de Broglie combined Einstien’s E = mcde Broglie combined Einstien’s E = mc22 and Planck’s E = hv and Planck’s E = hv

hv = mchv = mc22 Substitute v = c/Substitute v = c/λλ hchc = mc = mc22

λλ Divide both sides by c: Divide both sides by c: hh =mc =mc

λλ

Or Or λλ = = hh

mcmc

Wavelength could be predicted by the mass Wavelength could be predicted by the mass and speed of the particle.and speed of the particle.

momentum

Challenge Problem 3Challenge Problem 3

The diameter of a US penny is The diameter of a US penny is 19mm. The diameter of a silver atom 19mm. The diameter of a silver atom is only 2.88 Å. How many silver is only 2.88 Å. How many silver atoms could be arranged side by side atoms could be arranged side by side in a straight line across the diameter in a straight line across the diameter of a penny? (10of a penny? (1088Å = 1cm)Å = 1cm)

Young woman or old woman?

What do you see?

ReviewReview

Light of a particular wavelength (Light of a particular wavelength (λλ) has ) has a particular frequency (a particular frequency (vv) and energy.) and energy.

E = h∙E = h∙vv and c = and c = λλ∙∙vv

c=3.0 x 10c=3.0 x 1088 m/s speed of light m/s speed of light

h=6.63 x 10h=6.63 x 10-34-34 joule-sec joule-sec Plank’s constantPlank’s constant

Why each element produces a Why each element produces a unique line spectra?unique line spectra?

Newtonian mechanics-Newtonian mechanics- describes describes objects at ordinary velocities objects at ordinary velocities (classical mechanics)(classical mechanics)

Quantum mechanics- describes Quantum mechanics- describes particles at velocities near that of particles at velocities near that of light (subatomic particles).light (subatomic particles).

Quantum- a packet of energyQuantum- a packet of energy

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

It is impossible to know both the It is impossible to know both the location and the velocity of an location and the velocity of an electron at the same time.electron at the same time.

- to “see” an electron we would have - to “see” an electron we would have to bounce light off of it which would to bounce light off of it which would change its velocity. change its velocity.

Why did Werner Heisenberg Why did Werner Heisenberg hate driving cars?hate driving cars?

Because, every time he Because, every time he looked at the looked at the speedometer he got speedometer he got lost! lost!

SchrödingerSchrödinger Treated electrons as a waveTreated electrons as a wave

Radial Probability for an electronRadial Probability for an electron

The area of highest probability forms the electron The area of highest probability forms the electron cloud cloud

Locating ElectronsLocating Electrons

Principle quantum number (n)Principle quantum number (n)

Sublevel (Sublevel (ll))

Orbital (m)Orbital (m)

Spin (s)Spin (s)

Principle quantum number Principle quantum number (n)(n)

Energy levelsEnergy levels are a particular are a particular distance from the nucleus. distance from the nucleus.

2 8 18 32 electrons2 8 18 32 electrons

n = 1 2 3 4n = 1 2 3 4

Principal Quantum Number Principal Quantum Number (n)(n)

The maximum number of electrons at The maximum number of electrons at each energy level is 2neach energy level is 2n22..

at n = 1, there can be 2(1)at n = 1, there can be 2(1)22=2 electrons=2 electrons

at n = 2, there can be 2(2)at n = 2, there can be 2(2)22=8 electrons=8 electrons

at n = 3, there can be 2(3)at n = 3, there can be 2(3)22=18 =18 electronselectrons

Sublevel (Sublevel (l)l) Tells the shapeTells the shape Each energy level has a number of Each energy level has a number of

sublevels equal to n.sublevels equal to n.

Energy level Energy level (n)(n)

sublevelssublevels

11 1s1s

22 2s,2p2s,2p

33 3s,3p,3d3s,3p,3d

44 4s,4p,4d,4f4s,4p,4d,4f

Orbital Orientation (Orbital Orientation (mm) ) Each orbital can hold up to two Each orbital can hold up to two

electrons.electrons.

sublevel # orbitals # electrons

s 1 2

p 3 6

d 5 10

f 7 14

““d” orbitalsd” orbitals

Spin (s) Spin (s)

indicates the direction of spin on the indicates the direction of spin on the electron. electron.

Pauli Exclusion PrinciplePauli Exclusion Principle states states that no two electrons in an atom can that no two electrons in an atom can have the same set of four quantum have the same set of four quantum numbers.numbers.

The two electrons in an orbital must The two electrons in an orbital must have opposite spins.have opposite spins.

Electron configuration Electron configuration notationnotation

He has 2 electrons, so its electron He has 2 electrons, so its electron

configuration would be configuration would be 1s1s22

1s1s222s2s11

1s1s222s2s222p2p33

1s1s222s2s222p2p66

1s1s222s2s222p2p663s3s11 or [Ne]3s or [Ne]3s11

Principle quantum number

sublevel

No. of electrons

LiLi

NN

NeNe

NaNa

Degenerate orbitals have the same energy

1s1s

2s 2p2s 2p

3s 3p 3d3s 3p 3d

4s 4p 4d 4f4s 4p 4d 4f

5s 5p 5d 5f5s 5p 5d 5f

6s 6p 6d 6f6s 6p 6d 6f

7s 7p 7d 7f7s 7p 7d 7f

Sublevels fill in order of increasing energy.Sublevels fill in order of increasing energy.

1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f61s2s2p3s3p4s3d4p5s4d5p6s4f5d6p7s5f6d7pd7p

Predicting electron Predicting electron configurations from the configurations from the

periodic table.periodic table.

Aufbau Principle- electrons first Aufbau Principle- electrons first occupy the lowest energy level occupy the lowest energy level

available.available.

Electron Dot Notation- show only the Electron Dot Notation- show only the valence electrons, those in the valence electrons, those in the outermost energy level.outermost energy level.

H∙ He: Li∙ Be: Mg: H∙ He: Li∙ Be: Mg:

Orbital notation

1s 2s 2p 1s 2s 2p

N (7)N (7)

F (9) F (9)

Hund’s rule-Hund’s rule- orbitals of equal energy orbitals of equal energy are each occupied by one electron are each occupied by one electron before any orbital is occupied by a before any orbital is occupied by a second electron, and all electrons in second electron, and all electrons in singly occupied orbitals must have the singly occupied orbitals must have the same spin.same spin.

PrincipaPrincipal l quantuquantum m numbernumber

sublevesublevell

OrbitalOrbitals per s per sublevsublevelel

OrbitalOrbitals per s per energy energy levellevel

ElectronElectrons per s per sublevesublevell

Electrons Electrons per per energy energy levellevel

11 ss 11 11 22 22

22 ss

pp11

3344 22

6688

33 ss

pp

dd

11

33

5599

22

66

10101818

44 ss

pp

dd

ff

11

33

55

77

1616

22

66

1010

1414

3232

Excited state- electrons in a higher than Excited state- electrons in a higher than normal energy statenormal energy state

N: 1sN: 1s222s2s222p2p3 3 in ground statein ground state

1s1s222s2s222p2p223s3s11 or or

1s1s222s2s222p2p223p3p11 in excited state in excited state Ions- lost or gained electronsIons- lost or gained electrons

Anions are negatively charged, having Anions are negatively charged, having gainedgained

Cations are positively charged, having lostCations are positively charged, having lost NaNa+ + 1s1s222s2s222p2p663s3s11 ClCl-- 1s 1s222s2s222p2p663s3s223p3p5 65 6

Filled and half-filled sublevels are more Filled and half-filled sublevels are more stable than partially filled sublevels.stable than partially filled sublevels.

_ __ _1s 2s 2p 3s 3p 1s 2s 2p 3s 3p 3d 3d 4s 4s

Thus Cr takes an electron from 4s to Thus Cr takes an electron from 4s to put one electron in each of its 3d put one electron in each of its 3d orbitals and Cu takes a 4s electron to orbitals and Cu takes a 4s electron to fill each of its 3d orbitals. fill each of its 3d orbitals.