atlantic-pacific method for determining significant digits

Chapter 5

Quantum Theory and Electron Configurations

Quantum-Mechanical Model of the

Atom

• Since the Bohr model had a very limited use, a new and very different model of the atom exists

• The Quantum Mechanical Model

(1926) contains:Quantum energy levels

Dual wave/particle nature of electrons

Electron clouds

• In the new model, don’t know exactlywhere electrons are - only know probabilities of where they could be

• Heisenberg Uncertainty Principle =

impossible to know both the velocity (or momentum) and position of an electron at the same time

Heisenberg Uncertainty Principle

Chapter 5

The Quantum Mechanical Model

Quantum Mechanical Model

• Einstein (1905) Light consists of quanta, called

photons

Photoelectric Effect – Sunlight striking a sheet of metal will knock off the outermost electrons and move, causing an electric current

• de Broglie (1924) = Photons both particles and waves

• Davisson (1927) = Electrons both particles and waves

Quantum-Mechanical Model of the

Atom

• Orbital = region around nucleus where an electron with a given energy level will probably (90%) be found

• Four kinds of orbitals

s - spherical in shape, lowest orbital for every energy level

p - dumbbell shaped, second orbital

d - complex “flower” shape, third orbital

f - very complex shape, highest orbital

s-orbitals

• All s-orbitals are spherical.

• As n increases, the s-orbitals get larger.

p- orbitals

• Three p-orbitals: px, py, and pz Lie along the x-, y- and z- axes of a Cartesian

system.

Dumbbell shaped, gets larger as n increases

d and f - orbitals

• There are five d and seven f-orbitals.

Quantum Mechanical Model

• Principle Energy Levels (n)

Labeled from 1-7

First energy level is n=1

Contains sublevels (s, p, d and f)

• Each energy level contains the number of sublevels equal to it’s value

for n

– If n=3, there are three sublevels

Quantum Mechanical Model

• In each sublevel there are atomic orbitals

• Atomic orbitals – describe a space where an electron is

likely to be found

Type of

subshell

Shape of

orbitals

Number of

orbitals

Orbital

‘names’

s Spherical 1 s

p Dumbbell 3 px, py, pz

d Cloverleaf

(and one

donut)

5

f Multi-lobed 7

Quantum Mechanical Model

• Each orbital can contain two electrons.

• Since negative-negative repel, these electrons occupy

the orbital with opposite spins.

Quantum Mechanical Model

• The total number of orbitals of an energy level is n2.

For the third principle energy level, n=3, which means there are

9 orbitals

• These orbitals are 3s, 3px, 3p

y, 3p

z and the 5 d orbitals

• Remember, we no longer think of orbitals as concentric

circles, but we can say that n=4 extends farther from the

nucleus than n=1.

Valence Electrons

• Only those electrons in the highest principle energy

level

Electron Configuration and Orbital Notation

• Aufbau Principle – electrons fill lower energy orbitals first,

“bottom-up”

n=1 fills before n=3

• Will an electron fill the 1s or the 2s orbital first?

1s

2s2px 2py 2pzE

ne

rg

y

Electron Configuration &Orbital Notation

• Hund’s Rule – electrons enter same energy orbitals so that

each orbital has one electron before doubling up

Each of the first electrons to enter the equal energy orbitals must

have the same spin

If we have 7 electrons, how will they fill in the below orbitals?

1s

2s2px 2py 2pzE

ne

rg

y

Electron Configuration and Orbital Notation

• Pauli Exclusion Principle – an orbital can contain no more

than 2 electrons. Electrons in the same orbital must have

different spins.

• If we have 8 electrons, how will they be arranged?

1s

2s2px 2py 2pzE

ne

rg

y

Apartment Analogy

• Atom is the building

• Floors are energy levels

• Rooms are orbitals

• Only two people per room

Orbital Diagrams

• Draw each orbital as a box.

• Each electron is represented using an arrow.

Up arrows – clockwise spin

Down arrows – counter-clockwise spin

• Determine the total number of electrons involved.

• Start with the lowest energy level (1s) and start filling in

the boxes according the rules we just learned.

Transition Metal Exceptions

• Can move from the highest filled s orbital to create a fully

filled, or half filled d or f

• TRANSITION METAL EXCEPTIONS

Chapter 5

Total # of electrons in an Energy Level

• 2n2

• n=1 2 x 12 +

= 2

• n=2 2 x 22 +

= 8

• n=3 2 x 32 +

= 18

• n=4

• n=5

• n=6

• n=7

Chapter 5

Orbitals and Energy Levels

Principal

Energy Level

Sublevels Orbitals

n = 1 1s 1s (one)

n = 2 , 2s 2p 2s (one) + 2p (three)

, , n = 3 3s 3p 3d 3s (one) + 3p (three) + 3d (five)

n = 4 4s, 4p, 4d, 4f 4s (one) + 4p (three) + 4d (five)

+ 4f (seven)

Chapter 5

Summary

s

p

d

f

# of

shapes

Max

electrons

Starts at

energy level

Orbitals and Energy Levels

and so on....

1s

n = 1 2s

2p

n = 2 3s

3p

3d

n = 3

4s

4p

4d

4f

n = 4

Incre

asin

g e

nerg

y

Orbital Diagrams

• Orbital diagrams are used

to show placement of

electrons in orbitals.

• Need to follow three

rules (Aufbau, Pauli,

Hund’s) to complete

diagrams

Li

Be

B

C

N

Ne

Na

Orbital Diagram

2s

1s

3s

4s

2p

3p

4p

3d

Energ

y

Chapter 5

Electron Configuration

• Let’s determine the electron configuration for

Phosphorus

• Need to account for 15 electrons

Chapter 5

Incr

easi

ng e

ner

gy

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Chapter 5

• The first to electrons go into the

1s orbital

• Notice the opposite spins

• only 13 more

Incr

easi

ng e

ner

gy

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Chapter 5

• The next electrons go into the 2s

orbital

• only 11 more

Incr

easi

ng e

ner

gy

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Chapter 5

• The next electrons go

into the 2p orbital

• only 5 more

Incr

easi

ng e

ner

gy

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Chapter 5

• The next electrons go

into the 3s orbital

• only 3 more

Incr

easi

ng e

ner

gy

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Chapter 5

Incr

easi

ng e

ner

gy

1s

2s

3s

4s

5s

6s

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 shapes

• 3 unpaired electrons

• 1s22s22p63s23p3

Writing Electron Configuration

• Determine the total number of electrons.

• Write the principle energy level number as a coefficient,

the letter for the subshell, and an exponent to represent

the number of electrons in the subshell.

• He: 1s2

The Kernel (Noble Gas) Notation

• Determine the total number of electrons

• Find the previous noble gas and put its symbol in brackets

• Write the configuration from that noble gas forward as

usual

Chapter 5

Writing electron configurations

• Examples

• O 1s2

2s2

2p4

• Ti 1s2

2s2

2p6

3s2

3p6

3d2

4s2

• Br 1s2

2s2

2p6

3s2

3p6

3d10

4s2

4p5

• Core format

• O [He] 2s2

2p4

• Ti [Ar] 3d2

4s2

• Br [Ar] 3d10

4s2

4p5

Quantum Numbers

• Each electron can be described by four numbers unique to that electron (like a fingerprint)

• “n” – the principal quantum # describes the principal energy level, n=1, 2, 3…,7

• “l” – describes the shape of subshell s subshell = 0

p subshell = 1

d subshell = 2

f subshell = 3

• “m” –describes the orientation , m = -l….0….+l• “s” – describes the spin, s=1/2 or -1/2

Quantum Numbers

• Example: Look at carbon’s orbital diagram which contains 6

electrons. What are the quantum #s for the last electron to be

filled?

• Example: Look at Vanadium’s Kernel notation. Do the

orbital diagram for only the valence electrons. What are the

quantum #’s for the second to last electron to be filled?