atomic structure and periodicitychpro/chem/chap7.pdf · developed a quantum model for the hydrogen...
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Chapter seven:Chapter seven:
Atomic Structure andAtomic Structure andPeriodicityPeriodicity
p274
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p274Contents
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77--11 Electromagnetic RadiationElectromagnetic Radiationp275
Wave length
Frequency
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The NatureThe Nature
of Wavesof Waves
p276
Figure 7.1
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The brilliant red colors seen in fireworks are due to the
emission of light with wavelengths around 650 nm when
strontium salts such as Sr(NO3)2 and SrCO3 are heated. (This
can be easily demonstrated in the lab by dissolving ones of
these salts in methanol that contains a little water and igniting
the mixture in an evaporating dish.) Calculate the frequency
of red light of wavelength 6.50 × 102 nm.
P277P277Ex 7.1 Frequency of Electromagnetic Radiation
Solution:
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Classification ofClassification ofelectromagnetic radiationelectromagnetic radiation
Figure 7.2
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Flame TestsFlame Tests
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Electromagnetic WavesElectromagnetic Waves
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77--22 The Nature of MatterThe Nature of Matter p277
Planck’s constant: 6.626 x 10-34 J‧ s
where n is an integer (1, 2, 3….), ν is the
frequency of the electromagnetic radiation
absorbed or emitted.
Einstein suggested that electromagnetic radiation can be
viewed as a stream of “particles”called photons.
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The blue color in fireworks is often achieved by heating
copper(I) chloride (CuCl) to about 1200℃. Then the
compound emits blue light having a wavelength of 450 nm.
What is the increment of energy (the quantum) that is emitted
at 4.50 × 102 nm by CuCl?
P278P278Ex 7.2 The Energy of a Photon
Solution:
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The Photoelectric EffectThe Photoelectric Effect p279
1. Studies in which the frequency of the light is varied show
that no electrons are emitted by a given metal below a
specific threshold frequency ν0.
2. For light with frequency lower than the threshold
frequency, no electrons are emitted regardless of the
intensity of the light.
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3. For light with frequency greater than the
threshold frequency, the number of
electrons emitted increases with the
intensity of the light.
4. For light with frequency greater than the
threshold frequency, the kinetic energy, of
the emitted electrons increases linearly with
the frequency o the light.
The Photoelectric EffectThe Photoelectric Effect
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The Photoelectric EffectThe Photoelectric Effect
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Compare the wavelength for an electron (mass = 9.11 ×
10-31 kg) traveling at a speed of 1.0 × 107 m/s with that for
a ball (mass = 0.10 kg) traveling at 35 m/s.
P281P281Ex 7.3 Calculations of Wavelength
Solution:
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Pickle LightPickle Light
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77--33 The Atomic StructureThe Atomic Structureof Hydrogenof Hydrogen p284
Figure 7.6 (a) A continuous spectrum containing all wavelengths ofvisible light (indicated by the initial letters of the colors of therainbow). (b) the hydrogen line spectrum contains only a few discretewavelength.
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Emits a photon of lightEmits a photon of light
Figure 7.7A change between two discrete energy levelsemits a photon of light.
p285
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The Line Spectrum of HydrogenThe Line Spectrum of Hydrogen
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77--44 The Bohr ModelThe Bohr Model p285
a. In 1013, a Danish physicist named Niels Bohr (1885-1962),
aware o the experimental results we have just discussed,
developed a quantum model for the hydrogen atom.
b. Bohr proposed that the electron in hydrogen atom moves
around the nucleus only in certain allowed circular orbits.
c. He calculated the radii for these allowed orbits by using the
theories of classical physics and by making some new
assumptions.
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p285
Wavelength
Line spectrum
Figure 7.8
Electronic Transitions in the Bohr Model forElectronic Transitions in the Bohr Model forthe Hydrogen Atomthe Hydrogen Atom
Electronic transitions in the Bohr model for the hydrogen atom. (a)An energy-level diagram for electronic transitions. (b) an orbit-transition diagram, which accounts for the experimental spectrum.(Note that the orbits shown are schematic. They are not drawn toscale.) (c) The resulting line spectrum on a photographic plate. Notethat the lines in the visible region of the spectrum correspond totransitions from higher levels to the n = 2 level.
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Electronic Transitions in the BohrElectronic Transitions in the BohrModel for the Hydrogen AtomModel for the Hydrogen Atom
p285
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The most important equation to come from BohrThe most important equation to come from Bohr’’s models modelis the expression for the energy levels available to theis the expression for the energy levels available to theelectron in the hydrogen atom.electron in the hydrogen atom.
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(7.1)
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Ex 7.4Ex 7.4 Energy Quantization inEnergy Quantization inHydrogenHydrogen
P287P287
Calculate the energy requires to excite the hydrogen electronfrom level n = 1 level to level n = 2. Also calculate thewavelength of light that must be absorbed by a hydrogenatom in its ground state to reach this excited state.Solution:
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A typical aerial shell used in fireworks displays. TimeA typical aerial shell used in fireworks displays. Time--delayed fuses cause a shell to explode in stages. Indelayed fuses cause a shell to explode in stages. Inthis case a red starburst occurs first, followed by athis case a red starburst occurs first, followed by ablue starburst, and finally a flash and loud report.blue starburst, and finally a flash and loud report.
p288
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fireworksfireworks
p289
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Ex 7.5Ex 7.5 Electron EnergiesElectron Energies
Calculate the energy required to remove the
electron from a hydrogen atom in its ground state.
P290P290
Solution
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77--55 The Quantum MechanicalThe Quantum MechanicalModel of the AtomModel of the Atom
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Figure 7.9
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Wave function: is a function of coordinates (x, y, and z)Wave function: is a function of coordinates (x, y, and z)
electronelectron’’s position in threes position in three--dimensional space and Hdimensional space and H
represents a set of mathematical instructionrepresents a set of mathematical instruction’’s called ans called an
operator.operator.
p291Quantum Mechanical ModelQuantum Mechanical Model
In this case, the operator contained mathematical terms that
produce the total energy of the atom (the sum of the
potential energy due to the attraction between the proton
and electron and the kinetic energy of the moving electron).
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Quantum Mechanical ModelQuantum Mechanical Model
When this equation is analyzed, many solutions are
found. Each solution consists of a wave function ψ
that is characterized by a particular value of E.
A specific wave function is often called an
orbital.
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Quantum (wave) mechanical modelQuantum (wave) mechanical modelp291
A orbital is not a Bohr orbit.
The wave function gives us no information about
the detailed pathway of the electron.
When we solve problems involving the motions of
particles in macroscopic world, we are able to
predict their pathways.
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Heisenberg uncertainty principleHeisenberg uncertainty principle p291
There is a fundamental limitation to just how
we can know both the position and
momentum of a particle at a given time.
Stated mathematically, the uncertainty
principle is
Δx . Δ (m v) ≧ h /(4π)
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The physical meaning of a Wave FunctionThe physical meaning of a Wave Function p292
The square of the wave function is most conveniently
represented as a probability distribution , in which the
intensity of color is used to indicate the probability value
near a given point on space.
The probability distribution for the hydrogen 1s wave
function (orbital) is shown in Fig. 7.11(a).
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The physical meaning of a Wave FunctionThe physical meaning of a Wave Function
The more times the electrons visits a particular point,
the darker the negative becomes.
This diagram is also known as an electron density
map; electron density and electron probability mean
the same thing.
p292
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When the total probability of finding the electronWhen the total probability of finding the electron
in each spherical shell id plotted versus thein each spherical shell id plotted versus the
distance from the nucleus, the plot in Fig. 7.12(b)distance from the nucleus, the plot in Fig. 7.12(b)
is obtained.is obtained.
This graph is called the radialprobability distribution.
p292
(a)
Figure 7.11
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Radial ProbabilityRadial Probability
DistributionDistribution
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77--66 Quantum NumbersQuantum Numbers p293
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Quantum Numbers for the First FourQuantum Numbers for the First Four
Levels ofLevels of OrbitalsOrbitals in the Hydrogen Atomin the Hydrogen Atom
p294
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Ex 7.6Ex 7.6 ElectronElectron SubshellsSubshells
For principle quantum level n = 5, determine the number
of allowed subshells (different values of l), and give the
designation of each.
P294P294
Solution:
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77--77 Orbital Shapes andOrbital Shapes andEnergiesEnergies
p295
Figure 7.13
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The Boundary Surface RepresentationsThe Boundary Surface Representationsof All Three 2of All Three 2pp OrbitalsOrbitals
p296
Figure 7.14
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A Summary of the Hydrogen AtomA Summary of the Hydrogen Atomp296
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77--88 Electron Spin andElectron Spin and PauliPauliPrinciplePrinciple
p296
The Boundary Surfaces of All of the 3d Orbitals
Figure 7.16
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p297
Figure 7.17 Representation of the 4Representation of the 4ff oorbitalsrbitals inin tterms oferms of
ttheirheir bboundaryoundary ssurfacesurfaces..
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Orbital energy levelsOrbital energy levelsfor the hydrogen atomfor the hydrogen atom
Figure 7.18
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77--99 PolyelectronicPolyelectronic AtomsAtoms p298
Figure 7.19
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Consider the sodium atom,Consider the sodium atom,which has 11 electrons.which has 11 electrons.
p298
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A Comparison of the RadialA Comparison of the RadialProbability Distributions ofProbability Distributions ofthe 2the 2ss and 2and 2pp OrbitalsOrbitals
p299
Figure 7.20A comparison of the radial probabilitydistributions of the 2s and 2p orbitals.
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The Radial ProbabilityThe Radial ProbabilityDistribution of the 3Distribution of the 3ss OrbitalOrbital
p299
Figure 7.21 (a)
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A Comparison of the RadialA Comparison of the RadialProbability Distributions ofProbability Distributions ofthe 3the 3ss,, 33pp, and 3, and 3dd OrbitalsOrbitals
p299
Figure 7.21 (b)
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11ss OrbitalOrbital
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22ppxx OrbitalOrbital
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22ppyy OrbitalOrbital
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22ppzz OrbitalOrbital
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OrbitalOrbital2 23x y
d
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33ddxyxy OrbitalOrbital
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33ddxzxz OrbitalOrbital
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33ddyzyz OrbitalOrbital
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3d3dzz22 OrbitalOrbital
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77--1010 The History of TheThe History of ThePeriodic TablePeriodic Table
p299
Figure 7.22The orders of the energies of the orbitals in thefirst three levels of polyelectronic atoms.
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77--1111 TheThe AufbauAufbau Principle andPrinciple andPeriodic TablePeriodic Table
p302
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p304
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The electron configurationsThe electron configurationsp304
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Orbital EnergiesOrbital Energies
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The electron configuration ofThe electron configuration oftransition metalstransition metals
p305
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Electron configurations forElectron configurations forpotassium through krypton.potassium through krypton.
p306
Figure 7.26Electron configurations for potassium through krypton. The transitionmetals (scandium through zinc) have the general configuration[Ar]4s24dn, except for chromium and copper.
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TheThe OrbitalsOrbitals Being Filled for ElementsBeing Filled for Elementsin Various Parts of the Periodic Tablein Various Parts of the Periodic Table
p306
Figure 7.27
The orbitals being filled for electrons in various parts of theperiodic table. Note that in going along a horizontal row (aperiod), the (n + 1)s orbital fills before the nd orbital. Thegroup labels indicate the number of valence electrons (nsplus np electrons) foe the elements in each group.
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The periodic table with atomicThe periodic table with atomicsymbols, atomic numbers, andsymbols, atomic numbers, andpartial electron configurations.partial electron configurations.
p307
Figure 7.28
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Ex 7.7Ex 7.7 Electron ConfigurationsElectron ConfigurationsGive the electron configurations for sulfur (S), cadmium
(Cd), hafnium (Hf), and radium (Ra) using the periodic
table inside the front cover of this book.
P308P308
Solution:
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p308
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77--1212 Periodic Trends in AtomicPeriodic Trends in AtomicPropertiesProperties
Ionization Energy
p309
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First Ionization EnergiesFirst Ionization Energiesp310
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The Values of First IonizationThe Values of First Ionization
Energy for the Elements in theEnergy for the Elements in the
First Six PeriodsFirst Six Periods
p310
Figure 7.30
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Trends in IonizationTrends in Ionization
Energies(kJ/mol) for theEnergies(kJ/mol) for the
Representative elements.Representative elements.
Figure 7.31
p311
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The first ionization energy for phosphorus is 1060
KJ/mol, and that for sulfur is 1005 KJ/mol. Why?
P311P311
Ex 7.8 Trends in Ionization Energies
Solution:
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Consider atoms with the following electron
configurations:1s22s22p6;1s22s22p63s1;1s22s22p63s2
Which atom has the largest first ionization energy, and
which one has the smallest second ionization energy?
Explain your choices.
P311P311Ex 7.9 Ionization Energies
Solution:
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Ex 7.9 (continuous)Ex 7.9 (continuous) p312
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Atomic Radius of a MetalAtomic Radius of a Metal
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Atomic Radius of a NonmetalAtomic Radius of a Nonmetal
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Electron AffinityElectron Affinityp312
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Electron Affinities of the HalogensElectron Affinities of the Halogensp313
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Ex 7.10Ex 7.10 Trends in RadiiTrends in Radii
Predict the trend in radius for the following ions: Be+,
Mg2+, Ca2+, and Sr2+.
p313p313
Solution:
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Atomic Radii for Selected AtomsAtomic Radii for Selected Atoms p313
Figure 7.34
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77--1313 The Properties of aThe Properties of aGroup: The Alkali MetalGroup: The Alkali Metal
p314
Figure 7.35
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Special Names for groupsSpecial Names for groups
in the Periodic Tablein the Periodic Tablep315
Figure 7.35
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The Alkali MetalsThe Alkali Metals p316
2Na(s) + Cl2(g) → 2NaCl(s)
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Typical reactions for theTypical reactions for thenonmetal with alkali metalsnonmetal with alkali metals
p317
Potassium reacts violently with water.
The expected trend in reducingability: Cs > Rb > K > Na > Li
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Hydration Energies for Alkali IonsHydration Energies for Alkali Ionsp318
2M(s) + 2H2O(l) → H2(g) + 2M+ + 2OH-(aq) + energy