Chapter 7Chapter 7 Atomic Structure and Atomic Structure and

PeriodicityPeriodicity

TopicsTopics

Electromagnetic radiationElectromagnetic radiation The nature of matterThe nature of matter The atomic spectrum of hydrogenThe atomic spectrum of hydrogen The Bohr modelThe Bohr model The quantum mechanical model of the atomThe quantum mechanical model of the atom Quantum numbersQuantum numbers Orbital shapes and energiesOrbital shapes and energies Electron spin and Pauli exclusion principleElectron spin and Pauli exclusion principle Polyelectronic atomsPolyelectronic atoms The history of the periodic Table The history of the periodic Table The aufbau principle and Periodic TableThe aufbau principle and Periodic Table Periodic trends in atomic propertiesPeriodic trends in atomic properties

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.

7.1 Electromagnetic Radiation7.1 Electromagnetic Radiation

electromagnetic radiationelectromagnetic radiation: : form of energy that acts as a form of energy that acts as a

wave as it travelswave as it travels includes: X rays, Ultraviolet, includes: X rays, Ultraviolet,

visible light, infrared light, visible light, infrared light, microwaves, and radio wavesmicrowaves, and radio waves

travel at a speed of 2.9979 x 10travel at a speed of 2.9979 x 1088 m/s in a vacuumm/s in a vacuum

All forms of EMR are combined to All forms of EMR are combined to form form electromagnetic spectrumelectromagnetic spectrum

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

Gamma Rays

Low Frequency

High Frequency

Long Wavelength

Short WavelengthVisible Light

Low Energy

High Energy

Electromagnetic SpectrumElectromagnetic Spectrum

R O Y G B I V”

The whole range of frequenciesis called “Spectrum”

Parts of a wave

Wavelength

AmplitudeOrigin

Crest

Trough

Wavelength Wavelength λλ = Greek letter lambda= Greek letter lambda distance between points on distance between points on

adjacent waves (consicutive peaks adjacent waves (consicutive peaks or troughs)or troughs)

Units used are in Units used are in nmnm (10 (1099nm = 1m)nm = 1m) Frequency Frequency

= Greek letter nu= Greek letter nu number of wave cycles that passes number of wave cycles that passes

a point in a second. 10a point in a second. 1088 cycles/s= cycles/s= 101088 ss-1 -1

==101088 Hertz = 10 Hertz = 1088 Hz Hz in 1/second (Hertz = Hz)in 1/second (Hertz = Hz)

Equation:

c = speed of light, a constant (2.998 x 108 m/s)

(nu) = frequency, in units of hertz (hz or sec-1) (lambda) = wavelength, in meters

Electromagnetic radiation propagates through space as a wave moving at the speed of light.

c

c

7.2 Nature of Matter7.2 Nature of Matter

Before 1900, scientists thought Before 1900, scientists thought that matter and energy were that matter and energy were totally differenttotally different

mattermatter energyenergyparticleparticless

massmass

positiopositionn

wavewave

masslessmassless

delocalizdelocalizeded

In 1900In 1900

According to the old views, matter could According to the old views, matter could absorb or emit any quantity (frequency) of absorb or emit any quantity (frequency) of energyenergy. .

Max Planck found that as the cooling of hot Max Planck found that as the cooling of hot objects couldn’t be explained by viewing objects couldn’t be explained by viewing energy as a waveenergy as a wave..

Max Planck studied the radiation emitted by Max Planck studied the radiation emitted by solid bodies heated to incandescence. solid bodies heated to incandescence.

Max PlanckMax Planck postulated that energy can be postulated that energy can be gained or lost only in whole number gained or lost only in whole number multiples of the quantitymultiples of the quantity

h =Planck’s constant= 6.626x10h =Planck’s constant= 6.626x10-34-34 J.s J.s That is change in energy of a system, That is change in energy of a system, E is E is

h

nhE n is an integer; is the frequency of EMR

emitted or absorbed

Nature of MatterNature of Matter

Mack’s Planck suggested that an Mack’s Planck suggested that an object object emitsemits energy in the form of small packets energy in the form of small packets of energy called of energy called quanta. That is the energy is quantized

QuantumQuantum- the minimum amount of energy - the minimum amount of energy that can be gained or lost by an atom that can be gained or lost by an atom (energy in each packet)(energy in each packet)

Thus energy seems to have particulate Thus energy seems to have particulate propertiesproperties

hE

Nature of MatterNature of Matter

Einstein proposed that radiation Einstein proposed that radiation itself is really a stream of itself is really a stream of particles called particles called photonsphotons

Energy of each photon is :Energy of each photon is :

also showed that also showed that energy energy

has masshas mass

hc

hvEphoton

2mcE 2c

Em

Nature of MatterNature of Matter

hvE

vc c

v

hc

E

2mcE 2mc

hc

cm

h

shows that anything with both mass and velocity has a corresponding wavelength

Calculate the energy of red light vs. blue light.red light: 700 nm blue light: 400 nm

hc E

red:

hc E

hc Eblue:

m10x700

)s/m10x00.3)(sJ10x62.6( E

9

834

E = 2.85 x 10-19 J

m10x400

)s/m10x00.3)(sJ10x62.6( E

9

834

E = 4.96 x 10-19 J

What is light? Light has certain characteristics of

particulate matter Light is a wave - we can measure its

wavelength and it behaves as a wave If we combine E=mc2 , c=, E = 1/2 mv2

and E = hthen we can get: = h/mv (from Louis de Broglie)

called de Broglie’s equation This equation allows calculation of the

wavelength of a particle.

Wave-Particle DualityJ.J. Thomson won the Nobel prize for describing the electron as a particle.

His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron.

The electron is a particle!

The electron is an energy

wave!

7.3 The Atomic Spectrum of Hydrogen

Main experiments led to the information related to atom: Thompson discovery of electron Rutherford discovery of nucleus Study of emission of light by excited hydrogen

atom When H2 molecules absorb energy, some H-H

bonds are broken and excited H-atoms will be produced

The excited H-atoms release energy by emitting light at various wavelengths that is known as emission spectrum of H-atoms

• When sunlight is dispersed by rain drops the rainbow is

Produced; that is a continuous spectrum spectrum is produced. • continuous spectrum contains all colors; that is all wavelengths of the visible light

Spectroscopic analysis of the visible Spectroscopic analysis of the visible spectrumspectrum

White light

The Continuous The Continuous SpectrumSpectrum

The different colors of light correspond to different wavelengths and frequencies

~ 650 nm ~ 575 nm

~ 500 nm

~ 480 nm

~ 450 nm

Hydrogen emission spectrum is called “line spectrum”

Spectroscopic analysis of Spectroscopic analysis of the hydrogen spectrum…the hydrogen spectrum…

H receives a high energyspark

H-H bondsAre broken and H atoms are excited

• Line spectrum• Unique to each

element, like fingerprints!

• Very useful for identifying elements

Significance of the line spectrum Significance of the line spectrum of H-atomof H-atom

Only certain energies are allowed for the electron in Only certain energies are allowed for the electron in the hydrogen atomthe hydrogen atom

That is, the energy of an electron in a hydrogen atom That is, the energy of an electron in a hydrogen atom is quantized. is quantized.

Changes in energy between discrete energy levels in Changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of hydrogen will produce only certain wavelengths of emitted light.emitted light.

The discrete line spectrum of hydrogen shows that The discrete line spectrum of hydrogen shows that only certain energies are possible.only certain energies are possible.

The electron energy levels are quantized. If all The electron energy levels are quantized. If all energy levels are allowed the spectrum would be energy levels are allowed the spectrum would be continuouscontinuous

7.4 The Bohr Model7.4 The Bohr Model

Niels Bohr (Danish physicist) 1885-1962Niels Bohr (Danish physicist) 1885-1962 Developed a quantum modelDeveloped a quantum model

for H atom that explained the for H atom that explained the emission line emission line spectrumspectrum

Electron moves around the nucleus only in Electron moves around the nucleus only in certain allowed circular certain allowed circular orbitsorbits, in which it has , in which it has a certain amount of energya certain amount of energy

The electrons were attracted to the nucleus The electrons were attracted to the nucleus because of opposite chargesbecause of opposite charges..

But electron does not fall in to the nucleus But electron does not fall in to the nucleus because it is moving aroundbecause it is moving around..

The Bohr AtomThe Bohr Atom

He didn’t know why but only certain He didn’t know why but only certain energies were allowedenergies were allowed..

He called these allowed energies He called these allowed energies energy levelsenergy levels..

Putting Energy into the atom moved the Putting Energy into the atom moved the electron away from the nucleuselectron away from the nucleus.. From From ground stateground state to to excited stateexcited state..

When it returns to ground state it gives When it returns to ground state it gives off light of a certain energyoff light of a certain energy..

The Model: SummaryThe Model: Summary Space around nucleus is divided Space around nucleus is divided

into spherical (into spherical (circualrcircualr) paths ) paths ((orbitsorbits) each has a number called ) each has a number called ““Principal Quantum number”Principal Quantum number”

The electron can exist only in one The electron can exist only in one of these orbitals but not in betweenof these orbitals but not in between

Orbits possess fixed size and Orbits possess fixed size and energy, therefore electron has a energy, therefore electron has a definite energy characteristic of its definite energy characteristic of its orbitorbit

particle

J2.178x10 constant Rydberg R

electron of

18-

H

2

2

Energyn

ZREE Horbitn

An electron can pass only from An electron can pass only from one orbit to another. Absorption one orbit to another. Absorption or emission will occuror emission will occur

Energy of the outermost orbit is Energy of the outermost orbit is zero zero

2

/13121

1000

1

1

1002.610178.2 2

2318

n

molkJ

nX

J

kJX

mol

particlesXX

particle

JXEn

molen

kJEn 2

1312

The Bohr AtomThe Bohr Atom

n = 3n = 4

n = 2n = 1

Bohr ModelBohr Model

equation can be used twice to equation can be used twice to find the ∆E when an electron find the ∆E when an electron moves energy levelsmoves energy levels

)(10178.22

218

n

ZJE

)](10178.2[)](10178.2[ 2

218

2

2

18

i

i

f

f

n

ZJ

n

ZJE

)11

(10178.2 2218

if nnJE

Bohr ModelBohr Model Wavelength of photon released Wavelength of photon released

can be calculated by using can be calculated by using

E=0 is set at an E=0 is set at an distance of ∞ away distance of ∞ away fromfrom the nucleus and becomes the nucleus and becomes more negative as the electron more negative as the electron comes closer to the nucleuscomes closer to the nucleus

E

hc

0)1

(10178.2 18

JE

Example 1Example 1

Calculate the Calculate the energy required energy required to move the to move the hydrogen hydrogen electron from electron from n=1 to n=2. n=1 to n=2. Find the Find the wavelength of wavelength of radiation that radiation that had to be had to be absorbed by the absorbed by the electronelectron..

)11

(10178.2 2218

if nnJE

JJE 1822

18 10633.1)1

1

2

1(10178.2

Jsm

sJ

E

hc18

34

10633.1

)9979.2)(10626.6(

nmm

nmm 6.121

1

1010216.1

97

Example 2Example 2Calculate the Calculate the energy energy required to required to remove the remove the electron from electron from the hydrogen the hydrogen atom in its atom in its ground stateground state..

)11

(10178.2 2218

if nnJE

)1

11(10178.2

218

JE

JJE 1818 10178.2)10(10178.2 Energy was absorbed by the electron so the value of ∆E value is positive.

Bohr ModelBohr Model

problems:problems: did not work for other atomsdid not work for other atoms did not explain chemical did not explain chemical

behavior of atomsbehavior of atoms

Heisenberg’s Uncertainty PrincipleHeisenberg’s Uncertainty Principle

According to According to de Brogliede Broglie: Electron : Electron behaves like a wavebehaves like a wave

Is it possible to specify the position of a Is it possible to specify the position of a wave at a particular instant?wave at a particular instant?

Energy, wavelength and amplitude can be Energy, wavelength and amplitude can be determined determined

But exact position is impossible to be But exact position is impossible to be determineddetermined

The electron cannot be imagined as : The electron cannot be imagined as : moving particle moving particle In a path of the same radius (well defined In a path of the same radius (well defined

orbits)orbits) Thus, location, direction and speed of Thus, location, direction and speed of

motion of a particle cannot be motion of a particle cannot be determineddetermined

Then Bohr Model had to be “Abandoned Then Bohr Model had to be “Abandoned

Heissenberg Uncertainty Heissenberg Uncertainty PrinciplePrinciple

““It is impossible to determine both It is impossible to determine both the position and momentum of a the position and momentum of a subatomic particle (such as the subatomic particle (such as the electron) with arbitrarily high electron) with arbitrarily high accuracy”accuracy” The effect of this principle is to The effect of this principle is to

convert the laws of physics into convert the laws of physics into statements about relative, instead statements about relative, instead of absolute, certainties.of absolute, certainties.

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple

we cannot know we cannot know the exact the exact position and position and momentum momentum (motion) of the (motion) of the electronelectron

as more is known as more is known about position, about position, less is known less is known about momentumabout momentum

uncertainties are uncertainties are inversely inversely proportionalproportional

4)(

hmx

where

∆x: uncertainty in position

∆m : uncertainty in mometum

minimum minimum uncertainty uncertainty is h/4is h/4

7.57.5 The Quantum Mechanical The Quantum Mechanical ModelModel

Exact position of electron can not be Exact position of electron can not be defineddefined Exact bath of electron about nucleus Exact bath of electron about nucleus

can not be defined can not be defined Werner HeisenbergWerner Heisenberg, , Louis de BroglieLouis de Broglie

and and Erwin SchrodingerErwin Schrodinger made the made the approach called approach called “Quantum “Quantum MechanicsMechanics””

They assumed that the electron is a They assumed that the electron is a standing wavestanding wave

The Quantum Mechanical The Quantum Mechanical ModelModel

Waves are associated with electronsWaves are associated with electrons Information about energies of Information about energies of

electrons and their positions are electrons and their positions are obtained from studying the obtained from studying the associated wavesassociated waves

Description of electron is based uponDescription of electron is based upon

“ “ Probability of finding a particle Probability of finding a particle within a given region of spacewithin a given region of space” “ ” “ but but not on the exact position” not on the exact position”

Schrödinger EquationSchrödinger Equation Wave equation describing electron Wave equation describing electron

as being a waveas being a wave The amplitudes (height),The amplitudes (height), , of , of

electron wave at various points of electron wave at various points of space are calculatedspace are calculated

commonly called “wave function”commonly called “wave function” provides information about the provides information about the

allowable energiesallowable energies for an electron in for an electron in H atom. H atom.

corresponds to corresponds to a certain energy a certain energy and describes a region around and describes a region around nucleus nucleus “Orbital”“Orbital” where the electron where the electron having that energy may be foundhaving that energy may be found

Orbital:Orbital: Region around the nucleus where Region around the nucleus where the electron can be expected to be foundthe electron can be expected to be found

The Function The Function 22

22 describes the describes the probability of the probability of the position of the electron at a particular position of the electron at a particular pointpoint

22 Probability of finding a particle in a Probability of finding a particle in a given region of spacegiven region of space

22 Electric charge density at a given Electric charge density at a given region of spaceregion of space

ThusThus,,

The charge can be assumed to be The charge can be assumed to be spread out as a charge cloud by spread out as a charge cloud by rapid motion of electronrapid motion of electron

The cloud is denser in some The cloud is denser in some regions than othersregions than others

The probability of finding electron The probability of finding electron in a given region in space is in a given region in space is proportional to the density of the proportional to the density of the cloudcloud

Meaning of Wave Meaning of Wave FunctionFunction

the wave function itself does not the wave function itself does not have concrete meaninghave concrete meaning

the the square of the wave functionsquare of the wave function represents the probability of represents the probability of finding an electron at a certain finding an electron at a certain pointpoint

easily represented as probability easily represented as probability distribution where the deepness distribution where the deepness of color indicates the probabilityof color indicates the probability

Meaning of Wave Meaning of Wave FunctionFunction

(a) electron density (a) electron density mapmap

probability of finding probability of finding an electron is highest an electron is highest at short distances from at short distances from nucleusnucleus

(b) calculated (b) calculated probability of finding probability of finding an electron at certain an electron at certain distances from nucleus distances from nucleus in the 1s orbitalin the 1s orbital

7.6 Quantum Numbers7.6 Quantum Numbers

There are many solutions to There are many solutions to Schroedinger’s equation for H Schroedinger’s equation for H atomatom

Each solution is a wave function Each solution is a wave function calledcalled Orbital. .

Each orbital can be described Each orbital can be described with with quantum numbersquantum numbers that that describe properties of the orbitaldescribe properties of the orbital

Quantum numbers specify the Quantum numbers specify the properties of atomic orbitals and of properties of atomic orbitals and of electrons in orbitalselectrons in orbitals

the first three quantum numbers the first three quantum numbers come from the Schrödinger equation come from the Schrödinger equation and describe:and describe: main energy levelmain energy level shapeshape orientationorientation

44thth describes state of electron describes state of electron

PrincipalPrincipal Quantum Number, n Quantum Number, n Main energy level occupied by Main energy level occupied by

electron. They are called atomic electron. They are called atomic orbitalsorbitals regions where there is a high probability of

finding an electron. n is related to the n is related to the size and energy of the

orbital values are all positive integers values are all positive integers >0>0 (1,2,3, (1,2,3,

…)…) As n increases

size of orbital is larger and electron is less tightly size of orbital is larger and electron is less tightly bound to nucleusbound to nucleus

The electron spends more time further from nucleusThe electron spends more time further from nucleus electron has higher energyelectron has higher energy the electron’s average distance from the nucleus the electron’s average distance from the nucleus

increasesincreases

Principal Quantum Principal Quantum NumberNumber

Maximum number of electrons that can fit in an energy level:

2n2

Angular Momentum Quantum Angular Momentum Quantum Number: Number: ll

It indicates the It indicates the shape of the shape of the orbitalorbital

The number of possible shapes The number of possible shapes (or (or ll values) for an energy level is values) for an energy level is equal to equal to nn

The possible values of The possible values of ll are are 00 and and all positive integers less than or all positive integers less than or equal toequal to

n - 1

ll has integer values from 0 to n-1has integer values from 0 to n-1

ll = = 0 is called 0 is called ss ll = = 1 is called 1 is called pp ll = =2 is called 2 is called dd ll = =3 is called 3 is called ff ll = =4 is called 4 is called gg

Magnetic Quantum Number, Magnetic Quantum Number, mmll

mmll indicates the indicates the orientation of the orientation of the orbital in space relative to the other orbital in space relative to the other orbitals in the atomorbitals in the atom

mmll has integer values from has integer values from + + ll - - l including 0l including 0

each orbital holds maximum of each orbital holds maximum of 2 electrons

total number of orbitals is equal to total number of orbitals is equal to nn22 for an energy level for an energy level

number of possible number of possible mmll values for values for a certain subshell is equal to a certain subshell is equal to 22ll + 1+ 1

Quantum Numbers for the first Quantum Numbers for the first four levels of orbitals in the four levels of orbitals in the

hydrogen atomhydrogen atom

7.7 Orbital shapes and Energies7.7 Orbital shapes and Energies

s orbitalss orbitals: 1: s: 1: s spherical spherical ll value of 0 value of 0

Representations of the Hydrogen 1s, 2s, and Representations of the Hydrogen 1s, 2s, and 3s Orbitals3s Orbitals

A. The Electron A. The Electron Probability DistributionProbability Distribution

B. The surface B. The surface contains 90% of the contains 90% of the total electron total electron probability probability

p-orbitalsp-orbitals p orbitals: 3p orbitals: 3

2p2pxx, , 2p2pyy, , 2p2pzz

dumbbell-dumbbell-shapedshaped

ll value = 1 value = 1 No 1p No 1p

orbitalsorbitals 11stst occur at occur at

n=2n=2 for n>2, for n>2,

shape is shape is same but same but size size increasesincreases

+

--

-

+

+

-

d- orbitalsd- orbitals

d orbitals: 5: d orbitals: 5: 3d3dxzxz, , 3d3dyzyz, , 3d3dxyxy, , 3d3dx2-y2x2-y2, , ddz2z2

mostly cloverleafmostly cloverleaf ll value of 2value of 2 11stst occur at n=3; no d-orbitals for n=1 occur at n=3; no d-orbitals for n=1

or n=2or n=2 for n>3, same shape but larger sizefor n>3, same shape but larger size

+

+-

-

f-orbitalsf-orbitals

f orbitals: 7 typesf orbitals: 7 types various shapesvarious shapes ll value of 3value of 3 begin in n=4begin in n=4

Other shapes can exist in energy levels Other shapes can exist in energy levels as long as they follow the rulesas long as they follow the rules

g (g (ll =4) starts in 5 with 9 orbitals=4) starts in 5 with 9 orbitals

h (h (ll =5) starts in 6 with 11 orbitals, etc=5) starts in 6 with 11 orbitals, etc but no known elements have electrons but no known elements have electrons

in them at ground statein them at ground state Remember that all orbitals of the same Remember that all orbitals of the same

n has the same energy; they are called n has the same energy; they are called “degenerate“degenerate””

7.8 Electron spin and the Pauli 7.8 Electron spin and the Pauli PrinciplePrinciple

Spin Quantum Number: Spin Quantum Number: mmss Electron has a magnetic moment with two Electron has a magnetic moment with two

possible orientations when the atom is possible orientations when the atom is placed in an external magnetic field placed in an external magnetic field

The electron could have two spin states The electron could have two spin states only 2 possible directionsonly 2 possible directions mmss can have two possible values: +½ and -½ can have two possible values: +½ and -½ paired electrons must paired electrons must

have opposite spinshave opposite spins

Pauli Exclusion Principle:Pauli Exclusion Principle: In a given atom, no two electrons can In a given atom, no two electrons can

have the same set of four quantum have the same set of four quantum numbers (numbers (n, n, l, ml, mll , m , mss ))

An orbital can hold only two electrons An orbital can hold only two electrons and they must have opposite spins. and they must have opposite spins.

7.9 Polyelectronic Atoms7.9 Polyelectronic Atoms

Three energy contributions must be Three energy contributions must be consideredconsidered

in the description of polyelectronic atom: in the description of polyelectronic atom: Kinetic energy of electrons - as the Kinetic energy of electrons - as the

electrons move around the nucleuselectrons move around the nucleus Potential energy - from attraction Potential energy - from attraction

between electrons and nucleusbetween electrons and nucleus Potential energy of repulsion between Potential energy of repulsion between

two electronstwo electrons

Electron Correlation ProblemElectron Correlation Problem

can’t find the exact location of can’t find the exact location of electronselectrons

can’t find the specific repulsions can’t find the specific repulsions between electronsbetween electrons

so we must treat each electron as so we must treat each electron as if it has an average amount of if it has an average amount of attraction to nucleus and attraction to nucleus and repulsion to other electronsrepulsion to other electrons

Electron ShieldingElectron Shielding

occurs when an electron is not occurs when an electron is not attracted to the nucleusattracted to the nucleus

because of electrons in lower energy because of electrons in lower energy levels repelling it.levels repelling it.

Penetration EffectPenetration Effect all orbitals in the same energy level do all orbitals in the same energy level do NOTNOT have the have the

same amount of energy ( are not degenerate) same same amount of energy ( are not degenerate) same as the case in H-atomas the case in H-atom

EEnsns < E < Enpnp < E < Endnd < E < Enfnf

the amount of energy in each sublevel is determined the amount of energy in each sublevel is determined by its average distance from the nucleusby its average distance from the nucleus

For example, in He atom, 2p orbital has its For example, in He atom, 2p orbital has its maximum probability closer to the nucleus than 2s maximum probability closer to the nucleus than 2s orbital, thus we would predict 2p would have less orbital, thus we would predict 2p would have less energy than 2s. energy than 2s.

However, 2s electron spends more time closer to However, 2s electron spends more time closer to nucleus and usually has less energy.nucleus and usually has less energy.

That is 2s electron penetrates to the nucleus more That is 2s electron penetrates to the nucleus more than an electron in a 2p orbitalthan an electron in a 2p orbital

7.10 The history of the Periodic Table

Developed independently by German Julius Lothar Meyer and Russian Dmitri Mendeleev (1870’s).

They didn’t know much about atom. Elements were arranged in columns by

similar properties. Properties of missing elements were

predicted.

Mendeleev's Early Periodic Table, Published in 1872

7.11 The aufbau Principle and Periodic Table Electron Arrangement in Atoms

The way electrons are arranged in various orbitals around the nuclei of atoms.

Aufbau is a German word means “Building up” Aufbau principle - electrons enter the lowest

energy first.• Orbitals of different energies overlap •

Electron Configurations• Electron configuration describes the distribution of electrons among the various orbitals in the atom

The spdf notation uses numbers to designate a principal shell and the letters to identify a subshell; a superscript number indicates the number of electrons in a designated subshell

Orbital Diagram

EOS

Each box has arrows representing electron spins; opposing spins are paired together

An orbital diagram uses boxes to represent orbitals within subshells and arrows to represent electrons:

Rules for Electron ConfigurationsElectrons occupy the lowest available energy orbitals

Pauli exclusion principle – no two electrons in the same atom may have the same four quantum numbers

•Orbitals hold ahold a maximum of two electrons with opposed spins

Rules for Electron Configurations

For orbitals of identical energy, electrons enter empty orbitals whenever possible – Hund’s rule

Electrons in half-filled orbitals have parallel spins

EOS

When electrons occupy orbitals of equal energy,

they don’t pair up until they have to.

Rules for Electron Configurations

EOS

Capacities of shells (n) and subshells (l)

Rules for Electron Configurations

Subshell filling order :

Each subshell must be filled before moving to the next level

Electron Configurations

Let’s write the electron configuration for Phosphorus

We need to account for all 15 electrons in phosphorus

The first two electrons go into the 1s orbital

Notice the opposite direction of the spins

only 13 more to go Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

15P

The next electrons go into the 2s orbital

only 11 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 2p orbital

• only 5 more Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 3s orbital

• only 3 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The last three electrons go into the 3p orbitals.

They each go into separate orbitas (Hund’s)

• 3 unpaired electrons• = 1s1s222s2s222p2p663s3s223p3p33

The Aufbau Principle

A hypothetical building up of an atom from the one that precedes it in atomic number

(Z = 1) H 1s1

(Z = 2) He 1s2

(Z = 3) Li 1s22s1

EOS

(Z = 3) Li 1s22s1 [He]2s1

Abbreviated electron configuration

The Aufbau Principle [He]2p2

[He]2p3

[He]2p4

[He]2p5

EOS

[He]2p6

Orbital Diagram for A Nitrogen AtomOrbital Diagram for A Nitrogen Atom

77NN

1s 2s 2p1s 2s 2p 3s 3s

Orbital Diagram for A Fluorine AtomOrbital Diagram for A Fluorine Atom

99FF

1s 2s 2p1s 2s 2p 3s 3s

Orbital Diagram for A Magnesium AtomOrbital Diagram for A Magnesium Atom

1212MgMg

1s 2s 2p1s 2s 2p 3s 3s

88OO

1s 2s 2p1s 2s 2p 3s 3s

Write the orbital diagram for the Write the orbital diagram for the electrons in an iron atom electrons in an iron atom 2626FeFe

1s 2s 2p 3s 3p1s 2s 2p 3s 3p

3d3d

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

the orbital. Full orbitals are the absolute best situation.

However, half filled orbitals have a lower energy, and are next best• Makes them more stable.• Changes the filling order

Write the electron configurations for these elements:

Titanium - 22 electrons 1s22s22p63s23p64s23d2

Vanadium - 23 electrons 1s22s22p63s23p64s23d3

Chromium - 24 electrons 1s22s22p63s23p64s23d4 (expected)But this is not what happens!!

Chromium is actually:1s22s22p63s23p64s13d5

Why?This gives us two half filled

orbitals (the others are all still full)Half full is slightly lower in energy.The same principal applies to

copper.

Copper’s electron configuration

Copper has 29 electrons so we expect: 1s22s22p63s23p64s23d9

But the actual configuration is: 1s22s22p63s23p64s13d10

This change gives one more filled orbital and one that is half filled.

Remember these exceptions: d4, d9

Irregular configurations of Cr and Cu

Chromium steals a 4s electron to make its 3d sublevel HALF FULL

Copper steals a 4s electron to FILL its 3d sublevel

Electron Configurations of Ions

Cations: lose e– to attain a complete valence shell

Example:

(Z = 11) Na

(Z = 11) Na+

Details of the Periodic Table

Elements in the same column have the same electron configuration.

Elements in columns have similar properties.

Noble gases have filled energy levels. Transition metals are filling the d orbitals

Valence electrons- the electrons in the outermost energy levels (not d).

Core electrons- the inner electrons.

C 1s2 2s2 2p2

Valence Electrons and Core Electrons

Valence electrons are those with the highest principal quantum number

The electrons in the outermost energy levels (not d).

Sulfur has six valence electrons

Valence Electrons and Core Electrons

Electrons in inner shells are called core electrons

EOS

Sulfur has 10 core electrons

Periodic Relationships

We can deduce the general form of electron configurations directly from the periodic table

The Periodic Table

More exceptions

Lanthanum La: [Xe] 6s2 5d1 Cerium Ce: [Xe] 6s2 4f1 5d1

Promethium Pr: [Xe] 6s2 4f3 5d0

Gadolinium Gd: [Xe] 6s2 4f7 5d1

Lutetium Pr: [Xe] 6s2 4f14 5d1

We’ll just pretend that all except Cu and Cr follow the rules.

Main Group (Representative) and Transition Elements

Elements in which the orbitals being filled in the aufbau process are either s or p orbitals of the outermost shell are called main group (Representative) elements

“A” group designation on the periodic table

The first 20 elements are all main group elements

Transition Elements

In transition elements, the sublevel (shell) being filled in the aufbau process is in an inner principal shell (d or f)

f-Block transition elements: d sublevels are completely filled. Electrons enter f-sublevels

d-Block transition elements: Electrons enter the d-sublevels .

Lanthanides: electrons fill 4f subleve

Actinides: electrons fill 5f sublevels

Th

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Periodic Relationships

7.12 Periodic Trends 7.12 Periodic Trends in Atomic Propertiesin Atomic Properties

Ionization EnergyIonization Energy Ionization energy the energy required to Ionization energy the energy required to

remove an electron completely form a remove an electron completely form a ground state atom in the ground state atom in the gaseous phasegaseous phase

A (g) + energy A (g) + energy A A+ + (g) + e(g) + e--

Highest energy electron removed Highest energy electron removed firstfirst. .

First ionization energy First ionization energy ((II11) ) is that is that required to remove the first required to remove the first electronelectron..

Second ionization energy Second ionization energy ((II22) - ) - the the second electron,second electron, etcetc..

Successive ionization EnergiesSuccessive ionization Energies

for Mg for Mg • II11 = = 735 kJ735 kJ//molemole• II22 = = 1445 kJ1445 kJ//molemole• II33 = = 7730 kJ7730 kJ//molemole

The The effective nuclear chargeeffective nuclear charge increases as electronsincreases as electrons are removedare removed

It takes much more energy to It takes much more energy to remove a remove a core electron than a core electron than a valence electronvalence electron because there is because there is less shieldingless shielding..

Successive ionization EnergiesSuccessive ionization Energies

Continual removal of electrons increases ionization energy greatly

B B+ + e– I = 801 kJ mol–1

B+ B+2 + e– I = 2427 kJ mol–1

B+2 B+3 + e– I = 3660 kJ mol–1

B+3 B+4 + e– I = 25,025 kJ mol–1

B+4 B+5 + e– I = 32,822 kJ mol–1

Core electron

Ionization EnergyIonization Energy

First ionization energies across First ionization energies across Periods and GroupsPeriods and Groups

The Values of First Ionization Energy for The Values of First Ionization Energy for the Elements in the First Six Periodsthe Elements in the First Six Periods

For B electrons in 2s provide some shieldingFrom nucleus charge

E for O < E for N due to extra electron repulsion in the doubly occupied O 2p orbitals

Ionization EnergyIonization Energy

Ionization EnergyIonization Energy

Electron AffinityElectron Affinity

Electron AffinityElectron Affinity – the energy – the energy change when an electron is change when an electron is added to a gaseous neutral atom neutral atom

A + eA + e- - A A-- + energy + energy

Cl(g) + e- Cl-(g) E = -349 kJ/mol

• Electron affinities are expressed as negative because the process is exothermic

Electron affinity values

Ele

ctro

n A

ffin

ityEle

ctro

n A

ffin

ity

Electron AffinityElectron Affinity

Across Period:Across Period: releases more releases more

energy so number energy so number increases (gets increases (gets more negative)more negative)

because electrons because electrons added in the added in the same energy level same energy level do not shield do not shield electrons from electrons from nuclear chargenuclear charge

Down Group:Down Group: releases less releases less

energy so energy so number number decreases (gets decreases (gets less negative)less negative)

because the because the electrons being electrons being added are farther added are farther away from the away from the attracting attracting protonsprotons

Atomic RadiiAtomic Radii

Size of orbitals Size of orbitals can can notnot be specified be specified exactly, neither can exactly, neither can the size of atomthe size of atom

Atomic RadiiAtomic Radii – half – half the distance the distance between the nuclei between the nuclei of identical atoms of identical atoms that are bonded that are bonded togethertogether

Atomic RadiiAtomic Radii Across Period:Across Period:

atoms get smalleratoms get smaller because of the because of the

increased number increased number of protons of protons attracting the attracting the electronselectrons

the electrons added the electrons added in the same energy in the same energy level do not shield level do not shield electrons from electrons from nuclear chargenuclear charge

Down Group:Down Group: atoms get atoms get

largerlarger increasesincreases because the because the

energy levels energy levels being added to being added to the atomthe atom

Atomic Radii PropertiesAtomic Radii Properties

Summary of Periodic Trends