the four quantum numbers in the quantum mechanical model of the atom, each electron is described by...

The Four Quantum NumbersIn the quantum mechanical model of the atom, each electron is described by four quantum numbers, and no two electrons in an atom can have the same numbers.

The quantum numbers are:

n: the principle quantum number. n = 1, 2, 3, 4…

l: the angular quantum number. It describes the ‘shape’ of the orbital…the electronic distribution about the nucleus. l = n-1, n-2,… to 0

If l = 0, it’s an s orbitalIf l = 1, it’s a p orbitalIf l = 2, it’s a d orbitalIf l = 3, it’s an f orbital (and so on)

ml: the magnetic quantum number. It describes the orientation of the orbital on an xyz-coordinate axis. ml = -l…0…+l in integral values.

ms: the spin quantum number. It equals +½ or -½. Conventionally, the +½ is always given first.

A few examples:

1

n l ml

0 0

(all ms’s are ± ½, so won’t be shown here)

Notes

The 1s orbital

2 1

0 0

-1, 0, 1 The three 2p orbitals.

2 The 2s orbital

3 2 -2, -1, 0, +1, +2 The five 3d orbitals.

3 1 -1, 0, +1 The three 3p orbitals.

3 0 0 The 3s orbital

x

y

z

x

y

z

x

y

z

px pz py

The three p-orbitals are oriented along the x, y and z axes and can hold a maximum of 2 electrons each.

It’s been suggested that the p-orbitals look like peanuts if that helps you to remember their shape.

The d-orbitals

dxy dxz dyz

Even though the d-orbitals look like two p-orbitals, it is important to remember that each orbital can hold a maximum of 2 electrons regardless of how many lobes it has.

dx2-y2 dz2

The freaky (or flowery) f-orbitals

And Electron Configurations

Orbital Diagrams

H: 1 electron, 1s1

Electron configuration

Electrons behave as though they are spinning on their axis. A half arrow is used to indicate if the direction of the spin is up ( ) or down ( ).

Electrons behave as though they are spinning on their axis. A half arrow is used to indicate if the direction of the spin is up ( ) or down ( ).

He: 2 electrons, 1s2

Pauli Exclusion Principle:Each orbital can contain 2 electrons ONLY if the electron spins are in opposite directions.

Pauli Exclusion Principle:Each orbital can contain 2 electrons ONLY if the electron spins are in opposite directions.

Li: 3 electrons, 1s2 2s1

Auf bau principle: the electrons fill the orbitals starting with the lowest energy level and working their way up the energy ‘ladder’

Auf bau principle: the electrons fill the orbitals starting with the lowest energy level and working their way up the energy ‘ladder’

Be: 4 electrons, 1s2 2s2

B: 5 electrons, 1s2 2s2 2p1

C: 6 electrons, 1s2 2s2 2p2

Hund’s Rule: all sublevel orbitals of the same energy must be filled with a single electron before the electrons can begin to pair up.

Hund’s Rule: all sublevel orbitals of the same energy must be filled with a single electron before the electrons can begin to pair up.

Sc: 21 electrons , 1s2 2s2 2p6 3s2 3p6 4s2 3d1

Total electrons

241012182021

complete configuration

Shorthand notation: noble gas core configuration4s2 3d1[Ar]

n

1

2

3

4

5

6

7

n -1

n -2

d-block metals

f-block metals

s-block metals

p-block elements

1s1 1s2

2s1 2s2 2p1 2p2 2p3 2p4 2p5 2p6

3s1 3s2 3p1 3p6

4s1 4s2 3d1 3d10 4p1 4p6

4d1 4d10

5d1

We’ll look at the f-block tomorrow

4f14

5f14

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p4

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d8

Chemical reactivity depends upon the number of electrons in the highest energy level (the largest n).

• Electron dot structures show only the outermost electrons so that reactivity can be easily predicted.

• The outermost electrons are also called the valence electrons.

Electron Dot Structures

Rules to Drawing Electron Dot Structures

1. Electrons 1-4 are added singly.2. Exception: If there only two electrons, they’re

shown as a pair.3. Electrons 5-8 are paired with the single

electrons that are already there.

Xe

Sr

N

Examples:

1. What is the electron configuration of strontium (Sr)?

1s2 2s2 2p6 3s2 3p6 4s2 3d10 3p6 5s2

The highest energy level is n=5 and there are 2 electrons in it. Therefore, Sr has 2 valence electrons.

2. What is the electron configuration of nitrogen (N)?

1s2 2s2 2p3

The highest energy level is n=2 and there are 5 electrons in it. Therefore, N has 5 valence electrons.

3. What is the electron configuration of xenon (Xe)?

1s2 2s2 2p6 3s2 3p6 4s2 3d10 3p6 5s2 4d10 5p6

The highest energy level is n=5 and there are 8 electrons in it. Therefore, Xe has 8 valence electrons.

Excluding a few exceptions, how many valence electrons would all of the d-block and f-block elements have?

1

2 3 4 5 6 7

8

# Valence electrons

Electron Configuration Exceptions

Hund’s Rule (part 2): For n ≥ 4, the energy of the electrons decreases (and stability increases) when all of the boxes for a sublevel are either half-filled OR completely filled.

4s 3d

All of the orbitals are half-filled

Cr

4s 3d

Cu

[Ar]

[Ar] All of the 3d orbitals are filled and the 4s orbital is half-filled

Where would the exceptions be in the 5th through 7th periods?