1. Electrons in Atoms Part 2 – Quantum Mechanical Model

2. Quantum Mechanical Model
As we saw earlier, the Bohr Model had several short comings
The model currently used to describe the atom is the Quantum Mechanical Model of the atom
This is the current theoretical framework that is used to describe all of the information we have about atoms and how they function

3. Basic Definitions Quantum (plural ‘quanta’) Mechanical
A finite amount of energy
i.e. – an energy level in an atom
The amount of energy required to move an electron from its present energy level to the next higher one
Mechanical
Movement of parts in relation to a whole
i.e. – electrons in an atom
Hence the Quantum Mechanical Model deals with the movement and location of electrons in an atom

4. Uncertainty Principle
The double-slit experiment showed that electrons could be anywhere, they are not confined to one path
We cannot know where an electron is and where it is going
Because of this, we use probability to determine where an electron is most likely to be

5. Electron Clouds
Using the electron probabilities, we find areas where electrons are most likely to be
These areas are called electron clouds where the probabilities of finding electrons is very high
The shapes and distance from the nucleus of these electron clouds depends on several factors

6. Quantum Numbers
To describe electron clouds and where electrons probably are, we use quantum numbers
There are a total of four (4) quantum numbers as illustrated in the chart:
Principal Quantum Number
Angular Quantum Number
Magnetic Quantum Number
Spin Quantum Number

7. Quantum Numbers Principal Quantum Number n n can equal 1-7
Refers to the energy level or distance from the nucleus; Represented by the letter n. n is a number from 1-7 to describe the period on the periodic table the element is in
Angular Quantum Number L
L can equal
0 to (n-1)
The shape of the orbital; represented the letters s, p, d, and f. Each letter also has a corresponding number
s=0, p=1, d=2, f=3
Magnetic Quantum Number mL
ml = -L to +L
Determines the orientation of the orbital in space in reference to other orbitals
Spin Quantum Number ms
ms = +1/2 and -1/2
Specifies the value for spin; electrons in the same orbital must spin in opposite directions

8. Quantum Numbers Principal Quantum Number Energy level
Distance away from the nucleus
As # increases, distance from the nucleus also increases
As the number increases, so does the energy of the electrons in those orbitals
Represented by integers 1,2,3,4,5,6,7 that correspond to the seven horizontal rows on the periodic table
Determined by counting as you move down (top to bottom) the periodic table

9. Quantum Numbers Angular Quantum Number Also known as “sub-shells”
Refer to the shape of the orbital
There are four (4) different shapes
S, P, D, F
These correspond to the s, p, d, f blocks on the periodic table

10. Quantum Number “S” Sub-shell Spherical shape N=0
Only one (1) orbital per energy level
This is because the Magnetic Number, mL is from –L to +L
The 1 sub shell can hold 2 electrons
One with +1/2 spin
One with -1/2 spin

11. Quantum Numbers “P” Sub-shell Dumbbell shape n=1
Three (3) orbitals per energy level
mL and be from –L to +L
Each shell can hold 2 electrons
3 orbitals mean the p-shell can hold up to 6 electrons

12. Quantum Numbers “D” Sub-shell Tend to have a clover- leaf shape n=2
Five (5) orbitals per energy level
Each can hold a maximum of two (2) electrons
Can hold a max of 10 electrons

13. Quantum Numbers “F” Sub-shell Shape contains 6 lobes for the most part
Seven (7) orbitals per energy level
Each can hold a maximum of two (2) electrons
Fourteen (14) electrons total at each energy level

14. To Summarize Sub-shell Energy level (n) in which it is first found
Number of sub-shells at a level
Number of electrons in these sub-shells S 1 2 P 3 6 D 5 10 F 4 7 14

15. Quantum Numbers Spin Quantum Number
Remember, in each sub- shell there can be two (2) electrons
These electrons must have spins that go in opposite directions
Represented by arrows pointing in opposite directions

16. Quantum Number Example
Which of the following describes the 4p orbital?
n=1, L=0
n=4, L=1
n=2, L=-1
n=3, L=0
Which of the following is not a possible set of quantum numbers?
n=1, L=2, mL=-2
n=1, L=1, mL=-1
n=1, L=0, mL=1
n=1, L=0, mL= 0

17. Representing Electrons Using the Quantum Mechanical Model
There are two (2) different types of notation used to represent the quantum mechanical model:
Orbital Notation
Electron Configuration Notation

18. Orbital Notation
Illustrates the following quantum numbers: principal, second (shape), and spin
Use the template to draw and “fill” the sub- shells with electrons
Order of filling electrons is governed by three (3) rules:
Aufbau Principle
Pauli Exclusion Principle
Hund’s Rule

19. Orbital Notation Aufbau Principle: Pauli Exclusion Principle:
Electrons enter sub-shells of lowest energy first
1st energy level fills up before the next
Pauli Exclusion Principle:
All atomic sub-shells contain a maximum of two (2) electrons. Each MUST have a different spin
Hund’s Rule:
when electrons occupy sub-shells of equal energy, ONE electron enters EACH sub-shell until all the sub-shells contain one electron with identical directions
Electrons are added to sub-shells so that a maximum number of unpaired electrons result

20. Examples
Oxygen
Titanium
Strontium