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

Quantum (plural ‘quanta’)A finite amount of energy

i.e. – an energy level in an atomThe amount of energy required to move

an electron from its present energy level to the next higher one

MechanicalMovement 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

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

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

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 NumberAngular Quantum NumberMagnetic Quantum NumberSpin Quantum Number

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

Principal Quantum NumberEnergy levelDistance 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

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

“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

“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

“D” Sub-shellTend to have a

clover-leaf shapen=2Five (5) orbitals per

energy levelEach can hold a

maximum of two (2) electrons Can hold a max of 10

electrons

“F” Sub-shellShape 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

Sub-shellSub-shell Energy Energy level (n) in level (n) in which it is which it is first foundfirst found

Number of Number of sub-shells sub-shells at a levelat a level

Number of Number of electrons in electrons in these sub-these sub-shellsshells

SS 11 11 22

PP 22 33 66

DD 33 55 1010

FF 44 77 1414

Spin Quantum NumberRemember, 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

1. Which of the following describes the 4p orbital?

a. n=1, L=0b. n=4, L=1c. n=2, L=-1d. n=3, L=0

2. Which of the following is not a possible set of quantum numbers?

a. n=1, L=2, mL=-2

b. n=1, L=1, mL=-1

c. n=1, L=0, mL=1

d. n=1, L=0, mL= 0

There are two (2) different types of notation used to represent the quantum mechanical model:Orbital NotationElectron Configuration 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 PrinciplePauli Exclusion PrincipleHund’s Rule

Aufbau Principle:Electrons enter sub-shells of lowest

energy first1st 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

Oxygen

Titanium

Strontium