OFB Chapter 16 & 17 14/9/2004

Final Exam• Monday, April 26, 2004

– 2:50-5:40PM– Chem Annex Room 16

• Final 25% of Overall grade– Multiple Choice, no partial credit, no extra credit

• Chapters covered– Part A Chapters 1-6– Part B Chapters 7-10– Part C Chapters 11-14– Part D Chapters 16-17

• Crib Sheets allowed– 4 pages A-D above– single sided, handwritten

• Grade Improvement Plan– If Part A > Exam 1, Part A score replaces Exam 1– If Part B > Exam 2, Part B score replaces Exam 2– If Part C > Exam 3, Part C score replaces Exam 3– Will use Final Exam total, as sum Parts A+B+C+D

OFB Chapter 16 & 17 24/9/2004

Chapter 16Quantum Mechanics and the

Hydrogen Atom• 16-1 Waves and Light• 16-2 (skip) Paradoxes in

Classical Physics• 16-3 Planck, Einstein and Bohr• 16-4 Waves, Particles and the

Schrödinger Equation– only Schrödinger equation

• 16-5 The Hydrogen Atom

OFB Chapter 16 & 17 34/9/2004

16-1 Waves and Light“A Light Version”

• Electromagnetic Radiation– Energy travels through space by

electromagnetic radiation– Examples, sunlight, microwave ovens, cell

phones, X-rays, radiant heat forma fireplace, AM/FM radio, colors from fireworks

– All travel as waves– All travel as the speed of light

OFB Chapter 16 & 17 44/9/2004

OFB Chapter 16 & 17 54/9/2004

The electro magnetic spectrum.

The frequency doubles 80 times from right to left in the top diagram

The wavelength doubles 80 times from left to right in the top diagram

Visible light is confined within a single doubling near the middle

XXXXXXXXXXXXXXXXXXXXx

OFB Chapter 16 & 17 64/9/2004

OFB Chapter 16 & 17 74/9/2004

Important Equations

c = 3 x 108 m per secondλ = wavelengthν = frequency

h = Planck’s constanth = 6.62 x 10-34 Js orh = 6.62 x 10 -34 kg m2 s-1

OFB Chapter 16 & 17 84/9/2004

Radio Waves

• AM 890 kHz– 890,000 waves per second– Wavelength is 337 meters (about

1/5 mile)• FM 99.1 MHz

– 99,100,000 waves per second– Wavelength is 3 meters (about 10

feet)

c = λν

OFB Chapter 16 & 17 94/9/2004

Problems: General given two values, calculate the third, c is constant 3 X108

m/s

Problem

The laser in an audio compact disc (CD) player uses light with a wavelength of 780 nm. What is the frequency of the light emitted from the laser?

OFB Chapter 16 & 17 104/9/2004

Problem

The brilliant red color seen in fireworks displays is due to 4.62 x 1014 s-1

strontium emission. Calculate the wavelength of the light emitted.

c = λν

650nmλnm 1m 10

m6.5x10s4.62x10

m/s3x10νcλ

9-

7

114

8

==

=

==

−

−

OFB Chapter 16 & 17 114/9/2004

16-2 (skip) Paradoxes in Classical Physics

OFB Chapter 16 & 17 124/9/2004

16-3 Planck, Einstein, and Bohr

• 1901 Max Planck found that light (or energy) was quantized– Quite a surprise as light was thought to

be continuous• Energy can be gained or lost only in

integer multiples of hν.

n are whole numbers (1,2,3,…)• H is Planck’s constant• Determined experimentally

h = 6.628X10-34 J s• Each unit of size hν is called a

packet or quantum

OFB Chapter 16 & 17 134/9/2004

Problem

Blue fireworks (typically CuCl) emit light of 450 nm. What is the energy of the light emitted at 450 nm

c = λν E = hν

J4.41x10

m450x10m/s3x10sJ6.67x10

λchE

combineandRearrange

19

9

834

−

−−

=

•=

=

OFB Chapter 16 & 17 144/9/2004

• 1905 Einstein suggested that electromagnetic radiation can be viewed as a “stream of particles”called photons

• About the same time, Einstein derived his famous equation

E = mc2

• The main significance is that energy has mass

OFB Chapter 16 & 17 154/9/2004

E = mc2

• Rearrange

==

=

λchhνE

cEm

where

2

λch

cλch

m

cEm

photonaofmass

2

2

=

=

=

OFB Chapter 16 & 17 164/9/2004

Atomic Spectra of Hydrogen

emission hν H.)2

H H 1.)Decay Radiative

State) (Excited*

State) (Excited*Spark Energy High

2

→•

• →

emission green λhcE

22 =

emission blue λhcE

33 =

emission red λhcE

31 =

energy quantized λhcE

nn =

n is excited state orbitals

N = 1, 2, 3, …

OFB Chapter 16 & 17 174/9/2004

Quantized Emissions

Energy

n=3

n=2

n=1GS

emission green λhcE

22 =

emission blue λhcE

33 =

emission red λhcE

31 =

n=4

OFB Chapter 16 & 17 184/9/2004

The Bohr Model

nucleus

electron

called a Planetary Model

n=3n=2n=1

Orbital Transition Diagram

Eemission green

λhcE

22 =

emission blue λhcE

33 =

emission red λhcE

31 =

OFB Chapter 16 & 17 194/9/2004

Bohr calculated the angular momentum, radius and energy of the electrons traveling in discrete orbits

.1,2,3,.... n 2hn

vrmMomentumAngular e

==

=

π

etc.) He,for 2 H, of (1nucleus the on charge postive the is Z

state ground called 1n 1,2,3,...n states excited orbitals, n

constant a radius,bohr the called a

orbital each of radiusaZnr

0

0

2

n

===

==

)1018.2( 182

2Jx

nZEn

−−=Calculated levels match those on the photographic plate shown earlier

OFB Chapter 16 & 17 204/9/2004

Schrödinger EquationĤψ = Eψ

Results in many solutions, each solution consists of a wave function, ψ (n, l, ml) called quantum numbers

ψ = a wave function which defines an electrons position in 3D space (x, y, z), called an orbital

ψ2 = the probability that an electron is in a certain region of space

This defines the shape of the orbital (s, p, d, f)

OFB Chapter 16 & 17 214/9/2004

Solutions to the Schrödinger Equation

ψ (n, l, ml)• n = principal quantum number

n = 1, 2, 3, …n is related to the size and energy

of the orbital• l = azimuthal quantum number

l = 0, 1, …. (n-1)l is related to the shape of the

orbitall = 0 is called an s orbitall = 1 is called a p orbitall = 2 is called a d orbitall = 3 is called an f orbitall = 4 is called a g orbital

OFB Chapter 16 & 17 224/9/2004

Solutions to the Schrödinger Equation

• ml = magnetic quantum numberml = -l, … , 0, ….+lml relates to the orientation of the

orbital• Although not a solution to the

Schrödinger Equation, a 4th quantum number isms = electron spin quantum

numberms = +1/2, -1/2 denoted by ↑↓

OFB Chapter 16 & 17 234/9/2004

First four levels of Orbitals in hydrogenn l orbital

designationml # of

orbitals1 0 1s 0 1

0 2s 0 11 2p -1, 0, +1 30 3s 0 11 3p -1, 0, +1 32 3d -2, -1, 0, +1, +2 50 4s 0 11 4p -1, 0, +1 32 4d -2, -1, 0, +1, +2 53 4f -3, -2, -1, 0, +1, +2, +3 7

2

4

3

N vs l

– n is related to the size and energy of the orbital–l is related to the shape of the orbital–ml relates to the orientation of the orbital

l →

n →

OFB Chapter 16 & 17 244/9/2004

OFB Chapter 16 & 17 254/9/2004

n l orbital designation

ml # of orbitals

1 0 1s 0 10 2s 0 11 2p -1, 0, +1 30 3s 0 11 3p -1, 0, +1 32 3d -2, -1, 0, +1, +2 50 4s 0 11 4p -1, 0, +1 32 4d -2, -1, 0, +1, +2 53 4f -3, -2, -1, 0, +1, +2, +3 7

2

4

3

–n is related to the size and energy of the orbital–l is related to the shape of the orbital–ml relates to the orientation of the orbital

N vs l

OFB Chapter 16 & 17 264/9/2004

n l orbital designation

ml # of orbitals

1 0 1s 0 10 2s 0 11 2p -1, 0, +1 30 3s 0 11 3p -1, 0, +1 32 3d -2, -1, 0, +1, +2 50 4s 0 11 4p -1, 0, +1 32 4d -2, -1, 0, +1, +2 53 4f -3, -2, -1, 0, +1, +2, +3 7

2

4

3

– n is related to the size and energy of the orbital– l is related to the shape of the orbital– ml relates to the orientation of the orbital

OFB Chapter 16 & 17 274/9/2004

F- OrbitalsG-Orbitals

http://www.shef.ac.uk/chemistry/orbitron/

OFB Chapter 16 & 17 284/9/2004

Chapter 16Quantum Mechanics and the

Hydrogen Atom

• Example / exercise16-1, 16-5

• Problems14, 16, 22, 28, 34, 41

OFB Chapter 16 & 17 294/9/2004

Chapter 17Many-Electron Atoms and Chemical

Bonding• 17-1 Many-Electron Atoms and

the Periodic Table• 17-2 Experimental Measures of

Orbital Energies• 17-3 Sizes of Atoms and Ions• 17-4 Properties of the Chemical

Bond• 17-5 Ionic and Covalent Bonds• 17-6 Oxidation States and

Chemical Bonding

OFB Chapter 16 & 17 304/9/2004

Chapter 17Many Electron Atoms and Chemical

Bonding

• Aufbau Principle (building up)• Pauli Exclusion Principle

– No 2 electrons in an atom can have the same set of quantum numbers

n, l ml, ms

ψ (n, l, ml) called quantum numbers– n is related to the size and energy of the orbital– l is related to the shape of the orbital– ml relates to the orientation of the orbital– ms is electron spin quantum number

OFB Chapter 16 & 17 314/9/2004

Chapter 17Many Electron Atoms and

Chemical Bonding• Aufbau Principle (building up)• Pauli Exclusion Principle

– No 2 electrons in an atom can have the same set of quantum numbers

n, l ml, ms• Hund’s Rule

– When several orbitals are of equal energy, a single electron enters each orbital before a second electrons .

– In addition, the spins remain parallel until the second orbital enters the orbital.

OFB Chapter 16 & 17 324/9/2004

OFB Chapter 16 & 17 334/9/2004

• Hund’s Rule– When several orbitals are of equal

energy, a single electron enters each orbital before a second electrons .

– In addition, the spins remain parallel until the second orbital enters the orbital.

OFB Chapter 16 & 17 344/9/2004

Paramagnetic:

Attracted into a magnetic field

Have one or more un-paired electronsDiamagnetic:

Pushed out of a magnetic field

Have paired electrons

Carbon

(Z = 6)

paramagnetic

Xxxx

xxxxxBeryllium

(Z = 4)

diamagnetic

xxx

OFB Chapter 16 & 17 354/9/2004

Electron Configuration Nomenclature

1s22s22p6

10Ne:

1s22s22px22py

22pz2

[He]2s22p6

[Ne]

OFB Chapter 16 & 17 364/9/2004

OFB Chapter 16 & 17 374/9/2004

OFB Chapter 16 & 17 384/9/2004

Exercise (pg 730):

The ground-state electron configuration of an atom is 1s22s22p63s23p3. Name the atom. Is it paramagnetic? If so, state how many unpaired electrons it has.

15-electron atom;

Phosphorus

1s 2s 2px 2py 2pz 3s 3px 3py 3pz

This is paramagnetic with three unpaired electrons.

OFB Chapter 16 & 17 394/9/2004

• Valence Electrons– Are electrons that can become

directly involved in chemical bonding

– They occupy the outermost (highest energy) shell of an atom

– Beyond the immediately preceding noble-gas configuration

– Among the s-block and p-blockelements, the valence electrons include electrons in s and p sub shells only

OFB Chapter 16 & 17 404/9/2004

• Valence Electrons– Among the s-block and p-block

elements, the valence electrons include electrons in s and p sub shells only

– Among d-block and f-block(transition elements), valence electrons usually consist of electrons in s orbitals plus electrons in unfilled d and f sub shells

OFB Chapter 16 & 17 414/9/2004

Problem:

Write the valance-electron configuration and state the number of valence electrons in each of the following atoms and ions: (a) Y, (b) Lu, (c) Mg2+

(a) Y (Yttrium): atomic number Z = 39

[Kr] 5s2 4d 1 3 valence electrons

(b) Lu (Lutetium): Z = 71

[Xe] 6s 2 4f 14 5d 1

(c) Mg2+ (Magnesium (II) ion): Z = 12

This is the 2+ ion, thus 10 electrons

[Ne] configuration or 1s2 2s2 2p6

0 valence electrons

3 valence electronsNote filled 4f sub shell

OFB Chapter 16 & 17 424/9/2004

• Anomalous ground-state electron configurations are indicated explicitly

• All others can be derived from the position of the element in the table

The filling sub shells and the structure of the periodic table.

OFB Chapter 16 & 17 434/9/2004

PRS transmitters• Turn in your transmitters• Chem Annex Stockroom• Before the end of Finals week,

no extensions.• Make sure someone signs your

form indicating that they received the transmitter

• Otherwise, a $42 charge will be sent to the Bursar.

OFB Chapter 16 & 17 444/9/2004

Chapter 17Many-Electron Atoms and Chemical

Bonding

• Example / exercise17-1, 17-2

• HW problems1, 3, 5, 7

OFB Chapter 16 & 17 454/9/2004

Ionization energyof an atom is the minimum amount

of energy necessary to detach an electron form an atom that is in its ground state.

X → X + + e - ∆E = IE1

X+ → X 2+ + e - ∆E = IE2

OFB Chapter 16 & 17 464/9/2004

Ionization energyfirst ionization energies

IE tends to decrease in a group

E.g., Li to Na to K to Rb to Cs

E.g., F to Cl to Br to I

OFB Chapter 16 & 17 474/9/2004

Electron Affinityof an atom equals the negative

energy change of the system when a neutral atom in its ground state gains an electronX + e -→ X - ∆E = electron attachment energy

Electron Affinity = - ∆E = electron attachment energy

OFB Chapter 16 & 17 484/9/2004

Electron Affinity

X + e -→ X - ∆E = electron attachment energy

EA tends to parallel IE, but shifted one atomic number lower

E.g., Halogens much higher EA than noble gases

E.g., F to Cl to Br to I

OFB Chapter 16 & 17 494/9/2004

Sizes of Atoms and Ions

Atomic size generally increases moving down a group

Among s-block and p-block elements, atomic size generally decreases moving from left to right

OFB Chapter 16 & 17 504/9/2004

Sizes of Atoms and Ions

Ionic Radii vs Atomic Number

Each line connects a set ofatoms or ions having the same charge; all species have noble gas configuration

-2>-1>+1>+2>+3>+4

OFB Chapter 16 & 17 514/9/2004

As Bond length increases, bond enthalpy decreases

Properties of the Chemical Bond

OFB Chapter 16 & 17 524/9/2004

Bond Order and Bond Enthalpies

OFB Chapter 16 & 17 534/9/2004

Ionic and Covalent Bonds

Electronegativity

of an atom is a measure of its ability in a molecule to attract electrons to itself

CH3C

O

CH3

Acetone

CH3C

O

CH3

Acetone

O has a partial negative

C has a partial positivecharge

δ-

δ+

OFB Chapter 16 & 17 544/9/2004

Ionic and Covalent Bonds

Percent Ionic Character

OFB Chapter 16 & 17 554/9/2004

Oxidation State and Chemical Bonding

OFB Chapter 16 & 17 564/9/2004

Oxidation State and Chemical Bonding

OFB Chapter 16 & 17 574/9/2004

Transition Elements

Oxidation State and Chemical Bonding