The ElectronicThe ElectronicStructure of AtomsStructure of Atoms

Chapter VII

Do Do you seeyou see………… the the Ideas around you Ideas around you ??????

From clasicalphysics toquantum

theoryChapter VIIVII-I

Is Light a Wave or a Particle?

• 1690 Christian Huygens claimed that lightwas a wave.

• 1704 Isaac Newton claimed light was aparticle whose motion was governed byhis Laws of Motion.

Chapter VIIVII-I

Electromagnetic Waves

• Recall that moving chargescreate magnetic fields andmagnetic fields induce electriccurrents.

• An E-M waves are selfsustaining electric andmagnetic fields.

• Speed of light (c) invacuum C = 3 x 108 m/s

Maxwell (1873), proposed that visible light consists ofelectromagnetic waves.

Electromagnetic radiation is the emission and transmission ofenergy in the form of electromagnetic waves.

All electromagnetic radiationλ x ν = c Chapter VIIVII-I

ELECTROMAGNETICELECTROMAGNETICRADIATIONRADIATION

Electromagnetic wave• A wave of energy having a frequency

within the electromagnetic spectrumand propagated as a periodicdisturbance of the electromagnetic fieldwhen an electric charge oscillates oraccelerates.

Chapter VIIVII-I

Electromagnetic Radiation

E l e c t r o m a g n e t i cwave:

•wavelength

•frequency

•amplitude

Chapter VIIVII-I

VII-I Chapter VII

wavelength Visible light

wavelength

Ultaviolet radiation

Amplitude

Node

Wavelength (λ) is the distance between identical points on successive waves.

Amplitude is the vertical distance from the midline of a wave to the peak ortrough.

Properties of Waves

Frequency (ν) is the number of waves that pass through a particular point in 1second (Hz = 1 cycle/s).

The speed (u) of the wave = λ x ν Chapter VIIVII-I

Electromagnetic Radiation

νλ= c

where ν => frequency

λ => wavelength

c => speed of light

•• Waves have a frequencyWaves have a frequency•• Use the Greek letter Use the Greek letter ““nunu””, , νν, for frequency, and units are, for frequency, and units are

““cycles per seccycles per sec””•• All radiation: All radiation: λλ •• νν = c = c

where c = velocity of light = 3.00 x 10where c = velocity of light = 3.00 x 1088 m/sec m/sec

Chapter VIIVII-I

Electromagnetic Radiation

E = hc/λ

where E => energy

h => Planck's constant

c => speed of light λ => wavelength

Chapter VIIVII-I

Photons

The quantum of electromagneticenergy, generally regarded as adiscrete particle having zeromass, no electric charge, and anindefinitely long lifetime.

Chapter VIIVII-I

λ x ν = cλ = c/νλ = 3.00 x 108 m/s / 6.0 x 104 Hz λ = 5.0 x 103 m

Radio wave

A photon has a frequency of 6.0 x 104 Hz. Convertthis frequency into wavelength (nm). Does this frequencyfall in the visible region?

λ = 5.0 x 1012 nm

λ

ν

Chapter VIIVII-I

Max Planck (1858-1947)

• Resolved the problem in1900.

• Energy is not continuous.

• Energy is quantized isdiscrete packets.

• Each packet has aspecific amount ofenergy.

• E = hf h = 6.63x10-34 J-s

• Quantum physics wasborn.

Chapter VIIVII-I

Mystery #1, “Black Body Problem”Solved by Planck in 1900

Energy (light) is emitted orabsorbed in discrete units(quantum).

E = h x νPlanck’s constant (h)h = 6.63 x 10-34 J•s

Chapter VIIVII-I

Chapter VII

Photoelectric Effect

VII-II

Light has both:1. wave nature2. particle nature

hν = KE + W

Mystery #2, “Photoelectric Effect”Solved by Einstein in 1905

Photon is a “particle” of light

KE = hν -W

hν

KE e-

Chapter VII

E = hν

VII-II

The Photoelectric Effect• In the late 1800’s it was

observed that electronswere emitted by certainmetals when certainmetals were exposed tolight.

• If light were a wave itwould take time for thewave to transmit itsenergy to the electrons.

• However, it was observedthat the electron wasinstantly emitted.

• Shorter wavelength lightejected higher energyelectrons. Chapter VIIVII-II

The Photoelectric Effect

• In 1905 Albert Einsteinused Planck’s quantizedenergy to explain thephotoelectric effect.

• Light was quantized inpackets of energy hecalled photons.

• Therefore, only photonswith high enough energycould knock electrons outof an atom.

• E = hf

Chapter VIIVII-II

Photoelectric Effect

• the emission of electrons by substances,especially metals, when light falls on theirsurfaces.

Chapter VIIVII-II

E = h x ν

E = 6.63 x 10-34 (J•s) x 3.00 x 10 8 (m/s) / 0.154 x 10-9 (m)

E = 1.29 x 10 -15 J

E = h x c / λ

When copper is bombarded with high-energy electrons,X rays are emitted. Calculate the energy (in joules)associated with the photons if the wavelength of the Xrays is 0.154 nm.

Chapter VIIVII-II

Bohr’s theory of the hydrogen Atom

VII-III Chapter VII

Atomic Line EmissionAtomic Line EmissionSpectra and Spectra and Niels Niels BohrBohr

BohrBohr’’s greatest contribution tos greatest contribution toscience was in building ascience was in building asimple model of the atom. Itsimple model of the atom. Itwas based on anwas based on anunderstanding of theunderstanding of the LINELINEEMISSION SPECTRAEMISSION SPECTRA ofofexcited atoms.excited atoms.

•• Problem is that the modelProblem is that the modelonly works for Honly works for H

Niels Niels BohrBohr

(1885-1962)(1885-1962)

VII-III Chapter VII

1. e- can only have specific(quantized) energyvalues

2. light is emitted as e-

moves from one energylevel to a lower energylevel

Bohr’s Model ofthe Atom (1913)

En = -RH( )1n2

n (principal quantum number) = 1,2,3,…

RH (Rydberg constant) = 2.18 x 10-18JVII-III Chapter VII

Neil Bohr’s Model of Hydrogen(1913)

• Solves problem of whyelectrons to do fall intonucleus.

• Used quantized orbitswith specific energies.

• Electron can only movebetween orbits by gettingor losing the exactamount of energyrequired.

• It could not take fractionalsteps.

Neil Bohr’s Model of Hydrogen

• Bohr’s model alsoexplained Kirchhoff’sLaws of Spectroscopy.

• Absorption spectraproduced when electronabsorbed energy neededto go to a higher orbit.

• Emission spectraproduced when electronreleases energy anddrops to a lower orbit.

Explains:Quantized energyHydrogen spectra (only)

E = hν

E = hν

7.3VII-III

Ephoton = ΔE = Ef - Ei

Ef = -RH ( )1n2

f

Ei = -RH ( )1n2

i

i f

ΔE = RH( )1n2

1n2

nf = 1

ni = 2

nf = 1

ni = 3

nf = 2

ni = 3

When a photon is emitted:ni > nf

When a photon is absorbedni<nf

VII-III

Ephoton = 2.18 x 10-18 J x (1/25 - 1/9)

Ephoton = ΔE = -1.55 x 10-19 J

λ = 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J

λ = 1280 nm

Calculate the wavelength (in nm) of a photonemitted by a hydrogen atom when its electrondrops from the n = 5 state to the n = 3 state.

Ephoton = h x c / λ

λ = h x c / Ephoton

i f

ΔE = RH ( )1n2

1n2Ephoton =

VII-III

Photons

The quantum of electromagnetic energy,generally regarded as a discrete particlehaving zero mass, no electric charge, andan indefinitely long lifetime.

VII-III

Line Spectrum

A spectrum produced by a luminous gas orvapor and appearing as distinct linescharacteristic of the various elementsconstituting the gas.

VII-III

Emission Spectrum

The spectrum of bright lines, bands, orcontinuous radiation characteristic of anddetermined by a specific emittingsubstance subjected to a specific kind ofexcitation.

VII-III

Ground State

The state ofleast possibleenergy in aphysicalsystem, as ofelementaryparticles. Alsocalled groundlevel.

Excited State

Being at anenergy levelhigher than theground state.

VII-III

Photons

Line Spectrum

Emission Spectrum

Ground State

Excited State

VII-III

Absorption & Emission Spectra

• Bohr’s model alsoexplained Kirchhoff’sLaws of Spectroscopy.

• Emission spectraproduced when electronreleases energy anddrops to a lower orbit.

• Absorption spectraproduced when electronabsorbed energy neededto go to a higher orbit.

Bohr’s Hydrogen Atom

Hydrogen Energy Level Diagram

• Energy levels constructedbased on spectral linesobserved for Hydrogen.

• The Spectrum ofHydrogen is like a verymagnified view of theelectron energy levelsaround the atom.

• WAY COOL!!!!!!!!!!

Emission Line Spectra

Each element has itown unique electronenergy levels withdifferent energyspacing betweeneach level.

Emission Line Spectra

Each element has itown unique electronenergy levels withdifferent energyspacing betweeneach level.

Line Emission Spectrum of Hydrogen Atoms

VII-III

The dual natureof electron

VII-IV

Planck’s Constant

• ΔE = change in energy, in J

• h = Planck’s constant, 6.626 × 10−34 J s

• ν = frequency, in s−1

• λ = wavelength, in m

Transfer of energy is quantized, andTransfer of energy is quantized, andcan only occur in discrete units, calledcan only occur in discrete units, calledquanta.quanta.

VII-IV

Energy and Mass

• Einstein- When a system loses energy, itloses mass

• m = E/c2

• E = energy

• m = mass

• c = speed of light

VII-IV

Energy and Mass

Einstein’s calculations show that photons doexhibit momentum, and are affected by gravity.However, it is important to recognize that thephoton is in no sense a typical particle. Aphoton has mass only in a relativistic sense- ithas no rest mass.

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

VII-IV

Wavelength and Mass- Do allparticles exhibit wave properties?

• λ = wavelength, in m

• h = Planck’s constant, 6.626 × 10−34

J s = kg m2 s−1

• m = mass, in kg

• ν = frequency, in s−1

de de BroglieBroglie’’s s Equation- relates theEquation- relates thewavelength of a particle to itswavelength of a particle to itsmomentum.momentum.

VII-IV

Electromagnetic Radiation

VII-IV

Dual Nature of Light• Energy is quantized. It can be

transferred only in discrete units calledquanta.

• Electromagnetic radiation, which waspreviously though to exhibit only waveproperties, seems to show certaincharacteristics of particulate matter aswell.

VII-IV

Ephoton = 2.18 x 10-18 J x (1/25 - 1/9)

Ephoton = ΔE = -1.55 x 10-19 J

λ = 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J

λ = 1280 nm

Calculate the wavelength (in nm) of a photonemitted by a hydrogen atom when its electrondrops from the n = 5 state to the n = 3 state.

Ephoton = h x c / λ

λ = h x c / Ephoton

i f

ΔE = RH( )1n2

1n2Ephoton =

VII-IV

De Broglie (1924) reasonedthat e- is both particle andwave.

2πr = nλ n=1,2,3,4,…λ = h/mu

u = velocity of e-

m = mass of e-

Why is e- energy quantized?

VII-IV

The Standing Waves Causedby the Vibration of a GuitarString Fastened at Both Ends

The HydrogenElectron Visualized asa Standing WaveAround the Nucleus

λ = h/mu

λ = 6.63 x 10-34 / (2.5 x 10-3 x 15.6)

λ = 1.7 x 10-32 m = 1.7 x 10-23 nm

What is the de Broglie wavelength (in nm)associated with a 2.5 g Ping-Pong balltraveling at 15.6 m/s?

m in kgh in J•s u in (m/s)

VII-IV

Wave models for electron orbitals

QuantumMechanics

VII-V