ModernModern

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?

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

Blackbody Radiation

DefinitionA body that absorbs all incoming radiation and then emits radiation based only on its temperature.

Example• Sun

Ultraviolet Catastrophe

DefinitionContradiction between the prediction of classical physics and experimental data for blackbody radiation.

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

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?

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.

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.

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

Work FunctionThreshold Frequency

The minimum frequency of incident radiation (photons) at which electrons are ejected from a metal.

Symbol – ft Units – Hz

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)

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

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?

Photoelectric Effect Equation

Equation 

KE = E – W

KE = kinetic energy of the ejected electrons.E = energy of incident photonW = work function

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.

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?

Early Greeks - Aristotle

The early Greeks thought all matter was composed of four elements.

Earthly ElementsEarthWaterFireAir

Heavenly ElementQuintessence

Democritus 460-370 BC

Things are made up of extremely small particles called atoms. Atoms cannot break or be destroyed and they last forever.

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.

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.

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

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.

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

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

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

Types of Spectra

Continuous Spectrum

Produced by a glowing hot solid.

The filament in a incandescent light

is a heated, glowing piece of

metal..

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.

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.

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)

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

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)

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.

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.

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.

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.

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?

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.

Models of the Atom

Niels Bohr – Bohr Model

Ground State

• Lowest (deepest) energy level.• Closest to the nucleus.

Models of the Atom

Niels Bohr – Bohr Model

Excited State

• Elevated to an energy level above ground state.• Moved away from the nucleus.

Models of the Atom

Niels Bohr – Bohr Model

Equation (Hydrogen ONLY)

21

nn

EE

E1 = Ground state energyEn = Excited state energyn = Energy level number

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

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

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?

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

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?

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

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?

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

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?

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

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.

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

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

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?

De Broglie and Bohr Model

The orbital circumference must be an integral multiple of the electron’s wavelength.

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.

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.

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