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Electron Orbitals

Cartoon courtesy of lab-initio.com

The Bohr Model of the Atom

Neils Bohr

I pictured electrons orbiting the nucleus much like planets orbiting the sun.

But I was wrong! They’re more like bees around a hive.

DeBroglie Model

- Since light waves can have a particle behavior (as shown by Einstein), then it follows that particles could exhibit a wave behavior.

- Saw the electron as a wave.

Schrodinger and His Cat

• First to propose the idea of electron duality.• Proposed classic thought experiment involving a cat in a box.

• The electron is simultaneously a particle and a wave but cannot be observed in this state.

-When you observe it the electron adopts one state or the other.

Heisenberg Uncertainty Principle

You can find out where the electron is, but not where it is going.

OR…

You can find out where the electron is going, but not where it is!

“One cannot simultaneously determine both the position and momentum of an electron.”

WernerHeisenberg

Quantum MechanicalModel of the Atom

Mathematical laws can identify the regions outside of the nucleus where electrons are most likely to be found.

These laws are beyond the scope of this class…


• As in the the deBroglie and Bohr Models the electrons energy is quantized into distinct levels.• As the atom is excited electrons move into higher levels (further from nucleus) and vice versa.

• The Quantum Mechanical model, however, makes no attempt to predict the path of the electron (Heisenburg).• It does define the electrons most probable location based on a set of rules.

Levels of Organization

• The Quantum Mechanical model still relies on the idea of quantized energy levels HOWEVER each energy level is further subdivided into probability zones.oCalled OrbitalsoThe larger the energy

level the more probability zones it can contain.

You add a new set of orbitals with each successive energy level.

Four Quantum Numbers

• The Quantum Mechanical Model describes the location of each electron based upon successive levels of organization called Quantum Numbers.

1. Principal Quantum Number2. Orbital Quantum Number3. Magnetic Quantum Number4. Spin Quantum Number

• Each electron within the atom is assigned a unique combination of quantum numbers based upon the location of it’s electrons

– The 4 quantum numbers provide the specific location of each electron. Similar to an address.

Electron Energy Levels (Shell)

• First level of organization.• Similar to Bohr Model.

• The shell denotes the probable distance of the electron from the nucleus.

• Principle Quantum Number (N):• Indicates the relative size and

energy of a shell. • Denoted as “N”• As N increases the energy

level becomes larger and the electron spends more time farther from the nucleus.

• Not evenly spaced.

# of Electrons in Energy Levels

The larger the shell the more electrons it can hold.

As “N” increases so does the maximum number of electrons that can be in the shell.Number of

electrons that can fit in a shell:

2n2

Maximum # of electrons per shell

1st shell: 2

2nd shell: 8

3rd shell: 18

4th shell: 32

5th shell: 50

1

2

3

4

INC

RE

AS

ING

EN

ER

GY

/ D

ISTA

NC

E F

RO

M N

UC

LE

US

Orbital Sub-Levels

• Each main energy level (shell) can be subdivided into sublevels.

• Level 1 was split into 1 sub level

• Level 2 was split into 2 sub levels



• These sublevels are known as orbitals.

SUB LEVELSPRINCIPAL ENERGY LEVELS

Orbital Quantum Number, ℓ(Angular Momentum Quantum Number)

Indicates shape of orbital sublevels

ℓ = n-1 ℓ sublevel

0 s1 p2 d3 f4 g

Orbital Shapes are defined as the surface that contains 90% of the total electron probability.

Scientists calculate the shape of orbitals based upon probability.

Orbital Shape

• Each energy level contains one spherical S-Orbital

• Holds 2 Electrons

ℓ = 0 or S Orbital shape

• There are 3 dumbbell-shaped p orbitals beginning in n = 2

• Each assigned to its own axis (x, y and z) in space.

• Each P orbital contains two electrons.

2 x 3 = 6 Total

ℓ = 1 or P Orbitals shape

Things get a bit more complicated with the five d orbitals beginning in n = 3.

5 x 2 = 10 Electrons Total

To remember the shapes, think of “double dumbells”…and a “dumbell with a donut”!

ℓ = 2 or D Orbitals shape

ℓ = 3 or f Orbitals shape

Beginning in N=4 there are 7 f-orbitals.

7 x 2 = 14 Electrons Total

Energy

Level (n)

Orbital type in the

energy level (types = n)

Number oforbitals

Number ofElectrons

Number ofelectrons

perEnergy

level (2n2)

1 s 1 2 2

2 sp

13

26

8

3 spd

135

26

10

18

4 spdf

1357

26

1014

32

Energy Levels, Orbitals, Electrons

Magnetic Quantum Number, ml

Indicates the orientation of the orbital in space.

Values of ml : integers -ℓ to +ℓ

The number of values represents the number of orbitals.

Example: for ℓ= 2, ml = -2, -1, 0, +1,

+2

Which sublevel does this represent?

Answer: d

Electron Spin (ms or s)

Electron spin describes the behavior (direction of spin: clockwise or counterclockwise) of an electron within a magnetic field.Establishes a limit of 2 electrons per

orbitalPossibilities for electron spin:

1

2

1

2 OR

Quantum Mechanical Model Summary

Electrons are located in specific energy levels.

There is no exact path around the nucleus.

The model estimates the probability of finding an electron in a certain position.

n ---> energy level or shell 1, 2, 3, 4, ...

ℓ ---> subshell or orbitals 0, 1, 2, ... n – 1

ml ---> magnetic orientation -ℓ ... 0 ... +ℓ

ms ---> electron spin +1/2 and -

1/2

QUANTUM

NUMBERS

Electron Configurations

__

Rules for Filling The Diagram• Aufbau Principle: Electrons will fill

the lowest energy levels subshell first before moving to the next higher level.– The Concert Rule

• Hund's Rule: The most stable arrangement of electrons is that with the maximum number of unpaired electrons, all with the same spin direction. (Electrons won’t double up if they don’t have to, as long as they don’t violate the Aufbau Principle)– The Urinal Etiquette Rule

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. (Only 2 electrons can be in an orbital and they must have opposite spins)– Two is Company, but Three is a

Crowd Rule

Element Configuration notation

Orbital notation Noble gas notation

Lithium 1s22s1 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s1

Beryllium 1s22s2 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2

Boron 1s22s22p1 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p1

Carbon 1s22s22p2 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p2

Nitrogen 1s22s22p3 ____ ____ ____ ____ ____

1s 2s 2p

[He]2s2p3

Oxygen 1s22s22p4 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p4

Fluorine 1s22s22p5 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p5

Neon 1s22s22p6 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p6

Orbital filling table

Electron configuration of the elements of the first three

series

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