Quantum Mechanical Model(and periodicity)

New unit !

* the distribution of electrons within the orbitals of an

element’s atoms

* determines the chemical properties and reactivity of the elements

DeBroglie treated the electron as a function of a wave (Bohr treated as a particle)

Differs from Bohr model in several ways 2 of particular note

The kinetic energy of an electron is inversely related to the volume of the region to which it is confined (more common – electrostatic energy decreases as kinetic energy increases creating a balance )

It is impossible to specify the precise position of an electron in an atom at a given instant (the best that can be done is estimate the “probability” of finding an electron in a particular region

Schrodinger Wave function of electron Electron cloud

Quantum Mechanical ModelEach electron has it’s own region within the atom and has a number

designation describing that region

1. Principle quantum number (n) ~ main energy level or shell ~ represented by whole number

integers (1, 2, 3 ...the period number on the p-table) ~ number indicates the distance from the nucleus (the > the ‘pqn’ the farther the electrons are from the nucleus)

~ specifies the size of the ORBITAL

Sublevels, sublevels, sublevels2. Azimuthal quantum #~ represented by the letter ‘l ’~ shape of the electron cloud~ the # of sublevels is equal to

the value of the ‘pqn’(‘pqn’ = 2, then there are 2

sublevels)

l = integer from 0 to… (n-1)l = 0, 1, 2, 3…Ex. 1 – 1 = 0 (# representing the “s” sublevel)

Sublevels are?s..p..d..f..g..h..so on

s-sublevel----1 orbital----- ml = 0

p-sublevel ----3 orbitals ----- ml = -1, 0, +1

d-sublevel ----5 orbitals ----- ml = -2, -1, 0, +1, +2

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

ORBITALS

3. Magnetic Quantum number ( ml )

• the quantum number that represents the appropriate orbital

Orbital-orientation quantum #

Within sublevels each electron pair has a different place in space. This space is called an orbital. Max. 2

electrons per orbital

ml = - l to + l

4. Spin Quantum Number (ms)

~ NOT a property of the orbital

~ describes a property of the electron itself

~ indicates the direction of the electron spin ms= +1/2 or -1/2

Electron ConfigurationsElectron Configurations

Orbital notation# = main energy level (pqn, 1, 2, 3 etc…)

letter = sublevel (s, p, d, f)= orbital

= electrons

Here electron, come on boy! Aufbau principle~ electrons are added one

at a time~ you begin with the

lowest energy ~ you add electrons until

all electrons are accounted for

Pauli exclusion principle

~ an orbital can hold a maximum of 2 electrons

~ paired and unpaired

More assigning of electrons Hund’s rule~ all orbitals must have at least one

electron before a paired electron can be used

It doesn’t matter which one gets an electron first, but…

1. Each electron MUST have the SAME SPIN as the others in unfilled orbitals! (up or down)

2. NO electron pairs are allowed until every orbital in that subshell has one electron!

OK…WHY does 4s fill before 3d?

1st shell

Higher energy

“1s” subshell

“2s” subshell“2p” subshell

“3s” subshell“3p” subshell

“3d” subshell

Farther out than 1st shell, but both an equal distance from the nucleus. 2nd shell

3rd shell

Farther out than 2nd shell, but all 3 an equal distance from the nucleus.

Closest to the nucleus

Higher energy

“3s” subshell“3p” subshell

“3d” subshell3rd shellFarther out than 2nd shell, but all 3 an equal distance from the nucleus.

“4s” subshell“4p” subshell

“4d” subshell

4th shellFarther out than 3rd shell, but all 4 an equal distance from the nucleus.

“4f” subshell

Note that, even though the 4th shell is farther out than the 3rd shell, the energy of 4s is LESS than 3d!

1s2s

2p3s

3p3d4s

4p4d

4f5s

5p5d

5f6s

6p6d

6f7s

7p7d

7fHigher energy

•“d” subshells fill 1 shell behind!•3d fills after 4s•4d fills after 5s

•“f” subshells fill 2 shells behind! MORE complex!

•The first “f” subshell is in the 4th shell (4f)…•4f fills after 6s! (then comes 5d, and then 6p)

•5f fills after 7s, (then comes 6d, and then 7p)

Just follow the elements in orderJust follow the elements in order!!!!

““d” and “f ” Subshells Fill LATE d” and “f ” Subshells Fill LATE

Electron “Promotion”Electron “Promotion”A “d” subshell is more stable when it is…EXACTLY 1/2 FULL (5 electrons), or…EXACTLY FULL! (10 electrons)!The same is true for “f ” subshells! (7 or 14 electrons)When a “d” is ONE electron short of 1/2 full or full…It PROMOTES one electron from the nearest “s” subshell!

Electron “Promotion”Electron “Promotion”

Silver (Ag) 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s1, 4d10

5s4d

Example: Silver (Ag) 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d9

5s4d

4d9 – 1 short of full!29

110

Silver is now more stable with a full4d subshell! (4d10)

Electron “Promotion”Electron “Promotion”

Remember! One “s” electron will “promote” to the nearest “d” or “f ” subshell if……that “d” or “f ” is one electron short of being full or 1/2 full!Watch for d 4, d 9, f 6 or f 13!

With configuration notation, the concept of orbital notation is still used…BUT The orbitals are no longer represented by boxes

The energy level # and the sublevel are still used (1s, 2s 2p and so on)…BUT The arrows representing the electrons are not used

The number of electrons is still important AND The number of electrons are written as superscripts above the

sublevel designation

Example: Sodium, Na (11 electrons) 1s2 2s2 2p6 3s1

Configuration notationConfiguration notation

Short hand notationShort hand notation With shorthand notation, the same technique as

configuration notation is used. The difference is …

all of the electrons to the previous row NOBLE GAS are accounted for

the configuration continues from the end of the noble gas row and picks up at the beginning of the next energy level

the technique is to put the noble gas element symbol in brackets Ex. [Ar 18]

the configuration notation picks up and continues until all the electrons are accounted for

Ex. Cu29 [Ar18] 4s2 3d9

Practice quantum #’s Consider the following sets of quantum

numbers … a) 3, 1, 0, +1/2 b) 1, 1, 0, -1/2 c) 2, 0, 0, +1/2 d) 4, 3, 2, +1/2

which ones are valid If valid, identify the orbital involved

Atomic Orbital Shapes and Sizes Names derived from the characteristics of their

spectroscopic lines: sharp, principle, diffuse, and fundamental

s p d f and so on…g, h, …

VALENCE ELECTRONSVALENCE ELECTRONS The electrons in the outermost energy level

are called valence electronsvalence electrons. Valence electrons are the ones that cause

chemical properties and reactions Look for the highest “n” (principle energy

level), such as 3s, or 4p, etc. Valence electrons will ALWAYS be in “s” Valence electrons will ALWAYS be in “s”

or “p” subshells!or “p” subshells!

Lewis Dot StructuresLewis Dot StructuresThis is EASY!

The dots placed around the symbol of an element represent ONLY THE OUTSIDE ELECTRONS!These outside electrons are called the…

“valence electrons”!Remember, ONLY “s” AND “p” SUBSHELLS ARE ON

THE OUTSIDE!!!This means that the total number of dots around a

symbol can NEVER exceed 8!! (“s” = 2, “p” =6)This is called the “OCTET RULE”!

Lewis Dot Diagrams

• A Lewis dot diagram illustrates valence electrons as dots around the chemical symbol of an element.

Lewis Dot Diagrams• Each dot represents one valence electron.

• In the dot diagram, the element’s symbol represents the core of the atom—the nucleus plus all the inner electrons.

The dots are written around an imaginary box surrounding the element symbol, up to a maximum of eight!: (no pairs before 5!)

(the dots may start on any side)

Lewis Dot Diagrams Represent Valence Electrons

One outside electron: SyTwo outside electrons: Sy

Three outside electrons: SyFour outside electrons: Sy

Five outside electrons: SySix outside electrons: Sy