chapter 7 atomic structure and periodicity. democritus 400 bc greek philosopher suggested atoms used...

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

Copyright © Cengage Learning. All rights

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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

chapter 7 atomic structure and periodicity. democritus 400 bc greek philosopher suggested atoms used...

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