modern. light – wave or particle evidence supporting wave nature of light reflection refraction...
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ModernModern
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Light – Wave or Particle
Evidence Supporting Wave Nature of Light• Reflection• Refraction• Diffraction• InterferenceWhere did we observe these phenomena?
• PolarizationWhere did we observe this phenomena?
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Light – Wave or Particle
Evidence Supporting Particle Nature of LightPhysics had yet to explain the following as of 1900: • Blackbody Radiation
Absorption and Emission of Energy • Photoelectric Effect
Photoemission of Electrons
• Atomic SpectraCharacteristic Color Pattern
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Blackbody Radiation
DefinitionA body that absorbs all incoming radiation and then emits radiation based only on its temperature.
Example• Sun
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Ultraviolet Catastrophe
DefinitionContradiction between the prediction of classical physics and experimental data for blackbody radiation.
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Energy is Quantized
DefinitionEnergy comes in DISCRETE units called quanta (photons). (Birth of Quantum Mechanics)
Equation (Max Planck)
E = hfE = energyh = Planck’s constant
4.14 X 10-15 eVsf = frequency of photon
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Example #1
Human skin emits radiation at a peak value of = 8.23 m.
What’s the frequency of this radiation?
What type of electromagnetic waves are these?
How much energy is carried by one quantum of these electromagnetic waves?
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Photoelectric EffectClassical Physics vs. Experimental Evidence
Classical
Physics Experimental
Evidence
Occurs almost instantaneously above a certain frequency.
The kinetic energy of ejected electrons depends on
At low intensities,electron ejection …
Whether electrons are ejected depends on…
The frequency of the light.
Takes time.
The intensity of the light.
The intensity of the light.
The frequency of the light.
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Photoelectric EffectClassical vs. Experimental Evidence
• These observations support light being a particle rather than a wave. Explain.
• It requires that electromagnetic energy be quantized as Max Planck proposed earlier in his explanation of blackbody radiation. Explain
• Albert Einstein extended Planck’s quantized energy to a stream of photons.
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Work FunctionDefinition
The minimum amount of energy required for an electron to escape from a metal.
The value of the work function depends ONLY on the metal.
Symbol – W (work function)Units – eV
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Work FunctionThreshold Frequency
The minimum frequency of incident radiation (photons) at which electrons are ejected from a metal.
Symbol – ft Units – Hz
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Work FunctionThreshold Wavelength
The maximum wavelength of incident radiation in which electrons are ejected from a metal.
Symbol - λt
Units – m (usually expressed in nm)
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Work FunctionEquation
The energy of the incident radiation (photons) must be greater than or equal to that of the work function for the ejection of electrons to take place.
W = hft
W = work functionh = Planck’s constantft = threshold freqency
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Example #2
The threshold wavelength of sodium is 5.45 X 10-7 m. What’s the threshold frequency of sodium? What’s the work function of sodium in electron volts? What’s the kinetic energy of the ejected electrons if the incident photon has a wavelength of 5.45 X 10-7 m?
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Photoelectric Effect Equation
Equation
KE = E – W
KE = kinetic energy of the ejected electrons.E = energy of incident photonW = work function
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Example #3
Three different colors of light are focused onto the surface of potassium, W = 2.0 eV. The wavelengths of the different colors are: red, 700 nm; green, 550 nm; violet, 400 nm.
Complete the chart in your lecture notes.
Interactive Spreadsheet.
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Example #3Which color(s) eject electrons?
Which color(s) eject electrons with the greatest energy?
What’s the relationship between the energy of the incident photon, the work function and the ejection of electrons?
What’s the relationship between the frequency of the incident photon, threshold frequency and the ejection of electrons?
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Early Greeks - Aristotle
The early Greeks thought all matter was composed of four elements.
Earthly ElementsEarthWaterFireAir
Heavenly ElementQuintessence
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Democritus 460-370 BC
Things are made up of extremely small particles called atoms. Atoms cannot break or be destroyed and they last forever.
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John Dalton 1766-1844
Everything is made of atoms, small hard spheres.
Atoms can not be subdivided, created, destroyed.
Atoms combine to make compounds.
Chemical reactions occur when atoms combine.
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Models of the Atom
J.J. Thomson – Plum Pudding Model
If you’re not familiar with plum pudding think of the atom as a chocolate chip cookie.• Atom is electrically
neutral.• The positive material is
the pudding or cookie.• The negative material is
the plums or chocolate chips.
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Models of the Atom
Earnest Rutherford – Planetary ModelDescription• Nucleus at the center
(like the sun)• Nucleus contains all the
positive charge• Electrons in circular
orbits around nucleus (like the planets)
• Electrons contain all the negative charge
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Models of the Atom
Earnest Rutherford – Planetary ModelGold Foil Experiment
Screen
Alpha Source
Gold Foil
Experimental Results• Some deflected
through large angles.• Indications of a large
positive charge.• Some bounced
back.• Indications of a dense
nucleus.
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Models of the Atom
Earnest Rutherford – Planetary ModelProblems• Rutherford’s model didn’t explain atomic
absorption & emission spectrum.• Another issue: Electrons in circular orbits
– Must experience centripetal acceleration– Accelerated charges emit radiation– Radiation is energy– So electrons must lose energy over time– Eventually electrons should fall into nucleus
• So this model predicted an unstable atom
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Models of the Atom
Earnest Rutherford – Planetary ModelPoetry and Science
The Secret SitsRobert Frost
We dance round in a ring and suppose,
But the Secret sits in the middle and knows
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Types of Spectra
How are Spectra Produced?
Spectra are produced by the absorption or emission of photonic energy.
Types of Spectra• Continuous• Bright-Line or Emission• Dark-Line or Absorption
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Types of Spectra
Continuous Spectrum
Produced by a glowing hot solid.
The filament in a incandescent light
is a heated, glowing piece of
metal..
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Types of Spectra
Bright-Line or Emission Spectrum
Produced by a hot gas.
The light produced by a laser is due to electrons being raised to higher energy
levels, then dropping down after emitting photons.
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Types of Spectra
Dark-Line or Absorption Spectrum
Produced by a cool gas intervening between you and a hot solid
The cooler gas absorbs photons of specific wavelengths from the light as it passes through.
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Types of Spectra
Comparison
The absorption spectrum is a “photo-negative” of the emission spectrum
Dark lines (gaps) appear in precisely the same location as corresponding bright lines from the emission spectrum of the same gas.
Dark line (absorption)
Bright line (emission)
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Models of the Atom
Niels Bohr – Bohr Model
Description• The electrons only move in “stationary orbits”.• Only certain orbits are stable (so only certain
orbits are “permitted”). • In these orbits, electrons do not emit radiation.• Electrons can move “up” and “down” between
orbits.• He didn’t say how it was possible! • Based his postulates on evidence from
absorption and emission spectra
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Models of the Atom
Niels Bohr – Bohr ModelTransitions – Jumping Rules• Radiation is absorbed when an electron jumps “up” from a lower orbit to a higher orbit.
• Radiation is emitted when an electron falls “down” from a higher orbit to a lower orbit.
• Electrons can only jump between orbits (energy levels), can’t land in between (quantum idea)
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Models of the Atom
Niels Bohr – Bohr Model
Transitions – Bright-Line Spectra• Electrons falling toward
nucleus require a photon to be emitted
• Explains Bright-Line spectra.
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Models of the Atom
Niels Bohr – Bohr Model
Transitions – Dark-Line Spectra• Electrons jumping away
from nucleus require a photon to be absorbed
• Explains Dark-Line spectra.
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Models of the Atom
Niels Bohr – Bohr Model
Mathematical Description• Recall that spectra are unique.• Spectra are the result of electron transitions
between energy/orbital levels.• Energy/orbital levels are unique.
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Models of the Atom
Niels Bohr – Bohr Model
Mathematical Description
• Nucleus has positive charge, and electrons have negative charge.
• So the electrons have NEGATIVE ENERGY compared to free electrons.
• Like falling into a well: When you are below ground level, you have negative gravitational potential energy.
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Models of the Atom
Niels Bohr – Bohr Model
Mathematical Description
• The closer to the nucleus (the farther below ground level) the larger the negative potential energy.
• The farther from the nucleus (the closer to ground level) the smaller the negative potential energy.
• When is the energy equal to zero?
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Models of the Atom
Niels Bohr – Bohr Model
Energy Levels and Energy Level Numbers
• Energy levels are negative.• Negative electric potential energy.• “n” is Bohr’s principle quantum number or
energy level number.• Numbered from nucleus outward.
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Models of the Atom
Niels Bohr – Bohr Model
Ground State
• Lowest (deepest) energy level.• Closest to the nucleus.
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Models of the Atom
Niels Bohr – Bohr Model
Excited State
• Elevated to an energy level above ground state.• Moved away from the nucleus.
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Models of the Atom
Niels Bohr – Bohr Model
Equation (Hydrogen ONLY)
21
nn
EE
E1 = Ground state energyEn = Excited state energyn = Energy level number
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Example #4Using Bohr’s energy level equation for hydrogen, complete the energy level diagram.
En
erg
y (e
V)
En
erg
y L
evel
Nu
mb
ers2
1n
n
EE
E1 = -13.6 eV
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Hydrogen Energy Levels
En
erg
y (e
V)
En
erg
y L
evel
Nu
mb
ers
-13.6
-3.4
-1.5
-0.85-0.54
0.0
E1
E2
E3
E4
E5
Ionization
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Example #4
A photon with an energy of 11.15 eV enters a hydrogen atom in the ground state. Will it be absorbed by the atom? If yes, to what energy level does the electron rise?
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Hydrogen Energy Levels
En
erg
y (e
V)
En
erg
y L
evel
Nu
mb
ers
-13.6
-3.4
-1.5
-0.85-0.54
0.0
E1
E2
E3
E4
E5
Ionization
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Example #4
A hydrogen atom is in an excited state that has an energy of –1.50 eV. It absorbs a photon that raises it to the next higher energy level. What’s the energy of the photon? What’s the frequency of the photon?
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Hydrogen Energy Levels
En
erg
y (e
V)
En
erg
y L
evel
Nu
mb
ers
-13.6
-3.4
-1.5
-0.85-0.54
0.0
E1
E2
E3
E4
E5
Ionization
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Example #4
A hydrogen atom is in an excited state at the E2 energy level. How much energy would be needed to ionize the atom? How much energy would be released if the electron dropped down to E1?
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Hydrogen Energy Levels
En
erg
y (e
V)
En
erg
y L
evel
Nu
mb
ers
-13.6
-3.4
-1.5
-0.85-0.54
0.0
E1
E2
E3
E4
E5
Ionization
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Example #4
A hydrogen atom is an excited state when it energy level is 12.10 eV above the ground state. A photon of energy 0.961 eV strikes the hydrogen atom and is absorbed by it. To what energy level is the hydrogen atom raised?
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Hydrogen Energy Levels
En
erg
y (e
V)
En
erg
y L
evel
Nu
mb
ers
-13.6
-3.4
-1.5
-0.85-0.54
0.0
E1
E2
E3
E4
E5
Ionization
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Models of the Atom
Niels Bohr – Bohr Model
Problems with the Bohr Model
• Assumed electrons did not radiate energy. No explanation.
• Why certain energy levels are allowed and others are not. No explanation.
• Radically new ideas.
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Duality of Light
Light – Wave or Particle
PhenomenonCan be explainedin terms of particles
Reflection
Refraction
Interference
Diffraction
Polarization
PhotoelectricEffect
Can be explained in terms of waves
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Matter Waves- Louis De Broglie
QuestionIf light (wave) can behave like a particle can a particle behave like a wave?
DerivationDerive De Broglie wave equation.
p
h= wavelength
h = Planck’s constant in joulesp = momentum
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Example #5
The De Broglie wavelength of an electron is traveling at 1x106 m/s is 7.3x10-10 m. What is the de Broglie wavelength of a particle with 4 times the mass of an electron traveling at the same speed?
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De Broglie and Bohr Model
The orbital circumference must be an integral multiple of the electron’s wavelength.
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Heisenberg’s Uncertainty Principle
It is impossible to know simultaneously both the position and momentum of an object.
By measuring the position of an electron, we increase the uncertainty of the momentum. Vice-Versa for momentum and position.
By measuring something we are affecting it.
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Quantum Cloud Model-Schrodinger
Finite # of solutions • Quantized energy levels• Defines probability of finding an electronSchrodinger’s Cat• A cat is in a steel box. If a nucleus decays, the cat is killed by poison.
• Both states, dead cat – live cat exist until we open the box to check.
• Curiosity can kill the cat.
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Schrödinger Model
Electron Cloud• Orbitals replaced with Electron Cloud• Probability of finding an electron in a
given region of space.• 4 probability shapes
s p d f