Chapter seven:Chapter seven:

Atomic Structure andAtomic Structure andPeriodicityPeriodicity

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p274Contents

77--11 Electromagnetic RadiationElectromagnetic Radiationp275

Wave length

Frequency

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The NatureThe Nature

of Wavesof Waves

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Figure 7.1

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.

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:

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

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

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.

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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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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

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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)

Ex 7.4Ex 7.4 Energy Quantization inEnergy Quantization inHydrogenHydrogen

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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.

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fireworksfireworks

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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.

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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.

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(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

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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

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Figure 7.13

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The Boundary Surface RepresentationsThe Boundary Surface Representationsof All Three 2of All Three 2pp OrbitalsOrbitals

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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

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The Boundary Surfaces of All of the 3d Orbitals

Figure 7.16

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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

Consider the sodium atom,Consider the sodium atom,which has 11 electrons.which has 11 electrons.

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A Comparison of the RadialA Comparison of the RadialProbability Distributions ofProbability Distributions ofthe 2the 2ss and 2and 2pp OrbitalsOrbitals

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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

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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

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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

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Figure 7.22The orders of the energies of the orbitals in thefirst three levels of polyelectronic atoms.

77--1111 TheThe AufbauAufbau Principle andPrinciple andPeriodic TablePeriodic Table

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The electron configurationsThe electron configurationsp304

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Orbital EnergiesOrbital Energies

The electron configuration ofThe electron configuration oftransition metalstransition metals

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Electron configurations forElectron configurations forpotassium through krypton.potassium through krypton.

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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

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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.

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Figure 7.28

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

77--1212 Periodic Trends in AtomicPeriodic Trends in AtomicPropertiesProperties

Ionization Energy

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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

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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

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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:

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

Electron AffinityElectron Affinityp312

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Electron Affinities of the HalogensElectron Affinities of the Halogensp313

Ex 7.10Ex 7.10 Trends in RadiiTrends in Radii

Predict the trend in radius for the following ions: Be+,

Mg2+, Ca2+, and Sr2+.

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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

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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)

Typical reactions for theTypical reactions for thenonmetal with alkali metalsnonmetal with alkali metals

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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