Quantum Numbers:Much better than

stupid cat jokes

How did your results compare to the probability plot?

Mechanical Wave Lab results

The Quantum NumbersThe principal quantum number is n

It describes what energy level the electron is located in(n=1 is smallest (closest to nucleus). n also describes the number of sublevels contained in that energy level and the maximum number of electrons contained in that energy level

Principal energy level (n)

Number of sublevels (n)

Number of orbitals present

Total number of orbitals (n)2

Maximum number of electrons (2n2)

1 1 1 - - - 1 2

2 2 1 3 - - 4 8

3 3 1 3 5 - 9 18

4 4 1 3 5 7 16 32

s p d f

The value of n is used to calculate the total number of orbitals and the maximum # of electrons

n # also tells # of subshells or orbitals e.g. n= 1 has 1 orbital (s) n= 2 has 2 orbitals (s, p) n= 3 has 3 orbitals (s,p,d) n= 4 has 4 orbitals (s,p,d,f)

The quantum number l (The orbital quantum number)describes 3D shape of orbital also called subshell max. ℓ = n – 1 (ℓ = 0, 1, 2, 3,…..)

orbitals identified by letters s, p, d, f,…

n

Subleveltypes

Value of ℓ

1 1 s ℓ = 0

2 2 s p ℓ=0, ℓ =1

3 3 s p d ℓ =0, ℓ =1, ℓ =2

sublevels

Fill this in

: The secondary quantum number• If n can be thought of as shells, l can be

thought of as “subshells” dividing each shell into subsections … (l = 0 n - 1)

n = 1 = 0 (s)

n = 2 = 0 (s)l = 1 (p)

n = 3 = 0 (s)l = 1 (p)l = 2 (d)

For more lessons, visit www.chalkbored.com

l

l

ll

llll

The magnetic quantum number – m (mℓ) Describes the 3D orientation of the orbital

and how many of that type orbital existmℓ = - ℓ, …, 0, … + ℓ

Example:

n = 2 mℓ (for ℓ = 1) = -1, 0,+1 px, py, pz

sublevel

ℓ value

# orbitals

Shape of orbitals mℓ valueorbitals

s ℓ = 0 1 sphere mℓ = 0 1 orientation

p ℓ =1 3 dumbells mℓ = 3 orientations

d ℓ =2 5 4 leaf mℓ = 5 orientations

f

-1, 0,+1

FYI – its mℓ = -ℓ to +ℓ

-2, -1, 0, +1, +2

Fill in this

How many different ways are “s” orbitals oriented? How many different ways

are“p“ orbitals oriented?

How many different ways are “d” orbitals oriented?

How many different ways are “f” orbitals oriented?

Spin Quantum number: ms (or s) – describes the spin of the electron on its own axis

Clockwise spin is + ½ , counterclockwise spin is -½

Orbital notation uses arrows to represent spin

What “spins” do electrons have that share the same orbital?

Visualization of electron orbitals around a nucleus in an atom

The nucleus is located somewhere in the center

Slightly different diagram - 3d orbitals

This is a computer designed image of over-lapping s and p orbitals in an atom of neon. The bright center portion is the approximate position of nucleus

It probably won’t be hard as this…….

BUT.. NOT AS EASY AS THIS..

Electron Configurations1. Electrons are located in a very specific place in the energy levels of atom

2. They will fill orbitals in sequential order –based on the energy value of that orbital.

Which orbital has a higher energy 1s, 2s or 2p?

1s has the lowest energy

2p has a higher energy value

FYI –electron orbitals in the same energy level are called degenerate

2s

How many electrons can a “s” orbital hold?

Electron orbital Filling sequenceWhat is the electron configuration of Li (lithium)?Li has an atomic number (Z=3)(Contains 3 electrons)

1s

1s

1s

2How many electrons are left?

2 1

2

1

1s

2s

2 1Electron configuration of Li

Practice:

Z=7:

1s2 2s2 2p3

Z=15:

1s2 2s2 2p6 3s2 3p3

1s2 2s2 2p6 3s1

Z=11:

Orbital filling patterns of the Periodic Table

Including “f” orbitals in an electron configuration

The configuration of:

Lutetium Z=

This is 4f block sublevel

This is 5f block sublevel

FYI- f blocks are filled with 14 electrons

1s22s22p63s23p64s23d104p65s2 4d10 5p6 6s2 5d1 4f14

3456

11

32

54

76

Bismuth Z= 1s22s22p63s23p64s23d104p65s2 4d10 5p6 6s2 4f145d106p3 How many energy lvls? How many sublevels? How many valence electrons?

6 15

71

835

Abbreviated configuration of Bi: [Xe] 6s2 4f14 5d10 6p3

There are some “differences” in the sequential filling of orbitals in the “d” block “d” sublevel is full at 10 electrons, half full “d” orbital is more stable (at 5) Full d orbital (with 10 e - )is more stable than “almost full” d orbital (with 9e - )

Sc = [Ar] 4s23d1

Ti = [Ar] 4s23d2

V = [Ar] 4s23d3

Cr = [Ar] 4s13d5

Mn = [Ar] 4s23d5

Fe = [Ar] 4s23d6 

Co= [Ar] 3d7 4s2

Ni= [Ar] 4s23d8

Cu = [Ar] 4s13d10

Zn= [Ar] 4s23d10

Remember half full

Remember almost full

Exceptions list: Cr = [Ar] 4s1 3d5

Cu = [Ar] 4s13d10

Mo = [Ar] 5s14d5

Ag = [Ar] 5s14d10

Au = [Ar] 6s15d10

Orbital notation diagrams1. Each space represents a orbital, arrows are electrons. 2. Hund Rule: Every orbital in the SAME sublevel gets 1e- before any of them get 2 electrons

Chlorine (Cl) 1s2 2s2 2p6 3s2 3p5

____ _____ _____ _____ ____ ____ _____ _____ _____ 1s 2s 2p 3s 3p

Hint: circles can also be used to represent orbitals – just make sure to label, label, label

How to find an electron by it’s address-the 4 quantum numbers You don’t have to be a rocket scientist to do

this – just remember to label-label-label!

Chlorine (Cl) 1s2 2s2 2p6 3s2 3p5

Each circle represents an orbital

Arrows represent electrons. First arrow is always positive spin (pointing up). Remember Hunds Rule when filling in orbitals

1s 2s 2p 3s 3p

m= 0 0 -1 0 +1 0 -1 0 +1

Energy levels and sublevels

n= is energy level

ℓ = is sublevel 0,1,2,3 (s,p,d,f) m = is the orbital in the sublevel S =is the spin of the electron or

Remember:

___ ____ ____ ___

1 +12 +

½ n ℓ m s

NOW:

What are the addresses of the following electrons in Cl?

4th

12th

2 0 0 -½

This is the 7th electron

3 0 0 -½ Last

electron

3 1 0 -½

n ℓ m s

1 0 0 +½

n= 1, it is in the 1st energy level ℓ = 0, it is in the “s” sublevel (if ℓ =0, (m is also 0), s orbital

+½ is the spin of the electron

What’s that element ?These are the quantum numbers for the LAST ELECTRON

n m s

1s1First electron in H

2 1 1 -½

n m s

N= 2, it is in the 2nd energy level

ℓ = 1, it is in the “p” sublevel (m is 1), 2pz orbital

-½ is the spin of the electron second electron in

0

1s 2s 2px 2py 2pz

-1 0 +1

1s22s22p6 = Ne

4 2 0 -½

N= 4, be careful! ℓ = is sublevel 0,1,2,3 (s,p,d,f)

m=0 -½ is the spin of the electron

What’s that element ?These are the quantum numbers –for the LAST electron

n m s

2nd electron in

-2 -1 0 +1 +2

d sublevel

N=4, 4d’s start in which period?

ℓ = is sublevel 0,1,2,3 (s,p,d,f)

m=0, go to the d orbital designated as zero

Remember Hund’s Rule !

-½ is the spin of the electron - 2nd electron in

Where do 4d sublevels start?

Last electron is in 4d8

Element is Pd

4 2 0 -½

N= 4, it is in the 4th energy level ℓ = is sublevel 0,1,2,3 (s,p,d,f)

m=0 -½ is the spin of the electron

What’s that element ?These are the quantum numbers –for the LAST electron

n m s

2nd electron in

2 1 0 +½

n m s

N= 2, it is in the 2nd energy level

mℓ = 1, it is in the “p” sublevel (if ℓ =1, ( but m is 0)

+½ is the spin of the electron second electron in

1s22s22p5 F

_____ ______ ______ ______ _______ 1s 2s 2px 2py 2pz

-1 0 +1

in py

d sublevel

http://www.youtube.com/watch?v=a4fklbnHTYY

http://www.youtube.com/watch?v=A6DiVspoZ1E

Some really good websites to peruse at your leisure concerning quantum numbers

http://www.youtube.com/watch?v=yqzgYRBlslw