© 2006 brooks/cole - thomson breakraw % a15879% b12563% c9347% d6130% f00% approximate points...

© 2006 Brooks/Cole - Thomson

BreakRaw %

A 158 79%B 125 63%C 93 47%D 61 30%F 0 0%

approximate points needed for letter grade

100% A B C Dafter Exam 1 200 150 120 90 60after Exam 2 400 320 255 190 120after Exam 3 600 480 380 280 180after Exam 4 800 640 505 375 240after Final 1200 960 755 565 360

46%46%

63%63%

80%80%

97%97%29%29%

The way the real world worksThe way the real world works

++3%3%


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Excited Atoms& Atomic Structure


The Quantum Mechanical Picture of the Atom

Basic Postulates of Quantum Theory1. Atoms and molecules can exist only in certain energy states. In each energy

state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition).

2. Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

hc

h E


The Quantum Mechanical Picture of the Atom The allowed energy states of atoms and molecules can be described by sets of numbers called quantum

numbers.

• Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations.

• Four quantum numbers are necessary to describe energy states of electrons in atoms

– n, , m, ms

2

22

mr t V r t r t i

r t

t ( , ) ( , ) ( , )

( , )

Schroedinger 3-dimensional time independent equation

Heisenberg’s uncertainty Equation

Dirac’s quantum mechanical model

E. SchrodingerE. Schrodinger1887-19611887-1961

W. HeisenbergW. Heisenberg1901-19761901-1976


1. The principal quantum number has the symbol – n.

n = 1, 2, 3, 4, ...... “shells”

n = K, L, M, N, ......

The electron’s energy depends principally on n .

n

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7


= 0 = s

= 1 = p

= 2 = d

= 3 = f

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7

2. The angular momentum quantum number has the symbol . tells us the shape of the orbitals and when linked with n defines the energy of the electron

= 0, 1, 2, 3, 4, 5, .......(n-1) = s, p, d, f, g, h, .......(n-1)


Quantum Numbers3. The symbol for the magnetic quantum number is m.

m = - , (- + 1), (- +2), .....0, ......., ( -2), ( -1),

• If = 0 (or an s orbital), then m = 0. – Notice that there is only 1 value of m.

This implies that there is one s orbital per n value. n 1

• If = 1 (or a p orbital), then m = -1,0,+1.– There are 3 values of m.

Thus there are three p orbitals per n value. n 2

• If = 2 (or a d orbital), then m = -2,-1,0,+1,+2.– There are 5 values of m.

Thus there are five d orbitals per n value. n 3

• If = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. – There are 7 values of m.

Thus there are seven f orbitals per n value, n

• Theoretically, this series continues on to g,h,i, etc. orbitals.3. Practically speaking atoms that have been discovered or made up to this point in time only

have electrons in s, p, d, or f orbitals in their ground state configurations.


Atomic Orbitals• Atomic orbitals are regions of space

where the probability of finding an electron about an atom is highest.

• s orbital properties:

• There is one s orbital per n level. = 0

• 1 value of m

= 0 = s

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7


Atomic Orbitals• p orbitals are peanut or dumbbell shaped.

• They are directed along the axes of a Cartesian coordinate system.

• The first p orbitals appear in the n = 2 shell.

• There are 3 p orbitals per n level.

– The three orbitals are named px, py, pz.

– They have an = 1.

– m = -1,0,+1 3 values of m


Atomic Orbitals• d orbital properties:

– The first d orbitals appear in the n = 3 shell.• The five d orbitals have two different shapes:

– 4 are clover leaf shaped.– 1 is peanut shaped with a doughnut around it.– The orbitals lie directly on the Cartesian axes or

are rotated 45o from the axes.

222 zy-xxzyzxy d ,d ,d ,d ,d There are 5 d orbitals per n level.

–The five orbitals are named –They have an = 2.–m = -2,-1,0,+1,+2 5 values of m


Atomic Orbitals

• d orbital shapes


Atomic Orbitals

• f orbital properties:– The first f orbitals appear in the n = 4 shell.

• The f orbitals have the most complex shapes.• There are seven f orbitals per n level.

– The f orbitals have complicated names.– They have an = 3

– m = -3,-2,-1,0,+1,+2, +3 7 values of m

– The f orbitals have important effects in the lanthanide and actinide elements.


Atomic Orbitals• f orbital shapes


Quantum Numbers4. The last quantum number is the spin quantum number which

has the symbol ms.– The spin quantum number only has two possible values.

• ms = +1/2 or -1/2• ms = ± 1/2

– This quantum number tells us the spin and orientation of the magnetic field of the electrons.

– Wolfgang Pauli in 1925 discovered the Exclusion Principle.• No two electrons in an atom can have the same set of 4

quantum numbers.– Spin quantum number effects:

• Every orbital can hold up to two electrons.– Consequence of the Pauli Exclusion Principle.

• The two electrons are designated as having• one spin up ↑ and one spin down↓ • Spin describes the direction of the electron’s magnetic

fields.


c

E

(s-1)x(m) = c (ms-1)Frequency times wavelength equals the speed of light

Calculate the frequency, the energy, and determinethe color of light of an excited Li+ ion emitting radiation at 670.8nm.

(s-1) =(m)

c (ms-1)

E =


The Periodic Table and Electron Configurations

Note that the 3d subshell is higher in energy than the 4s subshell so appears in the 4th period


The principal quantum number has the symbol ~ n which defines the energy of the shell

n = 1, 2, 3, 4, ...... “shells”

The angular momentum quantum number has the symbol ~ which defines the subshells. = 0, 1, 2, 3, 4, 5, .......(n-1) = s, p, d, f, g, h, .......(n-1)

The symbol for the magnetic quantum number is m which defines the orbital.

m = - , (- + 1), (- +2), .....0, ......., ( -2), ( -1),

The last quantum number is the spin quantum number which has the symbol ms which characterizes the single electron.

The spin quantum number only has two possible values.ms = +1/2 or -1/2

one spin up ↑ and one spin down↓

Quantum Numbers

n and define the energy of the electron


Exam 1 Exam 2 Exam 3 Exam 4 Final

Muliple Choice

Muliple Choice

Muliple Choice

Muliple Choice

501 65% 505 64% All 65%

Free

ResponseFree

ResponseFree

ResponseFree

Response 501 54% 505 52% All 53%

A B C D F Q/W GPA501 17.0% 32.8% 30.3% 15.8% 4.1% 0.0% 2.43505 13.0% 30.8% 34.4% 19.0% 2.8% 0.0% 2.32All 14.8% 31.2% 32.0% 17.2% 3.4% 0.0% 2.37


The Nucleus:Build by adding the required number of protons (the atomic number) and neutrons (the mass of the atom)

Electrons:Hund’s Rule states that each orbital will be filled singlybefore pairing begins. The singly filled orbitals will have a parallel spin.

Pauli’s Exclusion Principle states that pairedelectrons in an orbital will have opposite spins.

Fill the electrons in starting with the lowest energy level adhering to Hund’s and Pauli’s rules.

Neon -



• Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples.– Na

• First for 11Na.– When completed there must be one set of 4 quantum numbers

for each of the 11 electrons in Na (remember Ne has 10 electrons)

111 s3 Ne NeNa

ionConfigurat 3p 3s

[Ne] = 1s22s22p6



electron s 31/2 0 0 3 e 11

electrons p 2

1/2 1 1 2 e 10

1/2 0 1 2 e 9

1/2 1 1 2 e 8

1/2 1 1 2 e 7

1/2 0 1 2 e 6

1/2 1- 1 2 e 5

electrons s 21/2 0 0 2 e 4

1/2 0 0 2 e 3

electrons s 11/2 0 0 1 e 2

1/2 0 0 1 e 1

m m n

-th

-th

-th

-th

-th

-th

-th

-th

-rd

-nd

-st

s

11Na

1s22s22p63s1


Electron Affinities of Some Elements

-400-350-300-250-200-150-100-50

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Atomic Number

Ele

ctr

on

Aff

init

y (

kJ/m

ol)


ElectronegativityIncreases

Incr

ease

s Increases


The Continuous Range of Bonding Types

• Covalent and ionic bonding represent two extremes.

1. In pure covalent bonds electrons are equally shared by the atoms.

2. In pure ionic bonds electrons are completely lost or gained by one of the atoms.

• Most compounds fall somewhere between these two extremes.

• All bonds have some ionic and some covalent character.

– For example, HI is about 17% ionic• The greater the electronegativity differences the more polar the bond.


• Guidelines for assigning oxidation numbers.1. The oxidation number of any free, uncombined element is zero.2. The oxidation number of an element in a simple (monatomic) ion is the

charge on the ion.3. In the formula for any compound, the sum of the oxidation numbers of all

elements in the compound is zero. 4. In a polyatomic ion, the sum of the oxidation numbers of the constituent

elements is equal to the charge on the ion.5. Fluorine has an oxidation number of –1 in its compounds.6. Hydrogen, H, has an oxidation number of +1 unless it is combined with

metals, where it has the oxidation number -1.– Examples – LiH, BaH2

7. Oxygen usually has the oxidation number -2.– Exceptions:– In peroxides O has oxidation number of –1.

• Examples - H2O2, CaO2, Na2O2

8. In OF2, O has oxidation number of +2. Use the periodic table to help with assigning oxidation numbers of other elements.

1. IA metals have oxidation numbers of +1.2. IIA metals have oxidation numbers of +2.3. IIIA metals have oxidation numbers of +3.4. VA elements have oxidation numbers of –3 in binary compounds with H,

metals or NH4+.

5. VIA elements below O have oxidation numbers of –2 in binary compounds with H, metals or NH4

+.


OXIDATION NUMBERSOXIDATION NUMBERS

NHNH33

ClOClO--

HH33POPO44

MnOMnO44- -

CrCr22OO772-2-

CC33HH88


Formal Charges

― The most likely formula for a molecule or ion is usually the one in which the formal charge on each atom is zero or as near zero as possible

― Negative formal charges are more likely to occur on the more electronegative elements

― Lewis dot formulas in which adjacent atoms have formula charges of the same sign are usually not accurate

Cl=N-O Cl=N-O


H

H

H∙∙O

H

H H

H

N Cl Al Cl

ClH

H H

H

B

H

H

H∙∙N H

∙∙H

∙∙S

+ +

+


Covalent Bonding• Covalent bonds are formed when atoms share electrons.• If the atoms share 2 electrons a single covalent bond is

formed.• If the atoms share 4 electrons a double covalent bond is

formed.• If the atoms share 6 electrons a triple covalent bond is

formed.– The attraction between the electrons is electrostatic

in nature• The atoms have a lower potential energy when

bound.

• Covalent bonds in which the electrons are shared equally are designated as nonpolar covalent bonds.– Nonpolar covalent bonds have a symmetrical charge

distribution.• To be nonpolar the two atoms involved in the bond

must be the same element to share equally.


Polar and Nonpolar Covalent Bonds

• Covalent bonds in which the electrons are not shared equally are designated as polar covalent bonds– Polar covalent bonds have an asymmetrical charge

distribution• To be a polar covalent bond the two atoms involved in the bond

must have different electronegativities.• Some examples of polar covalent bonds.• HF

bondpolar very 1.9 Difference

4.0 2.1 ativitiesElectroneg

F H

1.9

2.1 4.0



• Compare HF to HI.

bondpolar slightly 0.4 Difference

2.5 2.1 ativitiesElectroneg

I H

0.4

2.1 2.5



• Polar molecules can be attracted by magnetic and electric fields.


Dipole Moments• Molecules whose centers of positive and negative charge do not coincide, have an

asymmetric charge distribution, and are polar.

– These molecules have a dipole moment.

• The dipole moment has the symbol . is the product of the distance,d, separating charges of equal magnitude and opposite

sign, and the magnitude of the charge, q.

units Debye0.38 units Debye1.91

I- H F- H

--

• There are some nonpolar molecules that have polar bonds.• There are two conditions that must be true for a molecule to be polar.

1. There must be at least one polar bond present or one lone pair of electrons.2. The polar bonds, if there are more than one, and lone pairs must be arranged

so that their dipole moments do not cancel one another.


Ionic Polar Covalent CovalentDetermine Inductive effect

Count the number of electrons the element should haveDetermine how equally electrons are shared (EN) >1.7 consider it ionic

Oxidation number Formal charge

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