshell= 0 is called an s subshell ℓ ℓ = 1 is called a p subshell= 1 is called a p subshell ℓ ℓ = 2 is called a d subshell= 2 is called a d subshell ℓ ℓ = 3 is called a f subshell= 3 is called a f subshell

s Orbitals within an s Subshells Orbitals within an s Subshell Have a spherical shapeHave a spherical shape

p Orbitals within a p Subshellp Orbitals within a p Subshell

Have a dumbbell Have a dumbbell shapeshape

d Orbitals within a d Subshelld Orbitals within a d Subshell

Have a four leaf Have a four leaf clover shapeclover shape

f Orbitals within an f Subshellf Orbitals within an f Subshell

Look like two d Look like two d orbitals pushed orbitals pushed together in the middletogether in the middle

Magnetic Quantum NumberMagnetic Quantum Number Describe which direction Describe which direction

the shapes point in the shapes point in space.space.

Refers to specific orbitalsRefers to specific orbitals

OrbitalOrbital – area of space – area of space analogous to an orbit but analogous to an orbit but taking probability into taking probability into accountaccount

Each orbital holds up to Each orbital holds up to two electrons.two electrons.

mmℓℓm with a subscript L

Magnetic Quantum NumberMagnetic Quantum Number

Only one direction in space for a sphereOnly one direction in space for a sphere Only one s orbitalOnly one s orbital

Magnetic Quantum NumberMagnetic Quantum Number

There are three There are three directions for p directions for p orbitals to pointorbitals to point

There are three p There are three p orbitalsorbitals

Magnetic Quantum NumberMagnetic Quantum Number

There are There are five five solutions solutions for the d for the d orbitalsorbitals

Magnetic Quantum NumberMagnetic Quantum Number

Seven f Seven f orbitalsorbitals

Magnetic Quantum NumberMagnetic Quantum Number

n = 1 is where the s subshells startn = 1 is where the s subshells start

n = 2 is where the p subshells startn = 2 is where the p subshells start

n = 3 is where the d subshells startn = 3 is where the d subshells start

n = 4 is where the f subshells startn = 4 is where the f subshells start

Spin Quantum NumberSpin Quantum Number

Describes the spin Describes the spin of an electronof an electron

Imagine a top Imagine a top spinning on its axisspinning on its axis

Can either be +½ Can either be +½ or -½ or -½

mmssm with a subscript s

For the Math PeopleFor the Math People

For a given electronFor a given electron

n = [1, 2, 3, 4, 5, 6, or 7]n = [1, 2, 3, 4, 5, 6, or 7]

ℓ ℓ = [0, … n – 1]= [0, … n – 1]

mmℓ ℓ = [-= [-ℓ … +ℓ]ℓ … +ℓ]

mmss = [-½, +½] = [-½, +½]

How do we apply all this to How do we apply all this to electrons?electrons?

Aufbau Principle Aufbau Principle – fill up electrons in the – fill up electrons in the lowest energy firstlowest energy first

Use the diagonal line diagram.Use the diagonal line diagram.

HydrogenHydrogen

Start with the simplest atom.Start with the simplest atom.

Has one electronHas one electron

Orbital Filling DiagramsOrbital Filling Diagrams

Use horizontal lines to represent an orbitalUse horizontal lines to represent an orbital

Use half arrows to represent electronsUse half arrows to represent electronsArrow up means spin +½Arrow up means spin +½Arrow down means spin -½Arrow down means spin -½

HeliumHelium

Has two electronsHas two electrons

Where do you put the extra electron?Where do you put the extra electron?

Pauli Exclusion PrinciplePauli Exclusion Principle – No two electrons in – No two electrons in the same atom can have the same set of four the same atom can have the same set of four quantum numbersquantum numbers

Practically this means two electrons in the same Practically this means two electrons in the same orbital must have opposite spins.orbital must have opposite spins.

More ElementsMore Elements

LithiumLithiumThree electronsThree electrons

BerylliumBerylliumFour electronsFour electrons

BoronBoron

5 electrons5 electronsDoes it matter which p-orbital you put the Does it matter which p-orbital you put the

electron in?electron in?No because they are all equivalentNo because they are all equivalent

DegenerateDegenerate – have the same energy – have the same energy

CarbonCarbon

Six electronsSix electrons

Where does the sixth electron go?Where does the sixth electron go?

Hund’s RuleHund’s Rule – Electrons stay unpaired as – Electrons stay unpaired as long as possible.long as possible.

More ElementsMore Elements

NitrogenNitrogen7 electrons7 electrons

OxygenOxygen8 electrons8 electrons

FluorineFluorine9 electrons9 electrons

NeonNeon10 electrons10 electrons

More ElementsMore Elements

ChromiumChromium

KryptonKrypton

More ElementsMore Elements

TinTin

PromethiumPromethium

Even More ElementsEven More Elements

TungstenTungsten

LeadLead

Even More ElementsEven More Elements

PlutoniumPlutonium

BohriumBohrium