1Modern Atomic Theory

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Electromagnetic radiation.

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Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic RadiationRadiation

• Most subatomic particles behave as Most subatomic particles behave as PARTICLES and obey the physics of waves. PARTICLES and obey the physics of waves.

4

wavelength Visible light

wavelength

Ultaviolet radiation

Amplitude

Node

Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic RadiationRadiation

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• Waves have a frequencyWaves have a frequency• Use the Greek letter “nu”, Use the Greek letter “nu”, , for frequency, , for frequency,

and units are “cycles per sec”and units are “cycles per sec”

• All radiation: All radiation: • • = c = cwhere c = velocity of light = 3.00 x 10where c = velocity of light = 3.00 x 1088 m/sec m/sec

Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic RadiationRadiation

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Electromagnetic Electromagnetic SpectrumSpectrum

Electromagnetic Electromagnetic SpectrumSpectrum

Long wavelength --> small frequencyLong wavelength --> small frequency

Short wavelength --> high frequencyShort wavelength --> high frequency

increasing increasing frequencyfrequency

increasing increasing wavelengthwavelength

7 Electromagnetic Spectrum

Electromagnetic Spectrum

In increasing energyIn increasing energy, R, ROOYY GG BBIIVV

8Excited Gases Excited Gases & Atomic & Atomic StructureStructure

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Atomic Line Emission Atomic Line Emission Spectra and Niels BohrSpectra and Niels BohrAtomic Line Emission Atomic Line Emission

Spectra and Niels BohrSpectra and Niels Bohr

Bohr’s greatest contribution to Bohr’s greatest contribution to science was in building a simple science was in building a simple model of the atom. It was based model of the atom. It was based on an understanding of theon an understanding of the LINE LINE EMISSION SPECTRAEMISSION SPECTRA of excited of excited atoms.atoms.

•Problem is that the model only Problem is that the model only works for Hworks for H

Niels BohrNiels Bohr

(1885-1962)(1885-1962)

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Spectrum of White Spectrum of White LightLight

11Line Emission Line Emission Spectra Spectra

of Excited Atomsof Excited Atoms

Line Emission Line Emission Spectra Spectra

of Excited Atomsof Excited Atoms• Excited atoms emit light of only

certain wavelengths

• The wavelengths of emitted light depend on the element.

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Spectrum of Spectrum of Excited Hydrogen GasExcited Hydrogen Gas

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Line Spectra of Other Line Spectra of Other ElementsElements

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Atomic SpectraAtomic SpectraAtomic SpectraAtomic Spectra

+Electronorbit

One view of atomic structure in early 20th One view of atomic structure in early 20th century was that an electron (e-) traveled century was that an electron (e-) traveled about the nucleus in an orbit.about the nucleus in an orbit.

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Atomic Spectra and Atomic Spectra and BohrBohr

Atomic Spectra and Atomic Spectra and BohrBohr

Bohr said classical view is wrong. Bohr said classical view is wrong.

Need a new theory — now called Need a new theory — now called QUANTUMQUANTUM or or WAVE MECHANICSWAVE MECHANICS..

e- can only exist in certain discrete e- can only exist in certain discrete orbitsorbits

e- is restricted to e- is restricted to QUANTIZEDQUANTIZED energy energy state (quanta = bundles of energy)state (quanta = bundles of energy)

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Schrodinger applied idea of e- Schrodinger applied idea of e- behaving as a wave to the behaving as a wave to the problem of electrons in atoms.problem of electrons in atoms.

He developed the He developed the WAVE WAVE EQUATIONEQUATION

Solution gives set of math Solution gives set of math expressions called expressions called WAVE WAVE FUNCTIONS, FUNCTIONS,

Each describes an allowed energy Each describes an allowed energy state of an e-state of an e-

E. SchrodingerE. Schrodinger1887-19611887-1961

Quantum or Wave Quantum or Wave MechanicsMechanics

Quantum or Wave Quantum or Wave MechanicsMechanics

17Heisenberg Heisenberg Uncertainty PrincipleUncertainty Principle

• The problem of defining nature of electrons in atoms solved by W. Heisenberg.

• He observed that on cannot simultaneously define the position and momentum (= m•v) of an electron.

• If we define the energy exactly of an electron precisely we must accept limitation that we do not know exact position.

• The problem of defining nature of electrons in atoms solved by W. Heisenberg.

• He observed that on cannot simultaneously define the position and momentum (= m•v) of an electron.

• If we define the energy exactly of an electron precisely we must accept limitation that we do not know exact position.

W. HeisenbergW. Heisenberg1901-19761901-1976

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Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Electrons in atoms are arranged asElectrons in atoms are arranged as

LEVELSLEVELS (n) (n)

SUBLEVELSSUBLEVELS (l) (l)

ORBITALSORBITALS (m (mll))

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QUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERS

The The shape, size, and energyshape, size, and energy of each orbital is a function of each orbital is a function of 3 quantum numbers which describe the location of of 3 quantum numbers which describe the location of an electron within an atom or ionan electron within an atom or ion

nn (principal)(principal) ---> energy level---> energy level

ll (orbital) (orbital) ---> shape of orbital---> shape of orbital

mmll (magnetic)(magnetic) ---> designates a particular ---> designates a particular suborbitalsuborbital

The fourth quantum number is not derived from the The fourth quantum number is not derived from the wave functionwave function

ss (spin)(spin) ---> spin of the electron ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)(clockwise or counterclockwise: ½ or – ½)

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QUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERS

So… if two electrons are in the same place at So… if two electrons are in the same place at the same time, they must be repelling, so at the same time, they must be repelling, so at least the spin quantum number is different!least the spin quantum number is different!

The The Pauli Exclusion PrinciplePauli Exclusion Principle says that says that no two no two electrons within an atom (or ion) can have the electrons within an atom (or ion) can have the same four quantum numbers.same four quantum numbers.

If two electrons are in the same energy level, If two electrons are in the same energy level, the same sublevel, and the same orbital, they the same sublevel, and the same orbital, they must repel.must repel.

Think of the 4 quantum numbers as the address Think of the 4 quantum numbers as the address of an electron… Country > State > City > of an electron… Country > State > City > StreetStreet

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Energy LevelsEnergy LevelsEnergy LevelsEnergy Levels

• Each energy level has a number Each energy level has a number called thecalled the PRINCIPAL PRINCIPAL QUANTUM NUMBER, nQUANTUM NUMBER, n

• Currently n can be 1 thru 7, Currently n can be 1 thru 7, because there are 7 periods on because there are 7 periods on the periodic tablethe periodic table

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Energy LevelsEnergy LevelsEnergy LevelsEnergy Levels

n =n = 11

n = 2n = 2

n = 3n = 3

n = 4n = 4

23Relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen.

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Types of Orbitals

• The most probable area to find The most probable area to find these electrons takes on a shapethese electrons takes on a shape

• So far, we have 4 shapes. They So far, we have 4 shapes. They are named s, p, d, and f. are named s, p, d, and f.

• No more than 2 eNo more than 2 e-- can be assigned can be assigned to any single orbital – one spins to any single orbital – one spins clockwise, one spins clockwise, one spins counterclockwisecounterclockwise

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Types of Orbitals Types of Orbitals ((ll))

s orbitals orbital pp orbitalorbital dd orbitalorbital

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p Orbitalsp Orbitalsp Orbitalsp Orbitals

The The p sublevelp sublevel has has

3 orbitals3 orbitalsThey are designated as pThey are designated as pxx, p, pyy, ,

and pand pzz

The The p sublevelp sublevel has has

3 orbitals3 orbitalsThey are designated as pThey are designated as pxx, p, pyy, ,

and pand pzz

planar node

Typical p orbital

There is aThere is a PLANAR PLANAR NODENODE thru the thru the nucleus, which is nucleus, which is an area of zero an area of zero probability of probability of finding an electronfinding an electron

3p3pyy orbital orbital

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p Orbitalsp Orbitalsp Orbitalsp Orbitals

• The three p orbitals lie 90The three p orbitals lie 90oo apart in space apart in space

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d Orbitalsd Orbitalsd Orbitalsd Orbitals

• d sublevel has 5 d sublevel has 5 orbitalsorbitals

typical d orbital

planar node

planar node

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The shapes and labels of the five 3d orbitals.

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f Orbitalsf Orbitalsf Orbitalsf Orbitals

For l = 3, For l = 3, ---> f sublevel with 7 orbitals---> f sublevel with 7 orbitals

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Diagonal Rule• Must be able to write it for the test!

This will be question #1 ! Without it, you will not get correct answers !

• The diagonal rule is a memory device that helps you remember the order of the filling of the orbitals from lowest energy to highest energy

• _____________________ states that electrons fill from the lowest possible energy to the highest energy

32Diagonal Rule

ss

s 3p 3ds 3p 3d

ss 2p2p

s 4p 4d 4fs 4p 4d 4f

s 5p 5d 5f s 5p 5d 5f 5g?5g?

s 6p 6d s 6p 6d 6f 6g? 6h?6f 6g? 6h?

s 7p s 7p 7d 7f 7g? 7h? 7i?7d 7f 7g? 7h? 7i?

11

22

33

44

55

66

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Steps:Steps:

1.1. Write the energy levels top to bottom.Write the energy levels top to bottom.

2.2. Write the orbitals in s, p, d, f order. Write Write the orbitals in s, p, d, f order. Write the same number of orbitals as the energy the same number of orbitals as the energy level.level.

3.3. Draw diagonal lines from the top right to the Draw diagonal lines from the top right to the bottom left.bottom left.

4.4. To get the correct order, To get the correct order,

follow the arrows!follow the arrows!

By this point, we are past By this point, we are past the current periodic table the current periodic table so we can stop.so we can stop.

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Why are d and f orbitals always in lower energy levels?

• d and f orbitals require LARGE amounts of energy

• It requires less in energy to skip a sublevel that requires a large amount of energy such as d and f orbtials for one in a higher level but lower energy such as a s or p orbital

This is the reason for the diagonal rule! BE SURE TO FOLLOW THE ARROWS IN ORDER!

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s orbitalss orbitals d orbitalsd orbitals

Number ofNumber oforbitalsorbitals

Number of Number of electronselectrons

p orbitalsp orbitals f orbitalsf orbitals

How many electrons can be in a sublevel?How many electrons can be in a sublevel?

Remember: A maximum of two electrons can Remember: A maximum of two electrons can be placed in an orbital.be placed in an orbital.

1 3 5 71 3 5 7

22 6 10 14 6 10 14

35Electron Configurations

A list of all the electrons in an atom (or ion)

• Must go in order (Aufbau principle)

• 2 electrons per orbital, maximum

• We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons.

• The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule

1s1s22 2s 2s22 2p 2p66 3s 3s22 3p 3p66 4s 4s22 3d 3d1010 4p 4p66 5s 5s22 4d 4d1010 5p 5p66 6s 6s22 4f 4f1414… etc.… etc.

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Electron Configurations

2p4

EnergyEnergy LevelLevel

SublevelSublevel

Number of Number of electrons in electrons in the sublevelthe sublevel

1s1s22 2s 2s22 2p 2p66 3s 3s22 3p 3p66 4s 4s22 3d 3d1010 4p 4p66 5s 5s22 4d 4d1010 5p 5p66 6s6s22 4f 4f1414… etc.… etc.

37Let’s Try It!

• Write the electron configuration for the following elements:

H

Li

N

Ne

K

Zn

Pb

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An excited lithium atom emitting a photon of red light to drop to a

lower energy state.

39An excited H atom returns to a

lower energy level.

40Orbitals and the Orbitals and the Periodic TablePeriodic Table

• Orbitals grouped in s, p, d, and f orbitals Orbitals grouped in s, p, d, and f orbitals (sharp, proximal, diffuse, and fundamental)(sharp, proximal, diffuse, and fundamental)

s orbitalss orbitalsp orbitalsp orbitals

d orbitalsd orbitals

f orbitalsf orbitals

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Shorthand Notation

• A way of abbreviating long electron configurations

• Since we are only concerned about the outermost electrons, we can skip to places we know are completely full, i.e. the noble gases , and then finish the configuration

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Shorthand Notation

• Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). It will be at the end of the period above the element that you are working with Write the noble gas in brackets [ ].

• Step 2: Find where to resume by finding the next energy level.

• Step 3: Resume the configuration until it’s finished.

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Shorthand Notation• Chlorine

– Longhand is 1s2 2s2 2p6 3s2 3p5

You can abbreviate the first 10 electrons with a noble gas, Neon. [Ne] replaces 1s2 2s2 2p6

The next energy level after Neon is 3

So you start at level 3 on the diagonal rule (all levels start with s) and finish the configuration by adding 7 more electrons to bring the total to 17

[Ne] 3s2 3p5

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Practice Shorthand Notation

• Write the shorthand notation for each of the following atoms:

Cl

K

Ca

I

Bi

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Valence ElectronsValence ElectronsValence ElectronsValence ElectronsElectrons are divided between core and Electrons are divided between core and

valence electronsvalence electronsB B 1s1s22 2s2s22 2p 2p11

Core = [He]Core = [He] , , valence = 2svalence = 2s22 2p 2p11

Br Br [Ar][Ar] 4s4s22 3d3d1010 4p4p55

Core = [Ar] 3dCore = [Ar] 3d1010 , , valence = 4svalence = 4s22 4p 4p55

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Rules of the GameRules of the GameRules of the GameRules of the GameNo. of valence electrons of a main group No. of valence electrons of a main group

atom = Group number (for A groups)atom = Group number (for A groups)

Atoms like to either empty or fill their outermost Atoms like to either empty or fill their outermost level. Since the outer level contains two s level. Since the outer level contains two s electrons and six p electrons (d & f are always in electrons and six p electrons (d & f are always in lower levels), the optimum number of electrons lower levels), the optimum number of electrons is eight. This is called the is eight. This is called the octet ruleoctet rule..

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Keep an Eye On Those Ions!

• Electrons can be lost or gained by atoms to form ions

• negative ions have gained electrons, positive ions have lost electrons

• The electrons that are lost or gained should be added/removed from the highest energy level (not the highest orbital in energy!)

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Forming Ions!

• Tin

Atom: [Kr] 5s2 4d10 5p2

Sn+4 ion: [Kr] 4d10

Sn+2 ion: [Kr] 5s2 4d10

Note that the electrons came out of the highest energy level, not the highest energy orbital!

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Keep an Eye On Those Ions!

• Bromine

Atom: [Ar] 4s2 3d10 4p5

Br- ion: [Ar] 4s2 3d10 4p6

Note that the electrons went into the highest energy level, not the highest energy orbital!

50Try Some Ions!

• Write the longhand notation for these:

F-

Li+

Mg+2

• Write the shorthand notation for these:

Br-

Ba+2

Al+3

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Exceptions to the Aufbau Principle

• Remember d and f orbitals require LARGE amounts of energy

• If we can’t fill these sublevels, then the next best thing is to be HALF full (one electron in each orbital in the sublevel)

• There are many exceptions, but the most common ones are

d4 and d9

For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d4 or d9 are exceptions to the rule. This may or may not be true, it just depends on the atom.

52Exceptions to the Aufbau Principle

• d4 is one electron short of being HALF full

• In order to become more stable (require less energy), one of the closest s electrons will actually go into the d, making it d5 instead of d4.

• For example: Cr would be [Ar] 4s2 3d4, but since this ends exactly with a d4 it is an exception to the rule. Thus, Cr should be [Ar] 4s1 3d5.

• Procedure: Find the closest s orbital. Steal one electron from it, and add it to the d.

53Exceptions to the Aufbau

Principle

• s orbitals can also be subject to exceptions to the Aufbau process, especially in the d block elements

• Remember, half full is OK. When an s orbital loses 1 electron, it too becomes half full!

• Having the s half full and the d half full is usually lower in energy than having the s full and the d to have one empty orbital.

54Exceptions to the Aufbau Principle

• d9 is one electron short of being full

• Just like d4, one of the closest s electrons will go into the d, this time making it d10 instead of d9.

• Example: Au would be [Xe] 6s2 4f14 5d9, but since this ends exactly with a d9 it is an exception to the rule. Thus, Au should be [Xe] 6s1 4f14 5d10.

• Find the closest s orbital. Steal one electron from it, and add it to the d.

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Try These!

• Write the shorthand notation for:

Cu

W

Au

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Orbital Diagrams

• Graphical representation of an electron configuration

• One arrow represents one electron

• Shows spin and which orbital within a sublevel

• Same rules as before (Aufbau principle, d4 and d9 exceptions, two electrons in each orbital, etc. etc.)

57Orbital Diagrams

• One additional rule: Hund’s Rule

– In orbitals of EQUAL ENERGY (p, d, and f), place one electron in each orbital before making any pairs

– All single electrons must spin the same way

• Think of this rule as the “Monopoly Rule”

• In Monopoly, you have to build houses EVENLY. You can not put 2 houses on a property until all the properties has at least 1 house.

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LithiumLithiumLithiumLithium

Group 1AGroup 1A

Atomic number = 3Atomic number = 3

1s1s222s2s11 ---> 3 total electrons ---> 3 total electrons

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CarbonCarbonCarbonCarbon

Group 4AGroup 4A

Atomic number = 6Atomic number = 6

1s1s2 2 2s2s2 2 2p2p22 ---> --->

6 total electrons6 total electrons

Here we see for the first timeHere we see for the first time

HUND’S RULEHUND’S RULE.. When When placing electrons in a set of placing electrons in a set of orbitals having the same orbitals having the same energy, we place them singly energy, we place them singly as long as possible.as long as possible.

60Lanthanide Element Lanthanide Element

ConfigurationsConfigurations

4f orbitals used for Ce - Lu and 5f for Th - Lr

4f orbitals used for Ce - Lu and 5f for Th - Lr

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Draw these orbital diagrams!

• Oxygen (O)

• Chromium (Cr)

• Mercury (Hg)

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Ion ConfigurationsIon ConfigurationsIon ConfigurationsIon Configurations

To form anions from elements, add 1 or more To form anions from elements, add 1 or more e- from the highest sublevel.e- from the highest sublevel.

P [Ne] 3sP [Ne] 3s22 3p 3p33 + 3e- ---> P + 3e- ---> P3-3- [Ne] 3s [Ne] 3s22 3p 3p66 or [Ar] or [Ar]

1s

2s

3s3p

2p

1s

2s

3s3p

2p

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The End !!!!!!!!!!!!!!!!!!!