1 Electrons in Atoms. 2 Dalton’s Atomic Theory John Dalton (1766-1844) had four theories John Dalton (1766-1844) had four theories 1. All elements are

1

Electrons in Electrons in AtomsAtoms

2

Dalton’s Atomic TheoryDalton’s Atomic Theory John Dalton (1766-1844) had four theoriesJohn Dalton (1766-1844) had four theories

1.1. All elements are composed of submicroscopic All elements are composed of submicroscopic indivisible particles called atomsindivisible particles called atoms

2.2. Atoms of the same element are identical. The atoms of Atoms of the same element are identical. The atoms of anyone element are different from those of any other anyone element are different from those of any other elementelement

3.3. Atoms of different elements can physically mix together Atoms of different elements can physically mix together or can chemically combine w/ one another in simple or can chemically combine w/ one another in simple whole-number ratios to form compoundswhole-number ratios to form compounds

4.4. Chemical reactions occur when atoms are separated, Chemical reactions occur when atoms are separated, joined, or rearranged. However, atoms of one element joined, or rearranged. However, atoms of one element are never changed into atoms of another elements as a are never changed into atoms of another elements as a result of a chemical reactionresult of a chemical reaction

3

Thomson’s Atomic Thomson’s Atomic ModelModel Thomson’s Atomic ModelThomson’s Atomic Model

Thomson though electrons were like Thomson though electrons were like plums embedded in a positively plums embedded in a positively charged “pudding”, so his model was charged “pudding”, so his model was called the “plum pudding” modelcalled the “plum pudding” model

4

Thomson’s TheoryThomson’s Theory

Thomson stated: The atom had Thomson stated: The atom had negatively charged electrons stuck into negatively charged electrons stuck into a lump of positively charged protons.a lump of positively charged protons.

Thomson never explainedThomson never explained

1.1. Number of protons and neutronsNumber of protons and neutrons

2.2. The arrangement of the particles in the The arrangement of the particles in the atomatom

3.3. The ease with which atoms are stripped The ease with which atoms are stripped of electrons to form ions of electrons to form ions

5

Rutherford ModelRutherford Model Rutherford used the Gold Foil Rutherford used the Gold Foil

ExperimentExperiment Rutherford proposed the following:Rutherford proposed the following:1.1. Thomson model was incorrectThomson model was incorrect2.2. Most of the mass of the atom and all of Most of the mass of the atom and all of

its positive charge reside in a very small, its positive charge reside in a very small, extremely dense region, which he called extremely dense region, which he called the nucleusthe nucleus

3.3. Most of the total volume of the atom is Most of the total volume of the atom is empty space in which electrons move empty space in which electrons move around the nucleusaround the nucleus

Rutherford’s ModelRutherford’s Model Discovered dense Discovered dense

positive piece at positive piece at the center of the the center of the atomatom

NucleusNucleus Electrons moved Electrons moved

aroundaround Mostly empty Mostly empty

spacespace

7

Bohr ModelBohr Model Bohr changed the Rutherford model and Bohr changed the Rutherford model and

explained how the electrons travel.explained how the electrons travel. Bohr explained the following in his model:Bohr explained the following in his model:1.1. Electrons travel in definite orbits around Electrons travel in definite orbits around

the nucleusthe nucleus2.2. Electrons are arranged in concentric Electrons are arranged in concentric

circular paths or orbitals around the circular paths or orbitals around the nucleusnucleus

3.3. Electrons don’t fall into the nucleus Electrons don’t fall into the nucleus because electrons in particular path have because electrons in particular path have fixed energy and don’t lose energyfixed energy and don’t lose energy

4.4. His model was patterned after the motion His model was patterned after the motion of the planets around the sun. It is often of the planets around the sun. It is often called the Planetary model.called the Planetary model.

8

Bohr Model Cont.Bohr Model Cont.

Bohr’s ModelBohr’s Model

Nucleus

Electron

Orbit

Energy Levels

10

Quantum TheoryQuantum Theory

Bohr explained how electrons were Bohr explained how electrons were moving via Quantum Theorymoving via Quantum Theory

Key Terms:Key Terms:

1.1. Energy Levels- Regions around the Energy Levels- Regions around the nucleus where the electron is likely nucleus where the electron is likely movingmoving

2.2. Quantum- Amount of energy required to Quantum- Amount of energy required to move an electron from one energy level move an electron from one energy level to the nextto the next

3.3. Quantum Leap- Abrupt ChangeQuantum Leap- Abrupt Change

Bohr’s ModelBohr’s ModelIn

crea

sing

ene

rgy

Nucleus

First

Second

Third

Fourth

Fifth

} Further away Further away

from the from the nucleus means nucleus means more energy.more energy.

There is no “in There is no “in between” between” energyenergy

Energy LevelsEnergy Levels

12

Bohr’s Model cont.Bohr’s Model cont.

Energy levels are not equally spaced.Energy levels are not equally spaced. Energy levels more closely spaced Energy levels more closely spaced

further from the nucleusfurther from the nucleus Higher energy level occupied by an Higher energy level occupied by an

electron, the more energetic that electron, the more energetic that electron is.electron is.

Amount of energy gained or lost by an Amount of energy gained or lost by an electron is not always the same electron is not always the same amount.amount.

13

Bohr Model Cont.Bohr Model Cont.

The Bohr Model did not account The Bohr Model did not account for:for:

1.1. Emission spectra of atoms Emission spectra of atoms containing more than one electron.containing more than one electron.

So comes along the next model:So comes along the next model:

The Quantum The Quantum Mechanical ModelMechanical Model

Energy is quantized. It comes in chunks.Energy is quantized. It comes in chunks. A quanta is the amount of energy A quanta is the amount of energy

needed to move from one energy level to needed to move from one energy level to another.another.

Since the energy of an atom is never “in Since the energy of an atom is never “in between” there must be a quantum leap between” there must be a quantum leap in energy.in energy.

Schrodinger derived an equation that Schrodinger derived an equation that described the energy and position of the described the energy and position of the electrons in an atomelectrons in an atom

Things that are very small Things that are very small behave differently from behave differently from things big enough to see.things big enough to see.

The quantum mechanical The quantum mechanical model is a mathematical model is a mathematical solutionsolution

It is not like anything you It is not like anything you can see.can see.


Erwin SchrErwin Schröödinger: We can describe the dinger: We can describe the electron electron mathematicallymathematically, using , using quantum quantum mechanicsmechanics (wave mechanics).(wave mechanics).

Schrödinger developed a Schrödinger developed a wave equationwave equation to describe the hydrogen atom.to describe the hydrogen atom.

An acceptable solution to Schrödinger’s An acceptable solution to Schrödinger’s wave equation is called a wave equation is called a wave function.wave function.

A wave function represents an energy A wave function represents an energy state of the atom.state of the atom.

Wave FunctionsWave Functions

SchrSchröödinger’s Equationdinger’s Equation

The wave function is a F(x, y, z)The wave function is a F(x, y, z) Actually F(r,Actually F(r,θθ,,φφ)) Solutions to the equation are called Solutions to the equation are called

orbitals.orbitals. These are not Bohr orbits.These are not Bohr orbits. Each solution is tied to a certain Each solution is tied to a certain

energy energy These are the energy levelsThese are the energy levels

Animation


18

Has energy levels forHas energy levels for electrons.electrons.

Orbits are not circular.Orbits are not circular. It can only tell us theIt can only tell us the

probability of finding probability of finding an electron a certain distance from an electron a certain distance from the nucleus.the nucleus.


The atom is found The atom is found inside a blurry inside a blurry “electron cloud”“electron cloud”

A area where there A area where there is a chance of is a chance of finding an electron.finding an electron.

Draw a line at 90 %Draw a line at 90 %


Werner Heisenberg: We Werner Heisenberg: We can’t know exactly can’t know exactly where where a moving particle a moving particle is AND exactly is AND exactly how fasthow fast it is moving at the same it is moving at the same time.time.

The The Uncertainty Uncertainty

PrinciplePrinciple

The photon that will enter the microscope, so that we might “see” the electron …

… has enough momentum to deflect the electron.The act of measurement has interfered with the electron’s motion.

A wave function doesn’t tell us where the A wave function doesn’t tell us where the electron electron isis. The uncertainty principle tells . The uncertainty principle tells us that we us that we can’tcan’t know where the electron know where the electron is.is.

However, the square of a wave function However, the square of a wave function gives the gives the probabilityprobability of finding an of finding an electron at a given location in an atom.electron at a given location in an atom.

Analogy: We can’t tell where a single leaf Analogy: We can’t tell where a single leaf from a tree will fall. But (by viewing all the from a tree will fall. But (by viewing all the leaves under the tree) we can describe leaves under the tree) we can describe where a leaf is where a leaf is most likelymost likely to fall. to fall.

The Uncertainty The Uncertainty PrinciplePrinciple

23

Atomic OrbitalsAtomic Orbitals

There are the region of space which there There are the region of space which there is a high probability of finding an electronis a high probability of finding an electron

Within each energy level the complex Within each energy level the complex math of Schrodinger’s equation describes math of Schrodinger’s equation describes several shapes.several shapes.

These are called atomic orbitals These are called atomic orbitals Quantum Numbers- numbers that specify Quantum Numbers- numbers that specify

the properties of atomic orbitals and their the properties of atomic orbitals and their electronselectrons

24

Quantum NumbersQuantum Numbers

There are 4 types of Quantum There are 4 types of Quantum NumbersNumbers

1.1. Principal – distance from the nucleusPrincipal – distance from the nucleus2.2. Angular Momentum- Orbital ShapeAngular Momentum- Orbital Shape3.3. Magnetic- Orbital position with Magnetic- Orbital position with

respect to the X, Y, & Z axes.respect to the X, Y, & Z axes.4.4. Spin- Has only two values (+1/2 or –Spin- Has only two values (+1/2 or –

1/2) and is needed to specify 1 of 2 1/2) and is needed to specify 1 of 2 positional orientations of an electronpositional orientations of an electron

25

Principal Quantum Principal Quantum NumberNumber

Symbolized by the letter N, indicates the Symbolized by the letter N, indicates the main energy levels surrounding the nucleusmain energy levels surrounding the nucleus

There are 7 principal quantum numbersThere are 7 principal quantum numbers A.K.A. – ShellsA.K.A. – Shells Value of N is a whole number ex. 1,2,3 ect..Value of N is a whole number ex. 1,2,3 ect.. Main Energy Level – N=1; closest to the Main Energy Level – N=1; closest to the

nucleus or ground statenucleus or ground state Ground State- state of the lowest energy of Ground State- state of the lowest energy of

the atom.the atom. As N increases, the distance from the As N increases, the distance from the

nucleus increases and the energy increasesnucleus increases and the energy increases

26

Angular Momentum Angular Momentum Quantum NumberQuantum Number

Indicates the shape of the orbital.Indicates the shape of the orbital. Within each main energy level Within each main energy level

beyond the first, orbitals with beyond the first, orbitals with different shapes occupy different different shapes occupy different regionsregions

A.K.A. – Sublevels or SubshellsA.K.A. – Sublevels or Subshells The number of sublevels = Value of The number of sublevels = Value of

the Principal Quantum Numberthe Principal Quantum Number

27

Magnetic Quantum Magnetic Quantum NumberNumber

Indicates the orientation of a Indicates the orientation of a orbital about the nucleusorbital about the nucleus

There are 4 types of orbital There are 4 types of orbital orientationorientation

I.I. S OrbitalS Orbital

II.II. P OrbitalP Orbital

III.III. D OrbitalD Orbital

IV.IV. F OrbitalF Orbital

28

Spin Quantum NumberSpin Quantum Number

Has only two possible values: +1/2 Has only two possible values: +1/2 or –1/2. These values indicate two or –1/2. These values indicate two possible states of an electron in an possible states of an electron in an orbitalorbital

Spin Quantum # is significant Spin Quantum # is significant because each single orbital can hold because each single orbital can hold no more than two electrons, which no more than two electrons, which must have opposite spin.must have opposite spin.

1 s orbital for1 s orbital for every energyevery energy levellevel

Spherical Spherical shapedshaped

Each s orbital can hold 2 electronsEach s orbital can hold 2 electrons Called the 1s, 2s, 3s, etc.. orbitals.Called the 1s, 2s, 3s, etc.. orbitals.

S orbitalsS orbitals

P orbitalsP orbitals Start at the second energy level Start at the second energy level 3 different directions3 different directions 3 different shapes3 different shapes Each can hold 2 electronsEach can hold 2 electrons

P OrbitalsP Orbitals

D orbitalsD orbitals Start at the third energy level Start at the third energy level 5 different shapes5 different shapes Each can hold 2 electronsEach can hold 2 electrons

F orbitalsF orbitals Start at the fourth energy levelStart at the fourth energy level Have seven different shapesHave seven different shapes 2 electrons per shape2 electrons per shape

F orbitalsF orbitals

SummarySummary

s

p

d

f

# of shapes

Max electrons

Starts at energy level

1 2 1

3 6 2

5 10 3

7 14 4

By Energy LevelBy Energy Level First Energy First Energy

LevelLevel only s orbitalonly s orbital only 2 electronsonly 2 electrons 1s1s22

Second Energy Second Energy LevelLevel

s and p orbitals s and p orbitals are availableare available

2 in s, 6 in p2 in s, 6 in p 2s2s222p2p66

8 total electrons8 total electrons

By Energy LevelBy Energy Level Third energy Third energy

levellevel s, p, and d s, p, and d

orbitalsorbitals 2 in s, 6 in p, and 2 in s, 6 in p, and

10 in d10 in d 3s3s223p3p663d3d1010


Fourth energy Fourth energy levellevel

s,p,d, and f s,p,d, and f orbitalsorbitals

2 in s, 6 in p, 10 2 in s, 6 in p, 10 in d, ahd 14 in fin d, ahd 14 in f

4s4s224p4p664d4d10104f4f1414


By Energy LevelBy Energy Level Any more than Any more than

the fourth and the fourth and not all the not all the orbitals will fill orbitals will fill up.up.

You simply run You simply run out of electronsout of electrons

The orbitals do The orbitals do not fill up in a not fill up in a neat order.neat order.

The energy levels The energy levels overlapoverlap

Lowest energy fill Lowest energy fill first.first.

39

Question for YouQuestion for You

How many principal quantum How many principal quantum numbers are there?numbers are there?

What is the maximum number of What is the maximum number of electrons that can fill the 3electrons that can fill the 3rdrd energy energy level?level?

How many orbitals are in the sublevel How many orbitals are in the sublevel F?F?

What is the total number of orbitals What is the total number of orbitals for the 3for the 3rdrd main energy level? main energy level?

40

Electron ConfigurationElectron Configuration The way electrons are arranged in atomsThe way electrons are arranged in atoms There are three rules which help dictate There are three rules which help dictate

how electrons are arranged in the atoms.how electrons are arranged in the atoms.1)1) Aufbau Principle- electrons occupy the Aufbau Principle- electrons occupy the

orbitals of the lowest energy firstorbitals of the lowest energy first2)2) Hund’s Rule- Orbitals of equal energy are Hund’s Rule- Orbitals of equal energy are

each occupied by one electron before any each occupied by one electron before any one orbital is occupied by a second one orbital is occupied by a second electron. All electrons in a single occupied electron. All electrons in a single occupied orbital must have the same spin.orbital must have the same spin.

41

Electron Configuration Electron Configuration cont.cont.

Pauli Exclusion Principle- No two Pauli Exclusion Principle- No two electrons may occupy any given electrons may occupy any given orbital without having opposite spin. orbital without having opposite spin. No two electrons in the same atom No two electrons in the same atom can have the same set of four can have the same set of four quantum numbers.quantum numbers.

Let’s determine electron Let’s determine electron configuration.configuration.

Let’s start with Phosphorus.Let’s start with Phosphorus. Need to account for all 15 electronsNeed to account for all 15 electrons

Electron ConfigurationsElectron Configurations

Distribution of all Distribution of all electrons in an atomelectrons in an atom

Consist of Consist of Number denoting the Number denoting the

energy levelenergy level


Distribution of all Distribution of all electrons in an atomelectrons in an atom


energy levelenergy level Letter denoting the Letter denoting the

type of orbitaltype of orbital


Distribution of all Distribution of all electrons in an atom.electrons in an atom.


energy level.energy level. Letter denoting the Letter denoting the

type of orbital.type of orbital. Superscript denoting Superscript denoting

the number of the number of electrons in those electrons in those orbitals.orbitals.

An An electron configurationelectron configuration describes the describes the distribution of electrons among the various distribution of electrons among the various orbitals in the atom.orbitals in the atom.

Electron configuration is represented in two ways.Electron configuration is represented in two ways.


The spdf notation uses numbers to designate a principal shell and letters (s, p, d, f) to identify a subshell; a superscript indicates the number of electrons in a designated subshell.

46

Orbital DiagramsOrbital Diagrams

Each box represents Each box represents one orbital.one orbital.

Half-arrows Half-arrows represent the represent the electrons.electrons.

The direction of the The direction of the arrow represents arrow represents the spin of the the spin of the electron.electron.

Hund’s RuleHund’s Rule

““For degenerate For degenerate orbitals, the lowest orbitals, the lowest energy is attained energy is attained when the number when the number of electrons with of electrons with the same spin is the same spin is maximized.”maximized.”

Exceptions to Exceptions to Electron Electron

ConfigurationConfiguration

Orbitals fill in order Orbitals fill in order Lowest energy to higher energy.Lowest energy to higher energy. Adding electrons can change the Adding electrons can change the

energy of the orbital.energy of the orbital. Half filled orbitals have a lower Half filled orbitals have a lower

energy.energy. Makes them more stable.Makes them more stable. Changes the filling orderChanges the filling order

Write these electron Write these electron configurationsconfigurations

Titanium - 22 electronsTitanium - 22 electrons 1s1s222s2s222p2p663s3s223p3p664s4s223d3d22

Vanadium - 23 electrons Vanadium - 23 electrons 1s1s222s2s222p2p663s3s223p3p664s4s223d3d33

Chromium - 24 electronsChromium - 24 electrons 1s1s222s2s222p2p663s3s223p3p664s4s223d3d4 4 is expectedis expected But this is wrong!!But this is wrong!!

Chromium is actuallyChromium is actually 1s1s222s2s222p2p663s3s223p3p664s4s113d3d55

Why?Why? This gives us two half filled orbitals.This gives us two half filled orbitals. Slightly lower in energy.Slightly lower in energy. The same principal applies to The same principal applies to

copper.copper.

Copper’s electron Copper’s electron configurationconfiguration

Copper has 29 electrons so we Copper has 29 electrons so we expectexpect

1s1s222s2s222p2p663s3s223p3p664s4s223d3d99

But the actual configuration isBut the actual configuration is 1s1s222s2s222p2p663s3s223p3p664s4s113d3d1010

This gives one filled orbital and one This gives one filled orbital and one half filled orbital.half filled orbital.

Remember these exceptionsRemember these exceptions

54

Shortcuts for Electron Shortcuts for Electron ConfigurationConfiguration

There are two short handed methods of There are two short handed methods of writing the electron configuration.writing the electron configuration.

The 1The 1stst method is called the outer-level method is called the outer-level configuration. That tells you the outer-configuration. That tells you the outer-most configuration for that element.most configuration for that element.

The 2The 2ndnd method is called the Noble Gas method is called the Noble Gas Notation. This tells you the complete Notation. This tells you the complete notation using Noble Gases.notation using Noble Gases.

Let’s start with outer-level notation!!!Let’s start with outer-level notation!!!

Exceptions to the Aufbau Exceptions to the Aufbau PrinciplePrinciple

Half-filled d subshell plus half-filled s subshell has slightly lower in energy than s2

d4.Filled d subshell plus half-filled s subshell has slightly lower in energy than s2 d9.

More exceptions occur farther down the periodic table. They aren’t always predictable, because energy levels get closer together.

11ss11

1s1s2222ss11

1s1s222s2s222p2p6633ss11

1s1s222s2s222p2p663s3s223p3p6644ss11

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p6655ss11

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p665s5s224d4d10 10

5p5p6666ss11

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p665s5s224d4d10105p5p666s6s224f4f14145d5d10106p6p6677ss11

H1

Li3

Na11

K19

Rb37

Cs55

Fr87

He2

Ne10

Ar18

Kr36

Xe54

Rn86

11ss22

1s1s222s2s222p2p66

1s1s222s2s222p2p663s3s223p3p66

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p66

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p665s5s224d4d10105p5p66

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p665s5s224d4d10 10

5p5p666s6s224f4f14145d5d10106p6p66

58

Alkali metals all end in sAlkali metals all end in s11

Alkaline earth metals all end in Alkaline earth metals all end in ss22

really have to include He but it really have to include He but it fits better later.fits better later.

He has the properties of the He has the properties of the noble gases.noble gases.

s2s1 S- blockS- block

The P-The P-blockblock p1 p2 p3 p4 p5 p6

Transition Metals -d Transition Metals -d blockblock

d1 d2 d3s1

d5 d5 d6 d7 d8s1

d10 d10

F - blockF - block inner transition elementsinner transition elements

f1 f5f2 f3 f4

f6 f7 f8 f9 f10 f11 f12 f14

f13

Each row (or period) is the energy Each row (or period) is the energy level for s and p orbitals.level for s and p orbitals.

1

2

3

4

5

6

7

D orbitals fill up after previous energy level D orbitals fill up after previous energy level so first d is 3d even though it’s in row 4.so first d is 3d even though it’s in row 4.

1

2

3

4

5

6

7

3d

f orbitals start filling at 4ff orbitals start filling at 4f

1

2

3

4

5

6

7 4f

5f

66

Summary Outer-Level Summary Outer-Level ConfigurationConfiguration

Writing Electron Writing Electron configurations the configurations the

easy wayeasy wayYes there is a shorthandYes there is a shorthand

Electron Configurations Electron Configurations repeatrepeat

The shape of the periodic table is a The shape of the periodic table is a representation of this repetition.representation of this repetition.

When we get to the end of the When we get to the end of the column the outermost energy level is column the outermost energy level is full.full.

This is the basis for our shorthand.This is the basis for our shorthand.

The ShorthandThe Shorthand Write the symbol of the noble gas Write the symbol of the noble gas

before the element.before the element. Then the rest of the electrons.Then the rest of the electrons. Aluminum - full configuration.Aluminum - full configuration. 1s1s222s2s222p2p663s3s223p3p11

Ne is 1sNe is 1s222s2s222p2p66

so Al is [Ne] 3sso Al is [Ne] 3s223p3p11

More examplesMore examples Ge = 1sGe = 1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p22

Ge = [Ar] 4sGe = [Ar] 4s223d3d10104p4p22

Hf=1sHf=1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p665s5s2 2

4d4d10105p5p666s6s224f4f14145d5d22

Hf=[Xe]6sHf=[Xe]6s224f4f14145d5d22

The Shorthand AgainThe Shorthand Again

Sn- 50 electrons

The noble gas before it is Kr

[ Kr ]

Takes care of 36

Next 5s2

5s2

Then 4d10

4d10Finally 5p2

5p2


Solving the wave equation gives a Solving the wave equation gives a set of wave functions, or set of wave functions, or orbitalsorbitals, , and their corresponding energies.and their corresponding energies.

Each orbital describes a spatial Each orbital describes a spatial distribution of electron density.distribution of electron density.

An orbital is described by a set of An orbital is described by a set of three three quantum numbersquantum numbers..

The Wave-like ElectronThe Wave-like Electron

Louis deBroglie

The electron propagates through space as an

energy wave. To understand the atom, one

must understand the behavior of

electromagnetic waves.


A totally new approachA totally new approach De Broglie said matter could be like De Broglie said matter could be like

a wave.a wave. De Broglie said they were like De Broglie said they were like

standing waves.standing waves. The vibrations of a stringed The vibrations of a stringed

instrumentinstrument

What’s possible?What’s possible? You can only have a standing wave if You can only have a standing wave if

you have complete waves.you have complete waves. There are only certain allowed waves.There are only certain allowed waves. In the atom there are certain allowed In the atom there are certain allowed

waves called electrons.waves called electrons. 1925 Erwin Schroedinger described 1925 Erwin Schroedinger described

the wave function of the electronthe wave function of the electron Much math, but what is important Much math, but what is important

are the solutionsare the solutions


The wave function is a F(x, y, z)The wave function is a F(x, y, z) Actually F(r,Actually F(r,θθ,,φφ)) Solutions to the equation are called Solutions to the equation are called

orbitals.orbitals. These are not Bohr orbits.These are not Bohr orbits. Each solution is tied to a certain Each solution is tied to a certain

energy energy These are the energy levelsThese are the energy levels

Animation

What does the wave What does the wave Function mean?Function mean?

nothing.nothing. it is not possible to visually map it.it is not possible to visually map it. The square of the function is the The square of the function is the

probability of finding an electron probability of finding an electron near a particular spot.near a particular spot.

best way to visualize it is by best way to visualize it is by mapping the places where the mapping the places where the electron is likely to be found.electron is likely to be found.

Pro

bab

ilit

y

Distance from nucleus

Su

m o

f all

Pro

bab

ilit

ies

Su

m o

f all

Pro

bab

ilit

ies

Distance from nucleusDistance from nucleus

Defining the sizeDefining the size

The nodal surface.The nodal surface. The size that encloses 90% to the The size that encloses 90% to the

total electron probability.total electron probability. NOT at a certain distance, but a NOT at a certain distance, but a

most likely distance.most likely distance. For the first solution it is a a sphere. For the first solution it is a a sphere.

© 2009, Prentice-Hall, Inc.

Quantum MechanicsQuantum Mechanics

Erwin Schrödinger Erwin Schrödinger developed a developed a mathematical mathematical treatment into which treatment into which both the wave and both the wave and particle nature of particle nature of matter could be matter could be incorporated.incorporated.

It is known as It is known as quantum mechanicsquantum mechanics..


Quantum MechanicsQuantum Mechanics

The wave equation is The wave equation is designated with a lower designated with a lower case Greek case Greek psipsi ( ().).

The square of the wave The square of the wave equation, equation, 22, gives a , gives a probability density map probability density map of where an electron has of where an electron has a certain statistical a certain statistical likelihood of being at any likelihood of being at any given instant in time.given instant in time.



Solving the wave equation gives a Solving the wave equation gives a set of wave functions, or set of wave functions, or orbitalsorbitals, , and their corresponding energies.and their corresponding energies.

Each orbital describes a spatial Each orbital describes a spatial distribution of electron density.distribution of electron density.

An orbital is described by a set of An orbital is described by a set of three three quantum numbersquantum numbers..


There are many solutions to There are many solutions to SchrSchröödinger’s equationdinger’s equation

Each solution can be described with Each solution can be described with quantum numbers that describe quantum numbers that describe some aspect of the solution.some aspect of the solution.

Principal quantum number (n) size Principal quantum number (n) size and energy of an orbitaland energy of an orbital

Has integer values >0Has integer values >0


s s OrbitalsOrbitals

Observing a graph of Observing a graph of probabilities of probabilities of finding an electron finding an electron versus distance from versus distance from the nucleus, we see the nucleus, we see that that ss orbitals orbitals possess possess nn−1 −1 nodesnodes, , or regions where or regions where there is 0 probability there is 0 probability of finding an of finding an electron.electron.


pp Orbitals Orbitals

The value of The value of ll for for pp orbitals is 1. orbitals is 1. They have two lobes with a node between They have two lobes with a node between

them.them.


dd Orbitals Orbitals

The value of The value of ll for for a a dd orbital is 2. orbital is 2.

Four of the five Four of the five dd orbitals have 4 orbitals have 4 lobes; the other lobes; the other resembles a resembles a pp orbital with a orbital with a doughnut around doughnut around the center.the center.

Quantum numbersQuantum numbers Angular momentum quantum number Angular momentum quantum number l l shape of the orbitalshape of the orbital integer values from 0 to n-1integer values from 0 to n-1 ll = 0 is called s = 0 is called s l l = 1 is called p= 1 is called p l l =2 is called d=2 is called d ll =3 is called f =3 is called f l l =4 is called g=4 is called g


Magnetic Quantum Magnetic Quantum Number (Number (mmll))

The magnetic quantum number The magnetic quantum number describes the three-dimensional describes the three-dimensional orientation of the orbital.orientation of the orbital.

Allowed values of Allowed values of mmll are integers are integers ranging from ranging from --ll to to ll::

−−ll ≤ ≤ mmll ≤ ≤ l.l. Therefore, on any given energy level, Therefore, on any given energy level,

there can be up to 1 there can be up to 1 ss orbital, 3 orbital, 3 pp orbitals, 5 orbitals, 5 dd orbitals, 7 orbitals, 7 ff orbitals, etc. orbitals, etc.


Magnetic Quantum Magnetic Quantum Number (Number (mmll))

Orbitals with the same value of Orbitals with the same value of nn form a form a shellshell..

Different orbital types within a shell are Different orbital types within a shell are subshellssubshells..


Spin Quantum Number, Spin Quantum Number, mmss

This led to a fourth This led to a fourth quantum number, the quantum number, the spin quantum spin quantum number, number, mmss..

The spin quantum The spin quantum number has only 2 number has only 2 allowed values: +1/2 allowed values: +1/2 and −1/2.and −1/2.


Pauli Exclusion PrinciplePauli Exclusion Principle

No two electrons in No two electrons in the same atom can the same atom can have exactly the have exactly the same energy.same energy.

Therefore, no two Therefore, no two electrons in the same electrons in the same atom can have atom can have identical sets of identical sets of quantum numbers.quantum numbers.

Documents

1 Electrons in Atoms. 2 Dalton’s Atomic Theory John Dalton (1766-1844) had four theories John Dalton (1766-1844) had four theories 1. All elements are