Atomic Structure and Atomic Structure and PeriodicityPeriodicity

AtomsAtoms

ProtonsProtons

NeutronsNeutrons

ElectronsElectrons

1. Where are the electrons1. Where are the electrons

2. Do they have different energies2. Do they have different energies

07_103

Pro

babi

lity

(R2)

Distance from nucleus (r)

(b)(a)

07_104

Rad

ial p

roba

bilit

y (4

2R

2)

Distance from nucleus (r)

(b)(a)

Electromagnetic Electromagnetic RadiationRadiation

Radiant energy that exhibits Radiant energy that exhibits wavelength-like behavior and wavelength-like behavior and travels through space at the speed travels through space at the speed of light in a vacuum.of light in a vacuum.

07_94

10-12 10-10 10-8 4 x 10-7

Gammarays

X rays Ultraviolet Infrared Microwaves Radio waves

FM Shortwave AM

4 x 10-7

Wavelength in meters

5 x 10-7 6 x 10-7 7 x 10-7

7 x 10-7 10-4 10-2 1 102 104

Vis

ible

WavesWaves

Waves have 3 primary characteristics:Waves have 3 primary characteristics:

1.1. WavelengthWavelength: distance between two peaks : distance between two peaks in a wave.in a wave.

2.2. FrequencyFrequency: number of waves per second : number of waves per second that pass a given point in space.that pass a given point in space.

3.3. SpeedSpeed: speed of light is 2.9979 : speed of light is 2.9979 10 1088 m/s. m/s.

07_93 1 second

= 4 cycles/second = 4 hertz

= 8 cycles/second = 8 hertz

= 16 cycles/second = 16 hertz

Wavelength and frequency can be interconverted.Wavelength and frequency can be interconverted.

= = cc// = frequency (s= frequency (s11))

= wavelength (m)= wavelength (m)

cc = speed of light (m s = speed of light (m s11))

07_94

10-12 10-10 10-8 4 x 10-7

Gammarays

X rays Ultraviolet Infrared Microwaves Radio waves

FM Shortwave AM

4 x 10-7

Wavelength in meters

5 x 10-7 6 x 10-7 7 x 10-7

7 x 10-7 10-4 10-2 1 102 104

Vis

ible

07_101

Unplucked string

1 half-wavelength

2 half-wavelengths

3 half-wavelengths

Standing Waves

Quantization in Nature

Planck’s ConstantPlanck’s Constant

EE = change in energy, in J = change in energy, in J

hh = Planck’s constant, 6.626 = Planck’s constant, 6.626 10 103434 J s J s

= frequency, in s= frequency, in s11

= wavelength, in m= wavelength, in m

E hhc

= =

Transfer of energy is quantized, and can only Transfer of energy is quantized, and can only occur in discrete units, called quanta.occur in discrete units, called quanta.

Energy and MassEnergy and Mass

Energy has massEnergy has mass

EE = = mmcc22

EE = energy = energy

mm = mass = mass

cc = speed of light = speed of light

Energy and MassEnergy and Mass

Ehc

photon =

mhcphoton =

(Hence the (Hence the dualdual nature of light.) nature of light.)

Wavelength and MassWavelength and Mass

= wavelength, in m= wavelength, in m

hh = Planck’s constant, 6.626 = Planck’s constant, 6.626 10 103434 J s = kg m J s = kg m22 s s11

mm = mass, in kg = mass, in kg

= frequency, in s= frequency, in s11

= h

m

de Broglie’s Equationde Broglie’s Equation

Atomic Spectrum of HydrogenAtomic Spectrum of Hydrogen

Continuous spectrumContinuous spectrum: Contains : Contains allall the the wavelengths of light.wavelengths of light.

Line (discrete) spectrumLine (discrete) spectrum: Contains : Contains only only some some of the wavelengths of light.of the wavelengths of light.

07_97

Prism

Slit

Continuousspectrum

Electric arc(white lightsource)

(a)

Prism

Slit

Detector(photographic plate)

Hydrogen gas

(b)

Highvoltage

410 nm 434 nm 486 nm 656 nm

Detector(photographic plate)

Arc

V I B G Y O R

+

-

+

-

The Bohr ModelThe Bohr Model

EE = energy of the levels in the H-atom = energy of the levels in the H-atom

z z = nuclear charge (for H, = nuclear charge (for H, zz = 1) = 1)

nn = an integer = an integer

E = 2.178 10 J (18 2 z n/ )2

The electron in a hydrogen atom moves around the The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.nucleus only in certain allowed circular orbits.

The Bohr ModelThe Bohr Model

Ground StateGround State: The lowest : The lowest possible energy state for an possible energy state for an atom (atom (nn = 1). = 1).

Energy Changes in the Energy Changes in the Hydrogen AtomHydrogen Atom

EE = = EEfinal statefinal state EEinitial stateinitial state

= hcE

Quantum MechanicsQuantum Mechanics

Based on the Based on the wave properties wave properties of the atomof the atom

= wave function= wave function

= mathematical operator= mathematical operator

EE = total energy of the atom = total energy of the atom

A specific wave function is often called an A specific wave function is often called an orbitalorbital..

H E =

H

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple

x mvh

4

xx = position = position

mvmv = momentum = momentum

hh = Planck’s constant = Planck’s constant

The more accurately we know a particle’s The more accurately we know a particle’s position, the less accurately we can know its position, the less accurately we can know its momentum.momentum.

Probability DistributionProbability Distribution

- square of the wave functionsquare of the wave function

- probabilityprobability of finding an electron at a of finding an electron at a given positiongiven position

RadialRadial probability distribution is the probability distribution is the probability distribution in each spherical probability distribution in each spherical shell.shell.

Quantum Numbers (QN)Quantum Numbers (QN)

1.1. Principal QN Principal QN ((nn = 1, 2, 3, . . .) - related to = 1, 2, 3, . . .) - related to sizesize and and energyenergy of the orbital. of the orbital.

2.2. Angular Momentum QN Angular Momentum QN ((ll = 0 to = 0 to nn 1) - relates to 1) - relates to shapeshape of the orbital. of the orbital.

3.3. Magnetic QN Magnetic QN ((mmll = l to = l to l) - relates to l) - relates to orientationorientation

of the orbital in space relative to other orbitals.of the orbital in space relative to other orbitals.

4.4. Electron Spin QN Electron Spin QN ((mmss = += +11//22, , 11//22) - relates to the ) - relates to the

spin states spin states of the electrons.of the electrons.

Pauli Exclusion PrinciplePauli Exclusion Principle

In a given atom, no two electrons can have In a given atom, no two electrons can have the same set of four quantum numbers (the same set of four quantum numbers (nn, , ll, , mmll, , mmss).).

ThereforeTherefore, an orbital can hold only two , an orbital can hold only two electrons, and they must have opposite electrons, and they must have opposite spins.spins.

Aufbau PrincipleAufbau Principle

As protons are added one by one As protons are added one by one to the nucleus to build up the to the nucleus to build up the elements, electrons are similarly elements, electrons are similarly added to these hydrogen-like added to these hydrogen-like orbitals.orbitals.

Hund’s RuleHund’s Rule

The lowest energy configuration The lowest energy configuration for an atom is the one having the for an atom is the one having the maximum number of unpaired maximum number of unpaired electrons electrons allowed by the Pauli allowed by the Pauli principle in a particular set of principle in a particular set of degenerate orbitals.degenerate orbitals.

Valence ElectronsValence Electrons

Atom Valence Electrons

Ca 2

N 5

Br 7

The electrons in the outermost principle The electrons in the outermost principle quantum level of an atom.quantum level of an atom.

Inner electrons are called Inner electrons are called corecore electrons. electrons.

Broad Periodic Table Broad Periodic Table ClassificationsClassifications

Representative Elements Representative Elements (main group): (main group): filling filling ss and and pp orbitals (Na, Al, Ne, O) orbitals (Na, Al, Ne, O)

Transition ElementsTransition Elements: filling : filling dd orbitals (Fe, orbitals (Fe, Co, Ni)Co, Ni)

Lanthanide and Actinide Series Lanthanide and Actinide Series (inner (inner transition elements): filling transition elements): filling 44ff and and 55ff orbitals (Eu, Am, Es)orbitals (Eu, Am, Es)

Ionization EnergyIonization Energy

The quantity of energy The quantity of energy required to remove an electron required to remove an electron from the gaseous atom or ion.from the gaseous atom or ion.

Periodic TrendsPeriodic Trends

First ionization energyFirst ionization energy: :

increases increases from left to right across from left to right across a a periodperiod;;

decreasesdecreases going down a going down a groupgroup..

Electron AffinityElectron Affinity

The energy change associated The energy change associated with the addition of an electron to with the addition of an electron to a gaseous a gaseous atomatom..

X(X(gg) + e) + e X X((gg))

Periodic TrendsPeriodic Trends

Atomic RadiiAtomic Radii::

decreasedecrease going from left to right going from left to right across a across a periodperiod;;

increase increase going down a going down a groupgroup..

Information Contained in the Information Contained in the Periodic TablePeriodic Table

1.1. Each group member has the same valence electron Each group member has the same valence electron configuration (these electrons primarily determine an configuration (these electrons primarily determine an atom’s chemistry).atom’s chemistry).

2.2. The electron configuration of any representative The electron configuration of any representative element.element.

3.3. Certain groups have special names (alkali metals, Certain groups have special names (alkali metals, halogens, etc).halogens, etc).

4.4. Metals and nonmetals are characterized by their Metals and nonmetals are characterized by their chemical and physical properties.chemical and physical properties.