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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
nEn
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
18 11J 10178.2
if
fi nn
hchE
hEEE if
2
18 1J 10178.2
nEn
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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