Chapter 10

Quantum Numbers and Shapes

Chpt 10 – Quantum Numbers

An orbital is an orientation in space, so a series of steps (quantum numbers) are used to describe various properties of the orbital. The steps are:

1. principal energy level2. sublevels3. orbital's4. electron spin

Chpt 10 – Quantum Numbers

1. principal energy level Has whole numbers (1, 2, 3,…) that relate to

the size and energy of the orbital. The orbital becomes larger with an increase in

the principle energy level number, thus the electron spends more time away from the nucleus.

The energy is higher because the electron is not as tightly bound by the nucleus.

Chpt 10 – Quantum Numbers

2. sublevel’s “s” sublevels *contains 1 orbital “p” sublevels *contains 3 orbitals “d” sublevels *contains 5 orbitals “f” sublevels *contains 7 orbitals

Chpt 10 – Quantum Numbers

3. orbital’s Relates to the orientation of the orbital in

space. (Example: (p-sublevel) x, y, z) An orbital is the area that there is a 90%

chance of finding the electron in that area. The orbital’s of different sublevels have

different shapes based upon mathematical models.

nodes

90% boundary:Inside this lies90% of the probability

S orbitals are spherical in shape

P-orbitals

Node at nucleus

The Boundary Surface Representations of All Three 2p Orbitals

The Boundary Surfaces of All of the 3d Orbitals

Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

1

s

E

2

s

2p3

s

3p

3d4

s

4p5

s

4d

Remember the energies are < 0

THE MULTI-ELECTRON ATOM ENERGY LEVEL DIAGRAM

Sublevels and orbitals based on the Periodic Table

Alternative Periodic Table

THE BUILDING-UP PRINCIPLE.

assign electrons to orbitals one at a time

lowest energy electronic configuration

Electrons go into the available orbital of lowest energy.At least one electron is in each orbital of a sublevel before a second electron is added to the orbital.

A maximum of two electrons per orbital.

ELECTRONIC CONFIGURATIONS

GROUND STATE

Order of Filling Orbitals

THE AUFBAU (BUILDING-UP) PRINCIPLE:

The electron configuration of any atom or

ion…....

electrons are added to hydrogen-like atomic orbitals in order of increasing energy

can be represented by an orbital diagram

1

s

E

2

s

2p3

s

3p

3d4

s

4p5

s

4d

1s 2s 2p

He:

Hydrogen has its one electron in the 1s

orbital: 1s 2s 2p

H:

1s 2s 2p

He:

1s1

ORBITAL DIAGRAM

with opposite spins:

both occupy the 1s orbitalPauli principle

Helium has two electrons:

1s2

Hydrogen has its one electron in the 1s

orbital: 1s 2s 2p

H:

1s 2s 2p

He:

1s 2s 2p

He:

helium ground

state

Helium has two electrons:

1s1

1s12s1

1s2

ORBITAL DIAGRAM

Now onto the next atoms

Helium can also exist in an excited state such as:

with opposite spins:

both occupy the 1s orbitalPauli principle

Lithium has three electrons, so it must use the

2s orbital:

Beryllium has four electrons, which fill both the

1s and 2s orbitals:

Boron’s five electrons fill the 1s and 2s orbitals,

and begin to fill the 2p orbitals. Since all three

are degenerate, the order in which they are

filled does not matter.

1s 2s 2p

Li: 1s22s1

1s 2s 2p

Be: 1s2 2s2

1s 2s 2p

B: 1s22s22p1

1s 2s 2p

C: 1s22s22p2

1s 2s 2p

C: 1s22s22p2

How can we decide?????

A CHOICE

OR

CARBON Z=6

HUND’S RULEFOR THE GROUND STATE

ELECTRONS OCCUPY DEGENERATE ORBITALS SEPARATELY

THE SPINS ARE PARALLEL

SO FOR CARBON THE GROUND STATE IS

1s 2s 2p

C: 1s22s22p2

1

s

E

2

s

2p3

s

3p

3d4

s

4p5

s

4d

ENERGY LEVEL DIAGRAM FOR A MULTI-ELECTRON ATOM

BROMINE ELECTRONIC CONFIGURATION

[Ar] 4s23d104p5

The valence electron configuration of the

elements in the periodic table repeat

periodically! H He1s1 1s2

Li Be B C N O F Ne2s1 2s2 2p1 2p2 2p3 2p4 2p5

2p6

Na Mg Al Si P S Cl Ar3s1 3s2 3p1 3p2 3p3 3p4 3p5

3p6

Every element in a group

hasthe same valence electron configuration!

Chpt 10 – Quantum Numbers Electron Spin

4. electron spin The concept of electron spin was developed

to account for a magnetic moment. Classical physics indicates that a moving

(spinning) charge produces a magnetic moment (field).

Opposite spins produce opposite magnetic fields.

Electron Spin

In silver (and many other atoms) there is one more “spin up” electron than“spin down” or vice versa. This means that an atom of silver can interact with a magnetic field and be deflected up or down, depending on which type of spinis in excess.

This 2-valued electron spin can be shown in an experiment

Transition Metal Demonstration

dsArZnelectrons

dsArZnelectrons

dsArFeelectrons

dsArFeelectrons

dsArMnelectrons

dsArMnelectrons

dsArCrelectrons

dsArCrelectrons

34_28

34_30

34_23

34_26

34_23

34_25

34_21

34_24

2

2

2

3

The chromium, manganese, and iron ions will exhibit magnetic character because of the high number of unpaired electrons in the 3d orbitals.Will zinc show any magnetic character?