Modern Atomic Theory

ELECTROMAGNETIC ELECTROMAGNETIC RADIATIONRADIATION

ELECTROMAGNETIC ELECTROMAGNETIC RADIATIONRADIATION

Electromagnetic radiation

Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic RadiationRadiation

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

wavelength Visible light

wavelength

Ultraviolet radiation

Amplitude

Node

Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic RadiationRadiation

• Wavelength, , is how long the wave is, from peak to peak

• Waves have a frequency, : how often the waves pass through a given point in a certain time

• All radiation travels at the same speed:

• = cc = velocity of light = 3.00 x 108 m/sec= wavelength (meters) = frequency (Hz or sec-1)

Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic RadiationRadiation

Electromagnetic Electromagnetic SpectrumSpectrum

Electromagnetic Electromagnetic SpectrumSpectrum

Long wavelength --> small frequency = low energyLong wavelength --> small frequency = low energyShort wavelength --> high frequency = high energyShort wavelength --> high frequency = high energy

increasing increasing frequencyfrequency

increasing increasing wavelengthwavelength

ElectroElectromagneticmagnetic SpectrumSpectrum

ElectroElectromagneticmagnetic SpectrumSpectrum

In increasing energy, RIn increasing energy, ROOYY GG BBIIVV

Particle Nature of Light• Light as a WAVE explains most everyday

behavior, but not everything• Light is also a PARTICLE

• Explains why only certain frequencies of light are observed when something is heated (example: iron)

• Matter can only gain or lose energy in small, specific amounts called quanta (plural)

• WHOA! This wave/particle duality of light was the beginning of quantum physics and leads to our current understanding of the atom

• https://www.youtube.com/watch?v=DfPeprQ7oGc

Planck’s equation

• Energy and frequency are directly related• The higher the energy, the higher the frequency

• Each frequency carries a specific amount of energy

• Ephoton = h Ephoton = the energy (in Joules) of a photon (a

massless light particle carrying energy) h = Planck’s constant (6.626 x 10-34 J s) = frequency (in s-1)

• Underline what you know • What is given in the problem?

• Circle what you don’t know • What are you trying to find?

• List everything out and identify variables

• Write formula and solve for the unknown• Substitute in values w/units

• Cancel units to see if everything is set up correctly

• Calculate and verify • Round at end only (SIG FIGS)

• Does the answer have correct units and make sense?

• What is the wavelength of electromagnetic radiation with a frequency of 5.00 x 1012 Hz?  What kind of radiation is this?

• A photon has an energy of 2.93 x 10 -25 J. What is its frequency? What type of radiation is this?

Atomic Line Emission Atomic Line Emission Spectra and Niels Spectra and Niels

BohrBohr

Atomic Line Emission Atomic Line Emission Spectra and Niels Spectra and Niels

BohrBohrBohr’s greatest contribution: Bohr’s greatest contribution:

building a simple model of building a simple model of the atom. It was based on an the atom. It was based on an understanding of theunderstanding of the LINE LINE EMISSION SPECTRAEMISSION SPECTRA of of excited atoms.excited atoms.

• Problem: only works for HProblem: only works for HNiels BohrNiels Bohr

(1885-1962)(1885-1962)

Atomic SpectraAtomic SpectraAtomic SpectraAtomic Spectra

+Electronorbit

Thanks to Niels Bohr, atomic structure in Thanks to Niels Bohr, atomic structure in early 20th century was that an electron (e-) early 20th century was that an electron (e-) traveled about the nucleus in an orbit.traveled about the nucleus in an orbit.

Line Emission Spectra Line Emission Spectra of Excited Atomsof Excited Atoms

Line Emission Spectra Line Emission Spectra of Excited Atomsof Excited Atoms

• Excited atoms emit light of only certain wavelengths

• The wavelengths of emitted light depend on the element

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

to a lower energy state.

An excited H atom returns to a lower energy level.

Spectrum of White Spectrum of White LightLight

Spectrum of Spectrum of Excited Hydrogen GasExcited Hydrogen Gas

Line Spectra of Other Line Spectra of Other ElementsElements

Atomic Spectra and Atomic Spectra and BohrBohr

Atomic Spectra and Atomic Spectra and BohrBohr

Need a new theory — now Need a new theory — now called called QUANTUMQUANTUM or or WAVE WAVE MECHANICSMECHANICS..

e- can only exist in certain e- can only exist in certain discrete orbitalsdiscrete orbitals

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

• Schrodinger applied idea of eSchrodinger 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 Each describes an allowed energy state of an eenergy state of an e-

E. SchrodingerE. Schrodinger1887-19611887-1961

Quantum or Wave Quantum or Wave MechanicsMechanics

Quantum or Wave Quantum or Wave MechanicsMechanics

Heisenberg Heisenberg Uncertainty Uncertainty

PrinciplePrincipleProblem of defining nature of Problem of defining nature of

electrons in atoms solved by electrons in atoms solved by W. Heisenberg.W. Heisenberg.

Cannot simultaneously define Cannot simultaneously define the position and momentum the position and momentum (= m•v) of an electron.(= m•v) of an electron.

We define e- energy exactly We define e- energy exactly but accept limitation that we but accept limitation that we do not know exact position.do not know exact position.

Problem of defining nature of Problem of defining nature of electrons in atoms solved by electrons in atoms solved by W. Heisenberg.W. Heisenberg.

Cannot simultaneously define Cannot simultaneously define the position and momentum the position and momentum (= m•v) of an electron.(= m•v) of an electron.

We define e- energy exactly We define e- energy exactly but accept limitation that we but accept limitation that we do not know exact position.do not know exact position.

W. HeisenbergW. Heisenberg1901-19761901-1976

Bohr vs. Quantum

• Bohr: orbit• Fixed path for e-

• Like a ring

• Quantum: orbital• A region of space that says where I will

probably find an e-

• Based on wave equations• Like a box

QUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSThe shape, size, and energy of each orbital is a

function of 3 quantum numbers which describe the location of an electron within an atom or ion

n (principal) ---> energy level, or shelll (angular) ---> sublevel, or subshell = shape of orbital

ml (magnetic) ---> designates a particular orbital

The fourth quantum number is not derived from the wave function

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

QUANTUM NUMBERSQUANTUM NUMBERS

• 2 e- max. can be in an orbital

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

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

• + 1/2 or - 1/2 for spin

Energy LevelsEnergy LevelsEnergy LevelsEnergy Levels• Each energy level has a number

called the PRINCIPAL QUANTUM NUMBER, n

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

• Higher energy, bigger orbitals

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

hydrogen.

Energy LevelsEnergy LevelsEnergy LevelsEnergy Levelsn = 1

n = 2

n = 3

n = 4

Sublevel: Shapes of Orbitals

• The most probable area to find electrons in an energy sublevel takes on a shape

• The angular quantum number (l) can be any integer between 0 and n - 1.

• So far, we have 4 shapes. They are named:s (l = 0), p (l = 1), d (l = 2), and f (l = 3).

Shapes of Orbitals (Shapes of Orbitals (ll))

s orbitals orbital p orbitalp orbital d orbitald orbital

Magnetic Quantum Number (ml)

s orbitals only have one s orbitals only have one direction they can be oriented direction they can be oriented in space, so min space, so mll = 0 = 0

The magnetic quantum number (ml) can be any integer between -l and +l.

l = 0 for s orbitalsl = 0 for s orbitals

p Orbitalsp Orbitalsp Orbitalsp Orbitals

this is a this is a p sublevelp sublevel (l = 1) (l = 1)

with with 3 orbitals 3 orbitals

(m(mll = -1, 0, 1) = -1, 0, 1)These are called x, y, and zThese are called x, y, and z

this is a this is a p sublevelp sublevel (l = 1) (l = 1)

with with 3 orbitals 3 orbitals

(m(mll = -1, 0, 1) = -1, 0, 1)These are called x, y, and zThese are called x, y, and z

planar node

Typical p orbital

planar node

Typical p orbital

There is a There 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

p Orbitalsp Orbitalsp Orbitalsp Orbitals

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

d Orbitalsd Orbitalsd Orbitalsd Orbitals• d sublevel (l = 2)

has 5 orbitals• ml = -2, -1, 0, 1, 2

typical d orbital

planar node

planar node

The shapes and labels of the five 3d orbitals.

f Orbitalsf Orbitalsf Orbitalsf OrbitalsFor l = 3, For l = 3,

---> f sublevel with 7 orbitals ---> f sublevel with 7 orbitals (m(mll = -3, -2, -1, 0, 1, 2, 3) = -3, -2, -1, 0, 1, 2, 3)

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.

11

22

33

66

55

1010

77

1414

Aufbau Rule

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

• Aufbau = German word for “building up”

• Follow the arrows!

Diagonal Ruless

s 3p 3ds 3p 3d

s 2ps 2p

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

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

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

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

11

22

33

44

55

66

77

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!

Why are d and f orbitals always in lower energy levels?• d and f orbitals require LARGE amounts

of energy

• It’s better (lower in energy) to skip a sublevel that requires a large amount of energy (d and f orbitals) for one in a higher level but lower energy

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

• Must go in order (Aufbau principle)

• 2 electrons per orbital, maximum

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.

Electron Configurations

2p4

Energy LevelEnergy Level

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.

Let’s Try It!• Write the electron configuration for

the following elements:

HLiBNNe

Orbitals and the Periodic Orbitals and the Periodic TableTable

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

fundamental)fundamental)

s orbitalss orbitals

p orbitalsp orbitalsd orbitalsd orbitals

f orbitalsf orbitals

Orbital Diagrams• Graphical representation of an

electron configuration• One “box” is one orbital• One arrow represents one electron• Shows spin and which orbital within

a sublevel

Orbital 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

• I nickname this rule 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.

LithiumLithiumLithiumLithium

Group 1AGroup 1AAtomic number = 3Atomic number = 31s1s222s2s11 ---> 3 total electrons ---> 3 total electrons

1s

2s

3s3p

2p

CarbonCarbonCarbonCarbonGroup 4AGroup 4AAtomic number = 6Atomic number = 61s1s2 2 2s2s2 2 2p2p22 ---> ---> 6 total electrons6 total electrons

1s

2s

3s3p

2p

Draw these orbital diagrams!

• Oxygen (O)

• Aluminum (Al)

• Chlorine (Cl)

Shorthand Notation

• A way of abbreviating long electron configurations

• Also called “noble gas” notation

• We want to identify valence electrons

Shorthand Notation

• Step 1:Find the closest noble gas (group 8) to the atom WITHOUT GOING OVER the number of electrons in the atom. Write the symbol in brackets [ ].

• Step 2: Write the rest of the configuration by finding the next energy level on the periodic table.

Shorthand Notation

• Chlorine

Longhand is 1s2 2s2 2p63s2 3p5

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

[1s2 2s2 2p6]

[Ne] 3s2 3p5

Practice Shorthand Notation

• Write the shorthand notation for each of the following atoms:• Mg• K• Co• As• Rb• I• Bi

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.

Try These!

• Write the shorthand notation for:

CuWAu

Valence Electrons

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

• Electrons that are in the highest energy level, s and/or p sublevels

• ELECTRONS determine the chemical behavior of an atom, so….

• Valence electrons determine how atoms will bond.

Valence Valence ElectronsElectronsValence Valence

ElectronsElectronsElectrons are divided between core and Electrons are divided between core and

valence electronsvalence electronsB 1sB 1s22 2s 2s22 2p 2p11

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

Br [Ar] 4sBr [Ar] 4s22 3d 3d1010 4p 4p55

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

Lewis Dot StructuresLewis Dot Structures

Valence Electrons

• Write shorthand configurations and underline the valence electrons:• Mg• Ge• I

Write longhand AND shorthand configs AND

underline valence electrons--Any patterns? • Group 1

• Group 2• Group 3A• Group 4A• Group 5A• Group 6A• Group 7A• Group 8A

Practice

• Wksh 4B-4• Write shorthand configurations AND draw

the Lewis dot structure

• What is the relationship between group number and the number of valence electrons in an atom?

• So, if group # = # of v.e; and v.e determine the chemical properties, then…

• Elements in the same group have similar chemical properties!