Chapter 38B Chapter 38B -- Quantum PhysicsQuantum PhysicsA PowerPoint Presentation by

Paul E. Tippens, Professor of Physics

Southern Polytechnic State University

A PowerPoint Presentation byA PowerPoint Presentation by

Paul E. Tippens, Professor of PhysicsPaul E. Tippens, Professor of Physics

Southern Polytechnic State UniversitySouthern Polytechnic State University

© 2007

Objectives: Objectives: After completing this After completing this module, you should be able to:module, you should be able to:

•• Discuss the meaning of Discuss the meaning of quantum physicsquantum physics and and PlanckPlanck’’s constants constant for the description of for the description of matter in terms of waves or particles.matter in terms of waves or particles.

•• Demonstrate your understanding of the Demonstrate your understanding of the photoelectric effectphotoelectric effect, the , the stopping potentialstopping potential, , and the and the deBrogliedeBroglie wavelengthwavelength..

•• Explain and solve problems similar to those Explain and solve problems similar to those presented in this unit.presented in this unit.

PlankPlank’’s Constants ConstantIn his studies of blackIn his studies of black--body radiation, Maxwell body radiation, Maxwell Planck discovered that electromagnetic energy is Planck discovered that electromagnetic energy is emitted or absorbed in discrete quantities.emitted or absorbed in discrete quantities.

Planck’s Equation:

E = hf (h = 6.626 x 10-34 J s)

Apparently, light consists of tiny bundles of energy called photons, each having a well- defined quantum of energy.

Apparently, light consists of Apparently, light consists of tiny bundles of energy called tiny bundles of energy called photonsphotons, each having a well, each having a well-- defined defined quantumquantum of energy.of energy. E = hf

Photon

Energy in ElectronEnergy in Electron--voltsvoltsPhoton energies are so small that the energy is Photon energies are so small that the energy is better expressed in terms of the better expressed in terms of the electronelectron--voltvolt..

One electron-volt (eV) is the energy of an electron when accelerated through a potential difference of one volt.

One One electron-volt (eV) is the energy of an is the energy of an electron when accelerated through a potential electron when accelerated through a potential difference of one volt.difference of one volt.

1 eV = 1.60 x 10-19 J 1 keV = 1.6 x 10-16 J

1 MeV = 1.6 x 10-13 J

Example 1:Example 1: What is the energy of a photon of What is the energy of a photon of yellowyellow--green light (green light (

= 555 nm= 555 nm)?)?

First we find First we find f f from wave equation: from wave equation: c = f

; c hcf E hf

34 8

-9

(6.626 x 10 J s)(3 x 10 m/s)555 x 10 m

E

E = 3.58 x 10-19 JE = 3.58 x 10-19 J E = 2.24 eVE = 2.24 eVOrOr

Since 1 Since 1 eVeV = 1.60 x 10= 1.60 x 10--1919 JJ

Useful Energy ConversionUseful Energy ConversionSince light is often described by its wavelength in Since light is often described by its wavelength in nanometers (nm)nanometers (nm) and its energy and its energy E E is given in is given in eVeV, a , a conversion formula is useful. (1 nm = 1 x 10conversion formula is useful. (1 nm = 1 x 10--99 m)m)

-19(in Joules) ; 1 eV 1.60 x 10 JhcE

9

-19

(1 x 10 nm/m)(in eV)(1.6 x 10 J/eV)hcE

If If is inis in nmnm, the energy in, the energy in eVeV is found from:is found from:

1240E

Verify the answer Verify the answer in Example 1 . . .in Example 1 . . .

The PhotoThe Photo--Electric EffectElectric Effect

When light shines on When light shines on the cathode the cathode CC of a of a photocell, electrons are photocell, electrons are ejected from ejected from AA and and attracted by the positive attracted by the positive potential due to battery.potential due to battery.

Cathode AnodeIncident light

Ammeter++-- A

AC

There is a certain threshold energy, called the work function W, that must be overcome before any electrons can be emitted.

There is a certain There is a certain thresholdthreshold energy, called the energy, called the work function Wwork function W, that must be overcome , that must be overcome beforebefore anyany electrons can be emitted.electrons can be emitted.

PhotoPhoto--Electric EquationElectric Equation

Cathode AnodeIncident light

Ammeter++-- A

AC

The conservation of energy demands that the energy of the incoming light hc/ be equal to the work function W of the surface plus the kinetic energy ½mv2 of the emitted electrons.

The The conservation of energyconservation of energy demands that the demands that the energy of the incoming light energy of the incoming light hc/hc/ be equal to the be equal to the work function work function W W of the surface plus the kinetic of the surface plus the kinetic energy energy ½mv2 of the emitted electrons.of the emitted electrons.

212

hcE W mv

0

hcW

Threshold wavelength

Example 2:Example 2: The threshold wavelength of light The threshold wavelength of light for a given surface is for a given surface is 600 nm600 nm. What is the . What is the kinetic energy of emitted electrons if light of kinetic energy of emitted electrons if light of wavelength wavelength 450 nm450 nm shines on the metal?shines on the metal?

A

= 600 nmhc W K

0

hc hc K

0

1240 1240450 nm 600 nm

hc hcK

; K; K = 2.76 = 2.76 eVeV –– 2.07 2.07 eVeV

K = 0.690 eVK = 0.690 eV OrOr K = 1.10 x 10-19 JK = 1.10 x 10-19 J

Stopping PotentialStopping Potential

A

Cathode AnodeIncident light

Potentiometer++ --

V

A potentiometer is used A potentiometer is used to vary to the voltage to vary to the voltage V V between the electrodes.between the electrodes.

KKmaxmax = = eVeVoo

0E hf W eV Photoelectric equation:Photoelectric equation:

The stopping potential The stopping potential is that voltage is that voltage VVoo that that just stops the emission just stops the emission of electrons, and thus of electrons, and thus equals their original K.E.equals their original K.E.

0h WV fe e

Slope of a Straight Line (Review)Slope of a Straight Line (Review)The general equation for The general equation for a straight line is:a straight line is:

y = mx + by = mx + b

The The xx--interceptintercept xxoo occurs occurs when line crosses when line crosses xx axis axis or when or when y = 0y = 0. .

The slope of the line is The slope of the line is the rise over the run:the rise over the run:

ySlope mx

xo x

y

The slope of a line:

yx

Slope

Finding PlanckFinding Planck’’s Constant, hs Constant, hUsing the apparatus on the previous slide, we Using the apparatus on the previous slide, we determine the stopping potential for a number determine the stopping potential for a number of incident light frequencies, then plot a graph.of incident light frequencies, then plot a graph.

Note that the xNote that the x--intercept intercept ffoo is the is the threshold frequency.threshold frequency.

0h WV fe e

hSlopee

fo

Stopping potential

Frequency

V

Finding h constant

yx

Slope

Example 3:Example 3: In an experiment to determine In an experiment to determine PlanckPlanck’’s constant, a plot of stopping potential s constant, a plot of stopping potential versus frequency is made. The slope of the versus frequency is made. The slope of the curve is curve is 4.13 x 104.13 x 10--1515 V/HzV/Hz. What is Planck. What is Planck’’s s constant?constant?

fo

Stopping potential

Frequency

V

yx

Slope0

h WV fe e

-154.13 x 10 V/HzhSlopee

h = eh = e(slope) = (1.6 x 10(slope) = (1.6 x 10--1919C)(4.13 x 10C)(4.13 x 10--1515 V/Hz) V/Hz)

Experimental Planck’s h = 6.61 x 10-34 J/HzExperimental Planck’s h = 6.61 x 10-34 J/Hz

Example 4:Example 4: The threshold frequency for a given The threshold frequency for a given surface is surface is 1.09 x 101.09 x 1015 15 HzHz. What is the stopping . What is the stopping potential for incident light whose photon energy potential for incident light whose photon energy is is 8.48 x 108.48 x 10--19 19 JJ? ?

0E hf W eV Photoelectric Equation:Photoelectric Equation:

0 0; eV E W W hf

WW = (6.63 x 10= (6.63 x 10--34 34 Js)(1.09 x 10Js)(1.09 x 1015 15 Hz) =7.20 x 10Hz) =7.20 x 10--19 19 JJ-19 -19 -19

0 8.48 x 10 J 7.20 x 10 J 1.28 x 10 JeV -19

0 -19

1.28 x 10 J1.6 x 10 J

V Stopping potential: Vo = 0.800 V

A

Cathode AnodeIncident light

++ --

V

Total Relativistic EnergyTotal Relativistic EnergyRecall that the formula for the relativistic total Recall that the formula for the relativistic total energy was given by:energy was given by:

Total Energy, E 2 2 20( )E m c p c

For a particle with For a particle with zero zero momentummomentum p p = 0= 0::

A light photon has A light photon has mmoo = 0, but it does = 0, but it does have have momentum momentum pp::

E = moc2

E = pc

Waves and ParticlesWaves and ParticlesWe know that light behaves as both a wave and We know that light behaves as both a wave and a particle. The rest mass of a photon is zero, and a particle. The rest mass of a photon is zero, and its wavelength can be found from momentum.its wavelength can be found from momentum.

hcE pc

hp

Wavelength of a photon:

All objectsAll objects, not just EM waves, have wavelengths , not just EM waves, have wavelengths which can be found from their momentumwhich can be found from their momentum

de Broglie Wavelength:

hmv

Finding Momentum from K.E.Finding Momentum from K.E.In working with particles of momentum In working with particles of momentum p = p = mvmv, , it is often necessary to find the momentum from it is often necessary to find the momentum from the given kinetic energy K. Recall the formulas:the given kinetic energy K. Recall the formulas:

K = K = ½mv2 ; p = mv

mKmK == ½m2v2 = ½p2Multiply first Multiply first Equation by Equation by mm::

Momentum from K: 2p mK

Example 5:Example 5: What is the de Broglie wavelength What is the de Broglie wavelength of a 90of a 90--eV electron? (eV electron? (mmee = 9.1 x 10= 9.1 x 10--3131 kg.) kg.)

-ee-- 90 90 eVeV

Next, we find momentum Next, we find momentum from the kinetic energy:from the kinetic energy: 2p mK

-31 -172(9.1 x 10 kg)(1.44 x 10 J)p

-19-171.6 x 10 J90 eV 1.44 x 10 J

1 eVK

p = p = 5.125.12 x 10x 10--2424 kg m/skg m/s

h hp mv

-34

-24

6.23 x 10 J5.12 x 10 kg m/s

hp

= 0.122 nm

= 0.122 nm

SummarySummary

Planck’s Equation:

E = hf (h = 6.626 x 10-34 J s)

Apparently, light consists of tiny bundles of energy called photons, each having a well- defined quantum of energy.

Apparently, light consists of Apparently, light consists of tiny bundles of energy called tiny bundles of energy called photonsphotons, each having a well, each having a well-- defined defined quantumquantum of energy.of energy. E = hf

Photon

1 eV = 1.60 x 10-19 J

1 keV = 1.6 x 10-16 J 1 MeV = 1.6 x 10-13 J

The Electron-volt:

Summary (Cont.)Summary (Cont.)

If If is inis in nmnm, the energy in, the energy in eVeV is found from:is found from:

1240E

Wavelength in nm; Wavelength in nm;

Energy in Energy in eVeV

Cathode AnodeIncident light

Ammeter++-- A

AC

212

hcE W mv

0

hcW

Threshold wavelength

Summary (Cont.)Summary (Cont.)

A

Cathode AnodeIncident light

Potentiometer

++ --

V

KKmaxmax = = eVeVoo

0h WV fe e

hSlopee

PlanckPlanck’’s Experiment:s Experiment:

fo

Stopping potential

Frequency

V

yx

Slope

Summary (Cont.)Summary (Cont.)

For a particle with For a particle with zero zero momentummomentum p = 0:p = 0:

A light photon has A light photon has mmoo = 0= 0, but it does , but it does have have momentum momentum pp::

E = moc2

E = pc

Quantum physics works for waves or particles:Quantum physics works for waves or particles:Quantum physics works for waves or particles:

hp

Wavelength of a photon:

de Broglie Wavelength:

hmv

CONCLUSION: Chapter 38BCONCLUSION: Chapter 38B Quantum PhysicsQuantum Physics