Using Quantum Numbers Using Quantum Numbers to Describe Electronsto Describe Electrons

De BroglieDe Broglie

SchrodingerSchrodinger

Clouds probable location for Clouds probable location for electronselectrons

λ= h mυ

Quantum NumbersQuantum Numbers

Four numbers (variables) that describe Four numbers (variables) that describe the shape of the cloud and location of the shape of the cloud and location of electrons.electrons.

Described using the variables: n, l, m, s.Described using the variables: n, l, m, s.

““n” = the Principle n” = the Principle Quantum Number(Energy Quantum Number(Energy

Quantum #)Quantum #)

Corresponds to periodic table’s horizontal Corresponds to periodic table’s horizontal row.row.

n = 1n = 2n = 3

““n” = the Principle n” = the Principle Quantum Number(Energy Quantum Number(Energy

Quantum #)Quantum #) Higher number, more energy/ bigger Higher number, more energy/ bigger

cloudcloud 2n2n22 is how many electrons may have is how many electrons may have

that energythat energy

““l” sublevel of nl” sublevel of nShapeShape

Found within “n” (4 sublevels/orbital Found within “n” (4 sublevels/orbital types) types)

““s” has 1 orbital (spherical shaped).s” has 1 orbital (spherical shaped). Each orbital can have at most two Each orbital can have at most two

electrons.electrons.

““l” sublevel of nl” sublevel of nShapeShape

““p” sublevel is p” sublevel is barbell shapedbarbell shaped

three orbitals: px, py, three orbitals: px, py, pzpz

““l” sublevel of nl” sublevel of nShapeShape

““d” shaped” shape 5 orbitals :z5 orbitals :z22, xy, xz, yz, x, xy, xz, yz, x2 2 -- yy22

Each orbital can have how many electrons?Each orbital can have how many electrons? How many total electrons can the d orbitals How many total electrons can the d orbitals

have?have?

““l” sublevel of nl” sublevel of nShapeShape

““f” sublevelf” sublevel seven orbitalsseven orbitals How many total electrons possible in How many total electrons possible in

“f”?“f”?

““m” Quantum Numberm” Quantum Number

Determines the orientation in space Determines the orientation in space (which orbital is being filled)(which orbital is being filled)

““s” spin Quantum Numbers” spin Quantum Number

s = 1/2 is clockwise (up)s = 1/2 is clockwise (up) s = -1/2 is counter-clockwise (down)s = -1/2 is counter-clockwise (down)

Quantum NumberQuantum Number

Keep in mind are probabilities of finding Keep in mind are probabilities of finding electrons in certain places doing certain electrons in certain places doing certain things(spin).things(spin).

n = what energy level (1, 2, 3, 4 . . .)n = what energy level (1, 2, 3, 4 . . .) l = what sub-level (s, p, d, or f)l = what sub-level (s, p, d, or f) m = which orbital (s=1; p=3; d=5; f=?)m = which orbital (s=1; p=3; d=5; f=?) s = which spin (only two possibilities s = which spin (only two possibilities

up or down)up or down)

Pauli Exclusion PrinciplePauli Exclusion Principle

No two electrons No two electrons ever ever have the have the same same fourfour quantum numbers in the quantum numbers in the same atom.same atom.

Just as no two houses have the same Just as no two houses have the same address.address.

Quantum #’s can be Quantum #’s can be viewed as Addressesviewed as Addresses

Each town has two mains streets, one Each town has two mains streets, one running north-south and the other running running north-south and the other running east-westeast-west

N

S

W E

They are numbered according to how far they are They are numbered according to how far they are from the intersection of these two streets. 100, 200, from the intersection of these two streets. 100, 200, 300- for first block, second block, etc.300- for first block, second block, etc.

Quantum #’s can be Quantum #’s can be viewed as Addressesviewed as Addresses

N

S

W E100W

200W

Main S

t

Quantum #’s can be Quantum #’s can be viewed as Addressesviewed as Addresses

Even #s are on one side of the street Even #s are on one side of the street and odd #s are on the other side.and odd #s are on the other side.

W E1602 1508

15111627

Quantum #’s can be Quantum #’s can be viewed as Addressesviewed as Addresses

So an address tells you four thingsSo an address tells you four things which block its on, which block its on, How far down the street it isHow far down the street it is which side of the street it’s onwhich side of the street it’s on which house it is.which house it is.

Quantum #’s can be Quantum #’s can be viewed as Addressesviewed as Addresses

833 W. Electron Ave.833 W. Electron Ave.

700W

Electron Ave 833

876

Quantum #sQuantum #s

n - tells the size and energyn - tells the size and energy l - tells the shapel - tells the shape m - tells how the shape fits on the m - tells how the shape fits on the

x, y, z axesx, y, z axes s- tells about spin.s- tells about spin.