chapter 7 atomic structure and periodicity. democritus 400 bc greek philosopher suggested atoms used...
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Chapter 7Chapter 7
Atomic Structure and Periodicity
DemocritusDemocritus400 BC Greek philosopherSuggested atomsUsed intuition
LavoisierLavoisier1700’sQuantitative measurements
John DaltonJohn Dalton1766-1844Atomic theory
Quantum mechanics Quantum mechanics 20th century“New” physics that accounts for
the behavior of light and atoms
7.1 Electromagnetic 7.1 Electromagnetic RadiationRadiation
Wavelength (lambda) – distance between two consecutive crests and troughs
Frequency (nu) – number of waves (cycles) per second that pass a given point (Hertz)
All types of EM radiation travel at the speed of light – c
c = = m x waves/sec = m/s
2.9979 x 10 8 m/s
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Classification of Classification of Electromagnetic RadiationElectromagnetic Radiation
7.2 The Nature of Light7.2 The Nature of Light
1900 Max PlanckStudied radiation of solid bodies
heated to incandescence.
Energy can be lost or gained only in whole number multiples of h.
h = Planck’s constant = 6.626 x 10 -34 J.s
E = nh is the frequency of EM radiationn is a whole numberEnergy is quantized – a discrete
unit of hQuantum is a small “packet” of
energyEnergy has particle propertiesGeneral formula E = h
1879-1955 Albert Einstein1879-1955 Albert Einstein
EM is quantizedEM is stream of “particles” –
photonsEphoton = h= hc/Photoelectric effect
1905 Special Theory of 1905 Special Theory of RelativityRelativityE = mc2
Energy has mass m=E/c2
m=E = hc/ = h c2 c2 c Mass of a photon of wavelength
Depends on wavelengthRest mass is zero
1922 Arthur Compton (American 1922 Arthur Compton (American physicist)physicist)
X rays and electron collisionsDual nature of lightLight has both wave and particle
properties
work
1923 Loius deBroglie (French 1923 Loius deBroglie (French physicist)physicist)
m = h = h c nFor a particle with velocity v
Rearrange to get deBroglie’s equation
= h/mv
This allows us to calculate the wavelength of a particle.
An electron has a wavelength = 7.27 x 10-11 m
Same order as atomic spacing in a typical crystal
1927 Bell labs1927 Bell labs
Electron beams were diffracted Large objects are calculated to
have very small wavelengths. (This is impossible to verify)
Very small objects (photons)
have more wavelike properties.Electrons show both properties.
DiffractionDiffraction– scattering of lightThere is more diffraction when
wavelengths are close to the opening size
Ratio of wavelength to width is 1 or more for a lot of diffraction
Smaller the opening, the more diffraction
A pattern is produced by x-rays on crystals
Light areas show waves are in phase – constructive interference
Dark areas show waves are out of phase – destructive interference
Clinton Joseph Davisson (22 October 1881 – 1 February 1958), was an American physicist. In 1927 while working for Bell Labs he confirmed the De Broglie hypothesis that that all matter has a wave-like nature through the discovery of electron diffraction. He shared the Nobel Prize in Physics in 1937 with George Paget Thomson for the discovery of electron diffraction.
Problems
p.330 # 37 to 49 odd
P. 334 # 121, 122
Text problems on light and Text problems on light and mattermatter
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The Photoelectric EffectThe Photoelectric Effect
Photoelectric effectPhotoelectric effect
Intensity is a measure of the energy present
Metals eject electrons called photoelectrons when light shines on them
Classical explanation – weak light of any wavelength would eventually give an electron enough energy to leave an atom
However:However:
K metal – red light does not work, no matter how intense
Weak yellow light does(ROYGBIV) Einstein – threshold value
E = hf, so if the f is too low, no electrons will leave
Increasing the intensity increases the number of photons striking the metal, so more electrons leave.
Excess energy photons cause the electrons to travel faster.
7.3 Atomic Spectrum of 7.3 Atomic Spectrum of hydrogenhydrogenThompson – electronRutherford – nucleus
H2 + high energy spark some excited H atoms
Atoms can absorb energy from photons or high speed particles, they create photons as they give off energy.
Atoms absorb the same frequency of light they emit
Continuous spectrum Continuous spectrum white light contains all
wavelengths
Emission spectrum Emission spectrum release of excess energy of
various wavelengthssolids, liquids and dense gases
give off light with a continuous spectrum when heated
Line spectrum Line spectrum (click above for (click above for
reference lines)reference lines)
each line corresponds to a particular wavelength
Bright line spectrum – lines of light given off by a gas
“fingerprint”Each line represents a particular
frequency of emitted light.
Absorption spectrum – detect the absorbed light
White light is passed through a gas
Transmitted light is analyzedDark lines are at the same
frequency as the lines in the emission spectrum
Hydrogen atomsHydrogen atomsH – only certain energies are
allowed for the electronsThe energy of the electron is
quantized from Planck’s equationE = hThe change in energy is
proportional to the frequency of light emitted.
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The Line Spectrum of The Line Spectrum of HydrogenHydrogen
Ground state – no extra internal energy Excited state – absorbs energy (4.9 eV is
the smallest amount)
Excess energy is quickly emitted in the form of light. Emission can take place between levels as well as back to the ground state.
A change between two discrete levels emits a photon of light.
UV – Lyman series down to 1Visible – Balmer series down
to 2IR – Paschen series down to 3
Spectroscope – contains a slit that allows a narrow beam of light through. A prism separates the light into its component colors.
A very excited electron completely escapes the atom.
Ionization energyEnergy is too much to be absorbedAn electron is ejected and carries
away any excess energy1st IE is the energy to remove the most
loosely held electron
7.4 Bohr Model7.4 Bohr Model
1913 Niels Bohr (Danish physicist)
Quantum model – electrons move around the nucleus only in certain allowed circular orbits.
Used classical physics and new assumptions.
Classical physicsClassical physics
Newton’s first law – particles in motion continue in motion in a straight line
A centripetal (inward directed) force causes circular motion.
A charged particle under acceleration should radiate energy ( a change in direction is acceleration)
Therefore – the electron should lose energy and fall into the nucleus
Assume: Assume: The tendency to fly off is balanced by
the positively charged nucleus.The angular momentum of the electron
(m x v x radius) can occur only in certain increments
The energy levels available in a hydrogen atom.
E = -2.178 x 10-18 J (Z2 /n2)
N = integer (energy level)Z = nuclear charge
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For a single electron transition from one energy level to another:
ΔE = change in energy of the atom (energy of the emitted photon)
nfinal = integer; final distance from the nucleus
ninitial = integer; initial distance from the nucleus
182 2final initial
1 1 = 2.178 10 J
En n
Negative energy means energy near the nucleus is lower than it would be if the electron were at an infinite distance. At infinity, there is no interaction and therefore no energy.
E = final energy – initial energy
Negative means energy is lost and the electron is more stable.
The energy is carried away by a photon. E = h(c/) or = hc /E (Negative sign is not used here, note that energy
is emitted.)
Bohr’s modelBohr’s model
Model fits the quantized energy levels for H.
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Electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.
Bohr’s model gave hydrogen atom energy levels consistent with the hydrogen emission spectrum.
Ground state – lowest possible energy state (n = 1)
Bohr’s model does not apply to other atoms.
Concluded as fundamentally incorrect.
Current theory is not derived from Bohr.
Electrons do not move in circular orbits.
p. 331 # 53, 59, 61
7.5 The Quantum Mechanical 7.5 The Quantum Mechanical model of the Atommodel of the AtomWerner Heisenberg, Louis deBroglie,
Erwin SchrödingerMid – 1920’s
Schrödinger – emphasize wave properties
Electron behaves as a standing wave
Researched wave mechanical description (standing wave)
Standing wavesStanding wavesNode – zero displacementWhole number of ½ wavelengths
that fit into the standing wave.
Only certain orbits have a circumference that will hold a whole number of wavelengths.
Other sizes produce destructive interference
Relates the total energy of the atom to wave function.
Orbital – a specific wave function, not a circular orbit, we do not know the pathway
Quantum (wave) mechanical Quantum (wave) mechanical modelmodel
Probability depends on radius and volume of the shell.
Away from the nucleus, there are more possible locations.
1s for H = 5.29 x 10-2 nm (matches Bohr’s description)
No distinct sizeProbability never becomes zeroUse radius that encloses 90%
probabilityAn electron “in” a particular orbital
is assumed to exhibit the electron probability as shown by the orbital map
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Probability Distribution for Probability Distribution for the 1the 1ss Wave Function Wave Function
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Radial Probability Radial Probability DistributionDistribution
Heisenberg Uncertainty Heisenberg Uncertainty Principle Principle it is impossible to know exactly
the velocity (momentum) and position of an electron.
If we try to locate an electron by using a small wavelength photon, we can accurately describe the position of the electron, but less precisely know the momentum. If the wavelength is short, the frequency and the energy is high, so we change the momentum of the electron.
If we use a longer wavelength photon, we
are less certain about the position. (There is more diffraction = bending around objects.)
It is like searching in the dark for a ping pong
ball. If you touch it, you change its velocity.
Heisenberg UncertaintyHeisenberg Uncertainty There is a limitation to how precisely we can
know the position and momentum of a particle at the same time.
x . (mv) > h / 4 x is the uncertainty in position mv is the uncertainty in momentum h is Planck’s constant The more accurately we know the position, the
less accurately we know the momentum. (This becomes important for very small objects.)
The square of the wave function indicated the probability of finding an electron near a particular point in space.
Probability distribution (electron density map)
Like a 3-D time exposureMore times it is there, the darker the
image appearsRadial probability distributionTotal probability of finding an electron at
a particular distance.Think 3-D spherical shells
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Relative Orbital SizeRelative Orbital Size
Difficult to define precisely.Orbital is a wave function.Picture an orbital as a three-dimensional
electron density map.Hydrogen 1s orbital:
Radius of the sphere that encloses 90% of the total electron probability.
7.6 Quantum Numbers7.6 Quantum Numbers
Schrödinger’s equation solutions gives many wave functions (orbitals).
Each orbital has quantum numbers that describe its properties.
Principal (n)Principal (n)values are integers 1,2,3…Relates size and energyHigher n – larger orbital and
higher energyElectron is further from the
nucleus and less tightly bound
22ndnd - Angular momentum - Angular momentum (l) values of 0 to n-1Relates the shape of the orbital
(subshell)l =
◦ 0 is s◦1 is p◦2 is d◦3 is f
(derived from spectral studies)
Shapes of orbitalsShapes of orbitals
MagneticMagneticml values from l to –l and
includes zeroRelated to the orientation of the
orbital in space relative to the other orbitals
SpinSpin
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Quantum Numbers for the First Four Levels of Orbitals in Quantum Numbers for the First Four Levels of Orbitals in the Hydrogen Atomthe Hydrogen Atom
ProblemsProblemsP. 332 # 69, 70, 75
7.7 Orbital shapes and 7.7 Orbital shapes and energiesenergiesS is sphericalSurfaces get larger as n
increasesNumber of nodes = n-1Nodal surfaces are areas of zero
probability
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11ss Orbital Orbital
p orbitals p orbitals are two lobes separated by a
node at the nucleusLabeled by axis on the xyz
coordinate system2px lies along the x axis
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22ppxx Orbital Orbital
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22ppyy Orbital Orbital
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22ppzz Orbital Orbital
d orbitals d orbitals start at level 3There are five shapesFour have 4 lobes centered in the
plane dxy, dyz, dxz, and dx
2y2
The fifth shape is unique
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33ddxx22--yy22 OrbitalOrbital
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33ddxyxy Orbital Orbital
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33ddxzxz Orbital Orbital
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Orbital Orbital 23zd
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33ddyzyz Orbital Orbital
f orbitals f orbitals are more complexNot involved in the bonding of
most compounds
Meaning of s,p,d,fMeaning of s,p,d,fThese letters were chosen to
describe the emission spectrum lines as seen in a spectrograph
s = sharpp = principled = diffusef = fine
Bohr model Bohr model energies of the orbitals are
determined by the n value. All orbits with the same n value have the same energy, are degenerate
Ground state – lowest energy levelExcited – can move to allowed orbits if
energy is added
7.8 Electron Spin and Pauli 7.8 Electron Spin and Pauli PrinciplePrinciple
Developed by Samuel Gaudsmith and George Uhlenbeck – graduate students at the University of Leyden in the Netherlands
4th quantum number – necessary to account for the emission spectrum in an external magnetic field
A spinning charge produces a magnetic moment. (torque) They assumed two spin states with oppositely directed magnetic moments.
ms is the electron spin and it has values of +/- ½
Wolfgang Pauli – Pauli Wolfgang Pauli – Pauli Exclusion PrincipleExclusion PrincipleIn a given atom, no two electrons can
have the same set of four quantum numbers.
An orbital can hold only two electrons and they must have opposite spins.
7.9 Poly electronic Atoms7.9 Poly electronic Atoms
KE of electronsPE of nucleus and electron
attractionPE of repulsion between electrons
Schrödinger equation cannot be solved directly because pathways are not known, so repulsions are not known exactly.
There was an electron correlation problem.
Approximate results using field of charge that is the net result of the nuclear attraction and the average repulsion of the other electrons.
Electron is not bound as tightly as it would if it were alone
Electrons are ‘screened’ or “shielded” from the nuclear charge by the repulsion of the other electrons
Hydrogen-like orbitals, same general shape, but size and energy are different
Results in orbitals that are not degenerate
Ens< Enp< End <Enf
“Bumps” in radial probability profiles shows the electron spends some time closer to the nucleus.
If an electron is able to penetrate the shielding electrons, it is lower in energy.
s fills before d due to penetration near the nucleus – lower energy
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Penetration EffectPenetration Effect
A 2s electron penetrates to the nucleus more than one in the 2p orbital.
This causes an electron in a 2s orbital to be attracted to the nucleus more strongly than an electron in a 2p orbital.
Thus, the 2s orbital is lower in energy than the 2p orbitals in a polyelectronic atom.
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Orbital EnergiesOrbital Energies
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A Comparison of the Radial Probability Distributions of A Comparison of the Radial Probability Distributions of the 2the 2ss and 2 and 2pp Orbitals Orbitals
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The Radial Probability The Radial Probability Distribution of the 3Distribution of the 3ss Orbital Orbital
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A Comparison of the Radial Probability Distributions of A Comparison of the Radial Probability Distributions of the 3the 3ss,, 33pp, and 3, and 3dd Orbitals Orbitals
LanthanidesLanthanides14 elements after La lanthanum[Xe] 6s25d1
Fill 4f sublevelSometimes one electron occupies
5d instead since their energies are similar
ActinidesActinides14 after actinium[Rn] 7s26d1
Fill 5f orbitalsSometimes one or two electrons
occupy 6d first due to similar energy
“A” groups tell the number of valence electrons
Main group or representative elements Period number gives the highest occupied
energy level Use the diagonal rule or periodic table to
predict electron configurations As short hand, you can use the preceding
noble gas, and then add any additional electrons.
7-10 History of the Periodic 7-10 History of the Periodic TableTable
Represents patterns observed in the chemical properties of elements
Greeks – earth, air, fire, water Johann Dobereiner – triadsGroups of three elements with
similar propertiesEx. Cl, Br, I
John Newlands 1864 – octavesRepeating properties every
eighth element like a musical scale
Julius Meyer, Dmitri MendeleevPeriodic table like the current
modelMendeleev corrected formulas
based on incorrect assumptions and generally emphasized the usefulness of the table.
7.11 The Aufbau Principle 7.11 The Aufbau Principle and the Periodic Tableand the Periodic TableAufbau Principle – building upAs protons are added to the nucleus,
electrons are added to hydrogen-like orbitals. Assume all atoms have the same type of orbitals described for the hydrogen atoms.
Ex. All p orbitals have the same energy (degenerate)
Hund’s Rule Hund’s Rule
F. H. HundThe lowest energy configuration
for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli Principle in a particular set of degenerate orbitals. (Unpaired are represented with parallel spins with spin “up”.)
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Orbital DiagramOrbital Diagram
A notation that shows how many electrons an atom has in each of its occupied electron orbitals.
Oxygen: 1s22s22p4 Oxygen: 1s 2s 2p
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Valence ElectronsValence Electrons
The electrons in the outermost principal quantum level of an atom.
1s22s22p6 (valence electrons = 8)The elements in the same group on the
periodic table have the same valence electron configuration.
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The Orbitals Being Filled for Elements in Various Parts of The Orbitals Being Filled for Elements in Various Parts of the Periodic Tablethe Periodic Table
7.12 Periodic Trends in 7.12 Periodic Trends in Atomic PropertiesAtomic PropertiesIonization energy – energy
required to remove an electron from a gaseous atom or ion (in the ground state)
1st ionization energy – highest energy electron (the one least tightly bound) is removed first
Ionization EnergyIonization EnergyEnergy required to remove an electron
from a gaseous atom or ion. X(g) → X+(g) + e–
Mg → Mg+ + e– I1 = 735 kJ/mol(1st IE)
Mg+ → Mg2+ + e– I2 = 1445 kJ/mol(2nd IE)
Mg2+ → Mg3+ + e– I3 = 7730 kJ/mol*(3rd IE)
*Core electrons are bound much more tightly than valence electrons.
2nd ionization energy is always higher
Remove an electron from an ionElectrons are more tightly held
Core electrons are bound more tightly than valence electrons – large jump in IE
General increase across a periodElectrons are in the same energy levelDo not completely shield the nuclear
charge caused by additional electronsGeneral decrease down a groupThe electrons being removed are
further from the nucleus
Exceptions to the trend:Exceptions to the trend:Be B 2s shield for 2pN O extra repulsion due to 2e’s in
a p orbital
If there two electrons are in an orbital, there are e-e repulsions.
Core electrons are shielded from the nuclear charge. (Filled and half-filled sublevels are more stable than other configurations.)
Electron AffinityElectron AffinityEnergy change associated with the
addition of an electron to a gaseous atom. (exothermic is negative in this text.)
Generally become more negative across a period.
(Those values shown are stable, isolated, negative ions.)
If addition causes extra repulsion, it is unstable.
Nuclear charge may overcome repulsion.Generally more positive down a group.Changes are small, many exceptions.
Electron affinityElectron affinity
Atomic RadiusAtomic Radius
Covalent atomic radii – distance between atoms in covalent bonds (diatomic)
Metallic radii – half the distance
between metal atoms in solid crystals (noble gases are estimated)
When atoms form bonds, electrons clouds interpenetrate (space filling).
Decrease across a period.Due to increase in nuclear chargeResults in decreased shieldingValance electrons drawn closer
Atomic Radius of a MetalAtomic Radius of a Metal
Atomic Radius of a Atomic Radius of a NonmetalNonmetal
ProblemsProblemsP. 333 # 99, 101, 107, 109
7.13 The Properties of a 7.13 The Properties of a Group - Group - Alkali Alkali MetalsMetalsGroups exhibit similar chemical
propertiesProperties change in a regular
wayThe number and type of valance
electrons determine an atom’s chemistry
Metals are on the leftTend to lose electronsMP, density, and BP trends
Nonmetals are found on the right.
They form anionsThey have large IEUpper right are the most active.
Metalloids or semimetals – elements along the division line.
1A Alkali metals2A Alkaline EarthB Transition metals7A Halogens8A noble Gases
Chapter 7 Exercise WS Chapter 7 Exercise WS AnswersAnswers2. a. 3.33 x 10-14m
b. 2.39 x 10-38
3. 6.82 x 10-8 m
4. 1.3 x 106 J
5. a. 4.47 x 1014 Hz
b. 2.96 x 10-19 J, 178 kJ
6. 29.6 nm
7.a. IR
b. 5 x 10-6 m
c. 3.98 x 10-20 J / 24 kJ
d. less
8. 3.49 x 10 -20 J
9. 21 kJ
10. energy is proportional to frequency
11. c.
12. Probability decreases but never becomes zero.
13. 487 nm
14.a. K+, Ar, Cl-, S2-
b. F, C, Si, Al
c. Ar, P, Mg, Na
d. Ba+2, Cs+, Xe, I-
15. a. C, Ge
b. Cl+, Cl-
16. 1.5 x 10 23 atoms
17 On next page
18. Same valence electrons
19. X = Br
20. a. 2, b. 1, c. 0, d. 5, e. 1, f. 4, g. 0
17. B atomic number 5 17. B atomic number 5 1s1s22 2s 2s22 2p 2p11
n l m s1 0 0 + ½1 0 0 - ½2 0 0 + ½
2 0 0 - ½2 1 -1 + ½