Quantum Mechanical Model and Periodicity

New unit !

   DeBroglie   duality treated the electron as a function of a wave (Bohr treated as a particle)  “If waves of energy have some properties of particles, perhaps particles of matter have some properties of waves.”  Combined E=mc 2 with E=h x nu  Distinction between both particle and wave disappears at the atomic level 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 )

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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

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Wave function of electron

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Certain allowed amounts of energy due to the allowed wave-like motion of an electron

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Electron cloud

Quantum Mechanical Model

Each 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, sublevels

2.

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

s..p..d..f..g..h..so on



Atomic Orbital Shapes and Sizes

 Names derived from the characteristics of their spectroscopic lines:

s

harp,

p

rinciple,

d

iffuse, and

f

undamental  s  p  d  f  and so on…g, h, …

  3.

ORBITALS

http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Orbitals-896.html

Within sublevels each electron pair has a different place in space.

This space is called an orbital .

Magnetic Quantum number ( m l )

Max. 2 electrons per orbital Orbital-orientation quantum #

• the quantum number that represents the

appropriate orbital

m l = l to + l

s-sublevel----1 orbital-

----

m l = 0

p-sublevel ----3 orbitals

-----

m l = -1, 0, +1

d-sublevel ----5 orbitals

-----

m l = -2, -1, 0, +1, +2

f-sublevel ----7 orbitals

-----

m l = -3, -2, -1, 0, +1, +2, +3

4. Spin Quantum Number ( m

s

) ~ NOT a property of the orbital ~ describes a property of the electron itself ~ indicates the direction of the electron spin

m s

= +1/2 or -1/2

Main Energy Level • • •

represented by a whole number represented by the periods on the periodic table the size of the orbital

Sublevels • •

represented by s, p, d, f the shape of the orbital

Orbitals •

the different ways the orbital aligns around the x, y, z axis

Spin of electron

* the distribution of electrons within the orbitals of an element’s atoms * determines behavior and chemical properties and reactivity of the elements

Electron Configurations Orbital notation # = main energy level (pqn, 1, 2, 3 etc…) letter = sublevel (s, p, d, f) = orbital = electrons

1s 3s 2s 2p 2p 2p

Starting order of energy level with sublevel and orbital

Here electron, come on boy!

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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

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More assigning of electrons

Hund’s rule ~ all orbitals within a sublevel 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 sublevel has one electron!

2s 1s 4p 4p 4p 3d 3d 3d 3d 3d 4s 3p 3p 3p 3s 2p 2p 2p

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!

Configuration notation

(aka REGULAR NOTATION)

 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)  1s 2 2s 2 2p 6 3s 1

Short 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. Cu 29  [Ar 18 ] 4s 2 3d 9

“d” and “f ” Subshells Fill LATE

•“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 order !!

Electron “Promotion”

Example: Silver (Ag) 1s 2 , 2s 2 , 2p 6 , 3s 2 , 3p 6 , 4s 2 , 3d 10 , 4p 6 , 5s 2 , 4d 9

5s 2 1 4d 9 – 1 short of full!

Silver (Ag) 1s 2 , 2s 2 , 2p 6 , 3s 2 , 3p 6 , 4s 2 , 3d 10 , 4p 6 , 5s 1 , 4d 10

Silver is now more stable with a full 4d subshell! (4d 10 )

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

!

Practice quantum #’s

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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

VALENCE ELECTRONS

 The electrons in the outermost energy level are called

valence 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.

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Valence electrons will ALWAYS be in “s” or “p” subshells!

Lewis Dot Structures

This 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.

Lewis Dot Diagrams Represent Valence 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) One valence electron:

Sy

Two valence electrons:

Sy

Three valence electrons:

Sy

Four valence electrons: Five valence electrons:

Sy

Six valence electrons:

Sy Sy

OK… WHY does 4s fill before 3d?

Higher energy 2nd shell, but all 3 an equal distance from the nucleus.

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

“3d” subshell “3p” subshell “3s” subshell

3 rd shell

“2p” subshell “2s” subshell

2 nd shell Closest to the nucleus

“1s” subshell

1 st shell

Higher energy

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

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

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

“4f” subshell “4d” subshell “4p” subshell “3d” subshell “3p” subshell “3s” subshell

7s 6s 5s 4s 3s 2p 2s 1s 7p 6p 5p 7d 6d 5d 7f 6f 5f 4p 3p 4d 3d 4f Higher energy