Atomic Structure. Wave-Particle Duality All waves have a characteristic wavelength,, and amplitude,...

Atom ic H Spectrum

Heisenberg Uncertainty

Electron ConfigurationElectron AffinityIonization EnergyElectronegativityS ize

Applications

Quantum Num bers Energy Levels

Quantum M echanics

Quantization Bohr M odel

W ave/Partic le Concept

Atomic StructureAtomic Structure

Wave-Particle DualityWave-Particle Duality

• All waves have a characteristic wavelength, , and amplitude, A.• Frequency, , of a wave is the number of cycles which pass a

point in one second.• Speed of a wave, c, is given by its frequency multiplied by its

wavelength:

• For light, speed = c = 3.00x108 m s-1 . • The speed of light is constant! • Higher Quality video (2:30 into video).

The Wave Nature of LightThe Wave Nature of Light

c

The Wave Nature of LightThe Wave Nature of Light

The Wave Nature of LightThe Wave Nature of Light

The Wave Nature of LightThe Wave Nature of Light

X – rays Microwaves Comment(s)

Wavelength: λ (m) 1.00x10-10 m 1.00x10-2 m

Frequency: ν (s-1)

Energy: E (J)

• Planck: energy can only be absorbed or released from atoms in certain amounts called quanta.

• The relationship between energy and frequency is

where h is Planck’s constant ( 6.626 10-34 J s ) .

Quantized Energy and PhotonsQuantized Energy and Photons

hE

The Photoelectric Effect and Photons• Einstein assumed that light traveled in energy packets

called photons.• The energy of one photon is:

Quantized Energy and PhotonsQuantized Energy and Photons

hE

Nature of Waves: Quantized Energy and PhotonsNature of Waves: Quantized Energy and Photons

X – rays Microwaves Comment(s)

Wavelength: λ (m) 1.00x10-10 m 1.00x10-2 m

Frequency: ν (s-1) 3.00x10-18 s-1 3.00x10-10 s-1

Energy: E (J)

Line Spectra• Radiation composed of only one wavelength is called

monochromatic.• Radiation that spans a whole array of different

wavelengths is called continuous.• White light can be separated into a continuous spectrum of

colors.• Note that there are no dark spots on the continuous

spectrum that would correspond to different lines.

Line Spectra and the Bohr ModelLine Spectra and the Bohr Model

Bohr Model• Colors from excited gases arise because electrons move between energy states

in the atom. (Electronic Transition)

Line Spectra and the Bohr ModelLine Spectra and the Bohr Model

Bohr Video

Fall 12

Bohr Model• Since the energy states are quantized, the light emitted

from excited atoms must be quantized and appear as line spectra.

• After lots of math, Bohr showed that

where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else).

Line Spectra and the Bohr ModelLine Spectra and the Bohr Model

2

18 1J 10178.2

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Bohr Model

• We can show that

• When ni > nf, energy is emitted.

• When nf > ni, energy is absorbed

Line Spectra and the Bohr ModelLine Spectra and the Bohr Model

22

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fi nn

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Bohr Model

Line Spectra and Line Spectra and the Bohr Modelthe Bohr Model

CyberChem (Fireworks) video

Mathcad (Balmer Series)

Line Spectra and the Bohr Model: Balmer Series CalculationsLine Spectra and the Bohr Model: Balmer Series Calculations

Line Spectra and the Bohr Model: Balmer Series CalculationsLine Spectra and the Bohr Model: Balmer Series Calculations

Fall 2012

4to2 486.8nm4to26.62610

34 J s 3.00108 m s

1

E4to2

h c

E

E4to2 4.084 1019 JE4to2 2.178 10

18 J1

22

1

42

nf 2ni 4Blue Line:

E3to2 3.025 1019 JNote that:

3to2 657.1nm3to26.62610

34 J s 3.00108 m s

1

E3to2

h c

E

E3to2 3.025 1019 JE3to2 2.178 10

18 J1

22

1

32

Ei.to.f 2.178 1018 J

1

nf2

1

ni2

nf 2ni 3Red Line:

nm 109mc 3.0010

8 m s1h 6.62610

34 J s

Balmer Series: Electronic transitions from higher E-levels (ni>2) down to the second E-level (nf=2).

Calculation of the first two lines in the Balmer Series for the H-atom

Line Spectra and the Bohr Model: Balmer Series CalculationsLine Spectra and the Bohr Model: Balmer Series Calculations

Limitations of the Bohr Model• Can only explain the line spectrum of hydrogen

adequately.• Can only work for (at least) one electron atoms.• Cannot explain multi-lines with each color.

• Electrons are not completely described as small particles.• Electrons can have both wave and particle properties.

Line Spectra and the Bohr ModelLine Spectra and the Bohr Model

• Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature.

• Using Einstein’s and Planck’s equations, de Broglie showed:

• The momentum, mv, is a particle property, whereas is a wave property.

• de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

The Wave Behavior of MatterThe Wave Behavior of Matter

mvh

The Uncertainty Principle• Heisenberg’s Uncertainty Principle: on the mass scale

of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.

• For electrons: we cannot determine their momentum and position simultaneously.

• If x is the uncertainty in position and mv is the uncertainty in momentum, then

The Wave Behavior of MatterThe Wave Behavior of Matter

4·

hmvx

Energy and MatterEnergy and Matter

Size of Matter Particle Property Wave Property

Large – macroscopic

Mainly Unobservable

Intermediate – electron

Some Some

Small – photon Few Mainly

E = m c2E = m c2

• Schrödinger proposed an equation that contains both wave and particle terms.

• Solving the equation leads to wave functions. • The wave function gives the shape of the electronic orbital.

[“Shape” really refers to density of electronic charges.]• The square of the wave function, gives the probability of

finding the electron ( electron density ).

Quantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic Orbitals

EH^

TBBT: QM-joke

Quantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic Orbitals

Solving Schrodinger’s Equation gives rise to ‘Orbitals.’

These orbitals provide the electron density distributed about the nucleus.

Orbitals are described by quantum numbers.

Sledge-O-Matic- Analogy

Orbitals and Quantum Numbers• Schrödinger’s equation requires 3 quantum numbers:

1. Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. ( n = 1 , 2 , 3 , 4 , …. )

2. Angular Momentum Quantum Number, . This quantum number depends on the value of n. The values of begin at 0 and increase to (n - 1). We usually use letters for (s, p, d and f for = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.

3. Magnetic Quantum Number, m. This quantum number depends on . The magnetic quantum number has integral values between - and + . Magnetic quantum numbers give the 3D orientation of each orbital.

Quantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic Orbitals

Quantum Numbers of WavefuntionsQuantum Numbers of Wavefuntions

Quantum # Symbol Values Description

Principal n 1,2,3,4,… Size & Energy of orbital

Angular Momentum

0,1,2,…(n-1)

for each n

Shape of orbital

Magnetic m…,0,…+ for each

Relative orientation of orbitals within same

Spin ms +1/2 or –1/2 Spin up or Spin down

Angular Momentum Quantum # () Name of Orbital

0 s (sharp)

1 p (principal)

2 d (diffuse)

3 f (fundamental)

4 g

Quantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic Orbitals

n ℓ Orbital Name mℓ (“sub-orbitals) Comment

Orbitals and Quantum Numbers

Quantum Mechanics and Atomic OrbitalsQuantum Mechanics and Atomic Orbitals

The s-Orbitals

Representations of OrbitalsRepresentations of Orbitals

The p-Orbitals

Representations of OrbitalsRepresentations of Orbitals

d-orbitals

Many-Electron Atoms Many-Electron Atoms

Orbitals and Their Energies

Orbitals CD

Electron Spin and the Pauli Exclusion Principle

Many-Electron Atoms Many-Electron Atoms

Electron Spin and the Pauli Exclusion Principle

• Since electron spin is quantized, we define ms = spin quantum number = ½.

• Pauli’s Exclusions Principle:: no two electrons can have the same set of 4 quantum numbers.• Therefore, two electrons in the same orbital must have

opposite spins.

Many-Electron Atoms Many-Electron Atoms

Figure 6.27

Figure 6.27 Orbitals CD

Figure 6.28 Orbitals CD

Many-Electron Atoms Many-Electron Atoms

Orbitals and Their Energies

Orbitals CD

Electron Configurations – I Electron Configurations – I Species Electron Configuration Box Orbital Comment

Electron Configurations - II Electron Configurations - IISpecies Electron Configuration Box Orbital Comment

Metals, Nonmetals, and MetalloidsMetals, Nonmetals, and Metalloids

Metals

Figure 7.14

Two Major Factors:

•principal quantum number, n, and

•the effective nuclear charge, Zeff.

Periodic Trends Periodic Trends

Figure 7.5: Radius video Clip

Figure 7.6

Figure 7.10 IE clip

Figure 7.9

Electron AffinitiesElectron Affinities

• Electron affinity is the opposite of ionization energy.• Electron affinity: the energy change when a gaseous atom

gains an electron to form a gaseous ion:

Cl(g) + e- Cl-(g)• Electron affinity can either be exothermic (as the above

example) or endothermic:

Ar(g) + e- Ar-(g)

Figure 7.11: Electron AffinitiesFigure 7.11: Electron Affinities

Group Trends for the Active MetalsGroup Trends for the Active Metals

Group 1A: The Alkali Metals

Group Trends for the Active MetalsGroup Trends for the Active Metals

Group 2A: The Alkaline Earth Metals

Group Trends for Selected NonmetalsGroup Trends for Selected Nonmetals

Group 6A: The Oxygen Group

Group Trends for Selected NonmetalsGroup Trends for Selected Nonmetals

Group 7A: The Halogens

Group Trends for the Active MetalsGroup Trends for the Active Metals

Group 1A: The Alkali Metals• Alkali metals are all soft.• Chemistry dominated by the loss of their single s

electron:M M+ + e-

• Reactivity increases as we move down the group.• Alkali metals react with water to form MOH and

hydrogen gas:2M(s) + 2H2O(l) 2MOH(aq) + H2(g)

Group Trends for the Active MetalsGroup Trends for the Active Metals

Group 2A: The Alkaline Earth Metals• Alkaline earth metals are harder and more dense than the alkali

metals.

• The chemistry is dominated by the loss of two s electrons:M M2+ + 2e-.

Mg(s) + Cl2(g) MgCl2(s)2Mg(s) + O2(g) 2MgO(s)

• Be does not react with water. Mg will only react with steam. Ca onwards:

Ca(s) + 2H2O(l) Ca(OH)2(aq) + H2(g)

Atom ic H Spectrum

Heisenberg Uncertainty

Electron ConfigurationElectron AffinityIonization EnergyElectronegativityS ize

Applications

Quantum Num bers Energy Levels

Quantum M echanics

Quantization Bohr M odel

W ave/Partic le Concept

Atomic StructureAtomic Structure

c

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