Quanum Mechanical Model 3

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The Quantum

Mechanical Model

of the Atom

No more ³Bohr´ing-Rutherford!



Quantum Mechanical Model of

the Atom QM is a model that describes atoms as

having certain allowed quantities of energy

because of wave-like properties of their electrons

It consists of four ³numbers´ that describe

the electronic structure of the atom

These four numbers could be thought of

address of each electron.



First Quantum Number

The Principal Quantum Number (n)

Any whole number integer

Therefore n = 1,2,3, 4««

n values indicate the energy level therefore the bigger the number the higher the Energy Level.

The total number of electrons in any energy level is 2n2

n= 1 #electrons=2 n= 2 #electrons=8

n= 3 #electrons=18 n= 4 #electrons=32

Total number of orbitals in any energy level is given by n2



Second Quantum Number

Orbital Shape Quantum number (l)

Ranges from 0 to n-1

Number values represent a specific orbital

An atomic orbital is a 3-D region of spacearound the nucleus where there is a highprobability of finding an electron

Value of l 0 1 2 3 4 5Orbital

Shapes p d f g h



l start with 0 and has a maximum value of

l=(n-1)

If n=1 l=0 1s

n=2 l=1 and 0 2s and 2p

n=3 l=2, 1 and 0 3s, 3p and 3dn=4 l=3, 2 ,1 and 0 4s, 4p,4d and 4f



s orbital

l = 0



s orbital (cont¶d)



p orbital

l = 1



S orbital and p orbitals



d orbital

l = 2



Third Quantum Number

Magnetic Quantum Number (ml)

Determines the number of suborbital that

are available at any given orbital Ranges from - l to + l (including 0)

Example:

s = 0 ml= 0 1 1 option so only 1 s-orbital

p = 1 ml= -1,0,+1 3 options so there are 3 p-orbitalsd = 2 ml= -2,-1,0,+1,+2 5 options so 5 d-orbital

f = 3 ml= -3,-2,-1,0,+1,+2,+3 7 options so 7 f-orbitals

Each suborbital can only hold a maximum of 2 electrons!



Summary of the quantum numbers!



You should now be able

to see why the each

energy level can only

have maximum number

of electrons.

Only specific number of

orbitals in each energy

level and only 2 electron

in each orbital!!

It should all be coming

together by now!



Pauli Exclusion Principle

No two electrons may have all four

quantum numbers alike

The first three quantum numbersdetermine a specific orbital

As a result, only two electrons may exist in

the same orbital and these electrons must

have opposing spins or different ms value



m s = s pin magnetic p electron spin

m s = ±½ (-½ = E) (+½ = F)

Pauli exclusion principle states:

No two electrons in an atom share the same 4 quantumnumbers.

This means that two electrons in the same orbital must have

opposite spins (different ms values)

Electron spin is purely a quantum mechanical concept.

Magnetic Spin Quantum Number



Filling Orbitals

1. No more than two electrons can occupy onesub-level.

2. Electrons occupy the lowest energy orbitals

available.3. Each orbital on a sublevel is occupied by a

single electron before a second electronenters.

4. Oh what fun this is!!! I know you think so too.You are probably going to go home and tellyour family all about this stuff tonight at dinner.



Quantum Address for each electron

electron # n l ml ms

Hydrogen

1st electron 1 0 0 + 1/2

Helium


2nd electron 1 0 0 - 1/2

Lithium



3rd electron 2 0 0 + 1/2

Beryllium1st electron 1 0 0 + 1/2


3rd electron 2 0 0 + 1/2

4th electron 2 0 0 - 1/2



Electron Configuration



How do we use quantum numbers?

We use them to write ELECTRON

CONFIGURATIONS

Electron configurations of the first 11 elements, in orbital notation.

Notice how configurations can be built by adding one electron at a time.

atomZ ground state electronic configuration

H 1 1s1

He 2 1s2

Li 3 1s2 2s1

Be 4 1s2 2s2

B 5 1s2

2s2

2p1

C 6 1s2 2s2 2p2

N 7 1s2 2s2 2p3

O 8 1s2 2s2 2p4

F 9 1s2 2s2 2p5

Ne 10 1s2 2s2 2p6

Na 11 1s2 2s2 2p6 3s1



Note: The energy levels do not go

in order. As a result you need the

Aufbau Principle to determine theorder.



Aufbau Principle

States:

the number of electrons in

an atom is equal to the

atomic number;each added electron will

enter the orbitals in the

order of increasing

energy;

an orbital cannot take

more than 2 electrons.



Orbital Box Diagrams

Examples of ground state

electron configurations in

the orbital box notation that

shows electron spins.

atom

B

1s 2s

2p

C

1s 2s

2p

N

1s 2s

2p

O

1s 2s

2p

F

1s 2s

2p

Cl

1s 2s

2p

3s 3p

Mn

1s 2s

2p

3s 3p

«

4s3d



Hund's Rule

every orbital in a subshell is singly

occupied with one electron before any one

orbital is doubly occupied

and all electrons in singly occupied orbitals

must have the same spin.



Orbital Box Diagrams

Look at the p orbitals and

how the electrons are added

atom

B 1s

2s

2p

C 1s

2s

2p

N 1s

2s

2p

O 1s

2s

2p

F 1s

2s

2p

Cl 1s

2s

2p 3s

3p

Mn 1s

2s

2p 3s

3p

4s3d



What Happens?

Draw the orbital box diagrams for Be and

B, then N and O.

of Beryllium



Practice

http://www.chempractice.com/drills/java_A

O.php

Now do the electron configurations andorbital box diagrams for the first 20

elements

Homework: page 136 #1-5, page 138 #1-

2,5-6, page 145-146 #6-9



Short Forms

For atoms with many electrons, this notation canbecome lengthy.

It is often abbreviated by noting that the first few

orbitals are identical to those of one or another noble gas.

Phosphorus, for instance, differs from neon (1s2

2s2 2 p6) only by the presence of a third shell.

Thus, the electron configuration of neon is pulledout, and phosphorus is written as follows:[Ne]3s2 3 p3.



Look at how the periodic table

takes electron configurations into

account



Exceptions

Look at copper and chromium

They do not follow the Aufbau principle

Many of the transition elements like a half filled s sub-level.

You need to know these exceptions



Element Z Electron configuration Short electron conf.Scandium 21 1s

22s

22p

63s

23p

64s

23d

1[ Ar ] 4s

23d

1

Titanium 22 1s2

2s2

2p6

3s2

3p6

4s2

3d2

[ Ar ] 4s2

3d2

Vanadium 23 1s2

2s2

2p6

3s2

3p6

4s2

3d3

[ Ar ] 4s2

3d3

Chromium 24 1s2

2s2

2p6

3s2

3p6

4s1

3d5

[ Ar ] 4s1

3d5

Manganese 25 1s2 2s2 2p6 3s2 3p6 4s2 3d5 [ Ar ] 4s2 3d5

Iron 26 1s2

2s2

2p6

3s2

3p6

4s2

3d6

[ Ar ] 4s2

3d6

Cobalt 27 1s2

2s2

2p6

3s2

3p6

4s2

3d7

[ Ar ] 4s2

3d7

Nickel 28 1s2

2s2

2p6

3s2

3p6

4s2

3d8

[ Ar ] 4s2

3d8

Copper 29

1s

2

2s

2

2p

6

3s

2

3p

6

4s

1

3d

10

[ Ar ] 4s

1

3d

10

Zinc 30 1s2

2s2

2p6

3s2

3p6

4s2

3d10

[ Ar ] 4s2

3d10

Gallium 31 1s2

2s2

2p6

3s2

3p6

3d10

4s2

4p1

[ Ar ] 3d10

4s2

4p1



Electron Configurations for Ions

Because scandium is a metal in group 3

on the periodic table it can lose three

electrons and form +3 cation with the

stable 3s23p6 configuration of argon.

Sc Sc3+ + 3e-

[Ar] 3d 1 4s2 [Ar] or

[Ne] 3s2 3p6



Quantum "Addresses" for all the

electrons in Neon

1s2 2s2 2p6

s = p = = =



s = p = = =

n=1

n=2

n=3

n=4

n=5

n=6

n=7



Exceptions

When looking at the following Trends look

to answer the following questions:

What elements are the exceptions?

Why?



Electron Affinity Values

Quanum Mechanical Model 3

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