Quantum Model of the Atom Electrons in Atoms. zSchrödinger Wave Equation (1926) ydefines probability of finding an e -

Quantum Model of the Atom

Electrons in Atoms

σ3/2 Zπ

11s 0

eΨ a

Schrödinger Wave Equation (1926)

defines probability of finding an e-

Orbital

Orbital (“electron cloud”)

Region in space where there is 90% probability of finding an e-

OrbitalOrbital

A 3-dimensional space around a nucleus in A 3-dimensional space around a nucleus in

which electrons are most likely to be foundwhich electrons are most likely to be found

Shape represents electron density (Shape represents electron density (not a not a

path the electron follows)path the electron follows)

Each orbital can hold up to 2 electronsEach orbital can hold up to 2 electrons

Quantum Numbers

UPPER LEVEL

Four Quantum Numbers:

Specify the “address” of each electron in an atom

Quantum MechanicsQuantum Mechanics

Describes the arrangement and space Describes the arrangement and space occupied by electrons in atomsoccupied by electrons in atoms

Quantum MechanicsQuantum Mechanics

Describes the arrangement of electrons Describes the arrangement of electrons in atoms in terms of:in atoms in terms of:Main or principal energy levels or shells (n)Main or principal energy levels or shells (n)

(Oklahoma City)(Oklahoma City)Energy sublevels or subshellsEnergy sublevels or subshells

(Britton Road)(Britton Road)OrbitalsOrbitals

(house # 200)(house # 200)Electron spinElectron spin

(room # 4)(room # 4)

Quantum Numbers

1. Principal Quantum Number ( n )

Energy level or shell

Size of the orbital

Principal Quantum Number (Principal Quantum Number (nn))

Contain electrons that areContain electrons that are

Close in energyClose in energy

Similar distance from nucleusSimilar distance from nucleus

Have values of n = 1, 2, 3, 4, 5, 6…..Have values of n = 1, 2, 3, 4, 5, 6…..

Energy Levels (Shells)Energy Levels (Shells)

The first shell (n = 1) is lowest in The first shell (n = 1) is lowest in energy, 2energy, 2ndnd level next and so on level next and so on 1<2<3<41<2<3<4

Low energy electrons are closest Low energy electrons are closest to the nucleusto the nucleus

Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l )

Energy sublevel or subshell

Shape of the orbital

SubshellsSubshells

Energy sublevels within energy levelEnergy sublevels within energy level

All electrons in a subshell have the All electrons in a subshell have the

same energysame energy

Designated Designated s, p, d, f .. s, p, d, f ..

Sublevel energy: s<p<d<fSublevel energy: s<p<d<f

Main Main Energy Energy LevelsLevels SublevelsSublevels

n=4n=4 4s, 4p, 4d, 4f4s, 4p, 4d, 4f

n=3n=3 3s, 3p, 3d3s, 3p, 3d

n=2n=2 2s, 2p2s, 2p

n=1n=1 1s1s

nn == # of energy sublevels # of energy sublevels per energy levelper energy level

Sublevels in n = 1,2, 3Sublevels in n = 1,2, 3

n = 3n = 3 3d3d

3p3p

3s3s

n = 2 n = 2 2p2p

2s2s

n = 1n = 1 1s1s

Quantum Numbers

3. Magnetic Quantum Number ( ml )

Orientation of orbital

Specifies the exact orbital within each sublevel

s subshell contains 1 s subshell contains 1 s orbitals orbital

1s 2s 3s

p subshell contains 3 p p subshell contains 3 p orbitalsorbitals

px pz py

d subshell contains 5 d orbitals

f subshell contains 7 f orbitals

Quantum Numbers

n = # of energy sublevels per energy level

n2 = # of orbitals per energy level

Sublevel sets: 1 s, 3 p, 5 d, 7 f

Number of Electrons Number of Electrons

Each orbital can hold up to 2 Each orbital can hold up to 2 electronselectrons

Maximum number of electrons in any Maximum number of electrons in any energy level = 2nenergy level = 2n22

n =1n =1 2(2(11))22 = = 2 2

n =2n =2 2(2(22))22 == 8 8

n =3n =3 22(3(3))22 == 1818

Electrons AllowedElectrons Allowed

All 2s electrons have the same energyAll 2s electrons have the same energy

All 2p electrons have the same energy which is All 2p electrons have the same energy which is

slightly higher than the energy of the 2s slightly higher than the energy of the 2s electronselectrons

s sublevel s sublevel 22 electrons electrons

p sublevel p sublevel 66 electrons electrons

d sublevel d sublevel 1010 electrons electrons

f sublevel f sublevel 1414 electrons electrons

Quantum Numbers

Orbitals combine to form a spherical

shape.

2s

2pz2py

2px

Quantum Numbers

4. Spin Quantum Number ( ms )

Electron spin +½ or -½

An orbital can hold 2 electrons that spin in opposite directions

Quantum Numbers

1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin #

energy level

sublevel (s,p,d,f)

orbital

electron spin

Pauli Exclusion Principle

No two electrons in an atom can have the same 4 quantum numbers.

Each e- has a unique “address”

Pauli Exclusion Principle

Each orbital can hold TWO electrons

with opposite spins.

A. Number of electrons in a p orbital

1e or 2e

B. Number of orbitals in a p subshell

3

C. Number of orbitals in 4d subshell

5

D. Maximum number of electrons in a 3d subshell

10e

ORBITAL DIAGRAM

Shows the electrons in each orbital

Circles, boxes, or lines are used to represent orbitals

Arrows or half-arrows represent electrons

l = 0 s subshell

1 p

2 d

3 f

ml 0

s orbital

Ml -1 0 +1

p orbital

Ml -2 -1 0 +1 +2

d orbital

Ml -3 -2 -1 0 +1 +2 +3

f orbital

electron spin

ms +1/2 -1/2

Orbital diagram n l ml ms

7 0 0 +1/2

6 1 -1 +1/2

5 2 -2 -1/2

7s

6p

5d

-2 -1 0 +1 +2

-1 0 +1

Orbital diagram n l ml ms

4 3 -3 +1/2

4 2 -1 -1/2

5 3 2 -1/2

4f

-3 -2 -1 0 +1 +2 +3

4d

-2 -1 0 +1 +2 5f

-3 -2 -1 0 +1 +2 +3

Feeling overwhelmed?

Read Section 4-2!