Quantum Numbers

• Bohr model- required that electrons be confined to specific orbits which had specific corresponding energy

• Bohr equation:

• n represents the number of each orbit, starting closest to the nucleus

• His theory was widely accepted because the constants ended up to be equal to the Rydberg constant! And produced a model of the atom

• The energy difference between two given orbits is constant

• The same amount of energy needed to promote an electron to a higher orbit, will be released when the electron drops back

Wave mechanical model

• Describing the motion of an electron- very complicated wave equations- Schroedinger Equation

6 new ideas….

• 1. The wave equations require 3 numbers-quantum numbers-in order to solve the equations

Quantum numbers

• n- principal quantum number• l- azimuthal quantum number• ml –magnetic quantum number

• ms- spin quantum number

• 2. Changed the picture of the atom–Bohr’s fixed orbits replaced by a

“cloud”–Modern orbit is a region of space in

which the probability of finding the electron is the highest

• 3. Wave equations provide a shape for each of the clouds

• 4. arrangements of electrons agrees with element arrangement of the periodic table– Deeper understanding of chemical properties

based on shapes of clouds

• 5. Results of the wave equation agree completely with the Bohr model calculations

• 6. Heisenberg Uncertainty Principal– Position and momentum of an electron cannot be

exactly known at the same time

Electron Configuration

• Principal energy level – n (principal quantum number)

• Energy level increases in size and energy the farther the electron is from the nucleus- can hold more electrons

• Maximum number of electrons an energy

level 2n2

Sublevels - l- azimuthal quantum number (room type)

• Each principal quantum energy level contains sublevels

• # of sublevels = to the value of n for that energy level– Ex: for the third principal energy level (n=3)

contains a maximum of 3 sublevels

– Sublevels 5, 6, and 7 are theoretically possible but not currently needed

• Sublevels are numbered with consecutive whole numbers starting with 0

• The value of l can never be greater than n-1

• Each number corresponds to a letter s,p,d, or f (room type s,p,d,f)

Principal Level Sublevel number, l Sublevel letter1

1 0 s

2 0,1 s,p

3 0,1,2 s,p,d

4 0,1,2,3 s,p,d,f

5 0,1,2,3 s,p,d,f

6 0,1,2 s,p,d

7 0,1 s,p

Orbitals

• Each sublevel can contain one or more electron orbitals• Orbital-region of space that has

high electron density and each orbital may contain a MAXIMUM of 2 electrons

Orbitals

• To share an orbital the 2 electrons must have opposite spins (Pauli Exclusion Principle)

• ms - values for spin can be +1/2 or -1/2

• When 2 electrons share an orbital they are “paired”

• Orbitals have the same designation as the sublevel they are in (s,p,d,f)

• The number of orbitals that a sublevel can have depends on the azimuthal quantum number, l

• Can have 2l + 1 orbitals

ml magnetic quantum number (room number)

• Each orbital is given a number that range from

- l to +l including 0

Sublevel # l-

Sublevel letter

Number of orbitals2l + 1

Number of electrons per sublevel

ml values

0 s 1 2 0

1 p 3 6 -1, 0, +1

2 d 5 10 -2, -1, 0, +1, +2

3 f 7 14 -3, -2, -1, 0, +1, +2, +3

Electron ConfigurationsA list of all the electrons in an atom (or ion)• Must go in order (Aufbau principle)• 2 electrons per orbital, maximum• We need electron configurations so that we can

determine the number of electrons in the outermost energy level. These are called valence electrons.

• The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

Electron Configuration Rules

• The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called electron configurations.–Three rules—the aufbau principle, the Pauli exclusion principle, and Hund’s rule—tell you how to find the electron configurations of atoms.

Aufbau Principle

• electrons occupy the orbitals of lowest energy first. In the aufbau diagram below, each box represents an atomic orbital.

Pauli Exclusion Principle

• an atomic orbital may describe at most two electrons. To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired.

Hund’s Rule

• states that electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible.

1

2

3

4

5

6

7

6

7

1A

2A

3B 4B 5B 6B 7B 8B 8B 8B 1B 2B

3A 4A 5A 6A 7A

8Agroup # = # valence (outside) e-

d p

f

sRow

=# shells

Why are d and f orbitals always in lower energy levels?

• d and f orbitals require LARGE amounts of energy• It’s better (lower in energy) to skip a sublevel that

requires a large amount of energy (d and f orbtials) for one in a higher level but lower energy

This is the reason for the diagonal rule! BE SURE TO FOLLOW THE ARROWS IN ORDER!

1

2

3

4

5

6

7

6

7

perio

d #

= #

e- s

hells

1A

2A

3B 4B 5B 6B 7B 8B 8B 8B 1B 2B

3A 4A 5A 6A 7A

8Agroup # = # valence e-

d

f

3d4d5d6d

4f5f

Subshells d and f are “special”

Electron Configuration

1s1

row # (on periodic table) Also known as shell #

(principal quantum # n)possibilities are 1-7

7 rows subshellpossibilities are

s, p, d, or f4 subshells

# of electrons in that subshell

Diagonal Rule• Must be able to write it for the test! This will

be question #1 ! Without it, you will not get correct answers !

• The diagonal rule is a memory device that helps you remember the order of the filling of the orbitals from lowest energy to highest energy

• _____________________ states that electrons fill from the lowest possible energy to the highest energy

Order of Electron Subshell Filling:It does not go “in order”

1s2

2s2 2p6

3p6

4p6

5p6

6p6

7p6

3s2

4s2

5s2

6s2

7s2

3d10

4d10

5d10

6d10

4f14

5f14

1s2 2s2 2p6 3p63s2 4s2 4p6 5s23d10 5p6 6s24d10 6p6 7s25d104f14 7p66d105f14

Shorthand Notation

• A way of abbreviating long electron configurations

• Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration

Paramagnetic Atoms

• Lone atoms with one or more unpaired electrons and are attracted by magnetic fields

• _____ _____ ____ ____ ____ 1s 2s 2p

Diamagnetic Atoms

• Lone atoms with NO unpaired electrons are repelled by magnetic fields

• _____ _____ ____ ____ ____ 1s 2s 2p

• Ex: Neon

Iron