Class 23

Hw QuizA star is 15.6 light years away from Earth. If a spaceship travels at .99 times the speed of light how much time will elapse on the clocks aboard the ship when they reach their destination.?

a. 4.4 y b. 5.4y etc

Black Body Radiation.

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

The prediction of classical physics is that the intensity should go up in an unlimited manner as the wavelength gets shorter, I. e th ultraviolet end of the spectrum.

1.

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

Class 23

Plank's Quantum HypothesisPlank's hypothesis is that the radiant energy cannot take just any value.

Energy can only be radiated as multiples of a fundamental frequency.E=h f

where h is Plank's constant = 6.626∗10−34 J sSo the energy emitted is

E=n h fwhere n is an integer called the quantum number.

2.

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Black Body Radiation.

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

http://www.ux1.eiu.edu/~cfadd/1160/Ch28QM/Black.html

3.

http://www.ux1.eiu.edu/~cfadd/1160/Ch28QM/Black.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

Class 23

If a similar mechanism were to operate with a block sliding down a plane, we would find that the gravitational potential energy could only take on certain quantized values.

4.

Class 23

The Photoelectric EffectSimulation

http://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effect

Graphs

http://www.google.com/imgres?imgurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photef1.gif&imgrefurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photelec.htm&h=266&w=299&sz=4&tbnid=Yf5eTftWFUHQpM:&tbnh=103&tbnw=116&prev=/images%3Fq%3Dphotoelectric%2Beffect%2Bgraph&hl=en&usg=__Vu9KFaWPIQZNC4y_UQIIsbEbKhA=&ei=_hzCS86CLoOClAe627jaBA&sa=X&oi=image_result&resnum=1&ct=image&ved=0CAYQ9QEwAA

The Wave Theory vs Photon Theory

If the light intensity is increased, the number of electrons, and their maximum kinetic energy should increase, because the energy of the light wave is increased.

Increased intensity means more photons, but no increase in the energy of the photons which is determined solely by the wavelength. Therefore the maximum KE of the electrons is not affected by intensity

The wavelength of the light should not affect the maximum KE of the electrons. Max KE should only depend on intensity.

The maximum KE depends on the frequency of the light according to

KE−max=hf −W where W is the work-function of the material. If the frequency of the light is less than

f 0=W 0h

then no electrons are freed no matter

what the intensity.

5.

http://www.google.com/imgres?imgurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photef1.gif&imgrefurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photelec.htm&h=266&w=299&sz=4&tbnid=Yf5eTftWFUHQpM:&tbnh=103&tbnw=116&prev=/images%3Fq%3Dphotoelectric%2Beffect%2Bgraph&hl=en&usg=__Vu9KFaWPIQZNC4y_UQIIsbEbKhA=&ei=_hzCS86CLoOClAe627jaBA&sa=X&oi=image_result&resnum=1&ct=image&ved=0CAYQ9QEwAAhttp://www.google.com/imgres?imgurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photef1.gif&imgrefurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photelec.htm&h=266&w=299&sz=4&tbnid=Yf5eTftWFUHQpM:&tbnh=103&tbnw=116&prev=/images%3Fq%3Dphotoelectric%2Beffect%2Bgraph&hl=en&usg=__Vu9KFaWPIQZNC4y_UQIIsbEbKhA=&ei=_hzCS86CLoOClAe627jaBA&sa=X&oi=image_result&resnum=1&ct=image&ved=0CAYQ9QEwAAhttp://www.google.com/imgres?imgurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photef1.gif&imgrefurl=http://www.cobalt.chem.ucalgary.ca/ziegler/educmat/chm386/rudiment/tourexp/photelec.htm&h=266&w=299&sz=4&tbnid=Yf5eTftWFUHQpM:&tbnh=103&tbnw=116&prev=/images%3Fq%3Dphotoelectric%2Beffect%2Bgraph&hl=en&usg=__Vu9KFaWPIQZNC4y_UQIIsbEbKhA=&ei=_hzCS86CLoOClAe627jaBA&sa=X&oi=image_result&resnum=1&ct=image&ved=0CAYQ9QEwAAhttp://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effecthttp://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effecthttp://phet.colorado.edu/simulations/sims.php?sim=Photoelectric_Effect

Class 23

The plot of the photoelectric effect for a particular material is

The equation for this graph is

KEMAX=hf −W 0The work function of the material is the value of W 0 when the frequency of the light is the smallest frequency which will emit photo electrons.

The experimental data confirmed Einstein's theory and served as a second measurement of Plank's constant.

Clicker Quiz Problem 19

energy of a photon is E=hc=1.24 [eV ]

[m]

The highest energy visible light is 400 nm

6.

Class 23

The Compton Effect

The result is that the scattered photon has a longer wavelength, smaller energy than the incident photon. The difference in the energies of the incident and scattered photon is given by

'= hm0 c1−cos

This effect cannot be explained by the classical wave theory of light. Only a particle theory of light can produce the theory which matches the experimental result.

Pair ProductionThe final possibility of an interaction of a photon with matter is pair production. If a photon of sufficient energy passes close to the nucleus of an atom a spontaneous creation of an electron and a positron occurs.

AntimatterEvery particle in nature has a twin antimatter particle. The antimatter particle twin of an electron is a positron.

7.

Class 23

The election-positron pair do not live long. After a very short time, a few nano-seconds the positron and the electron annihilate each other resulting in the emission of gamma rays.

3 interactions of a Photon with Matter1. Photoelectric effect ---- electron is kicked out of the material and the photon is absorbed

2. Compton effect ----------electron is given a new momentum and the photon energy is decreased.

3. Pair production-----------Photon turns into an electron-positron pair.

The momentum of a photonThe relativistic energy of a photon is all in its kinetic energy since it has zero rest mass

E photon=hf

According to classical theory p=mv , so a photon, which has zero mass, should have zero momentum.

However, according to relativistic theory the massless photon has momentum given by

p= Ec =hfc =

h

Wave-Particle Duality: the Principle of ComplementarityWe have seen that the photoelectric effect, Compton effect, and pair production firmly establish the particle nature of light.

The diffraction and interference effect also establish the light's wave nature.

8.

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Wave Nature of Matter

9.

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Rutherford Scattering

10.

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11.

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not done in 201

12.

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13.

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1=R [ 122− 1n2 ] n = 3,4,.... Balmer series

1=R [ 112− 1n2 ] n = 2, 3, …. Lyman series

1=R [ 132− 1n2 ] n = 4, 5... Paschen series

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The Bohr Model – quantization of angular momentum

The centripetal force is the Coulomb force between the positive nucleus and the negative electron.

Angular moment is assumed to be quantized

L=n h2

This assumption, and some algebra ( pg. 724) yields an expression for the energy levels of an atom

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Class 23

En=−13.6eV Z 2

n2

The hydrogen atomFor hydrogen Z = 1

E2=−13.6eV

4=−3.40eV

E3=−13.6eV

9=−1.51 eV

Note that all the energies are negative meaning that you go up in energy as you go toward large n.

Ionization EnergyThe amount of energy to remove an electron completely from the atom is to go from -13.6eV to zero, or 13.6eV.

16.

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17.

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The Correspondence pricipleWe saw that the equations of special relativity became well approximated by classical equations at speeds much less than the speed of light.

Similarly, the equations of Quantum mechanics become well approximated by classical equations as the dimension become those of the everyday world.

The model of a planetary does not turn out to be a good model. Modern physics sees electrons as “probability clouds” , clouds of probability.

de Broglie's hypothesis applied to atoms

Standing waves in a circle.

You can only fit an integer number of wavelengths in the circle.

18.

Class 23

The circumference must equal an integer number of wavelengths.

2 rn=n

If we add the condition de Broglie's hypothesis,that the wavelength of a quantum particle like an electron is

= hmv deBroglie's hypothesis

we get exactly the quantization condition proposed by Bohr, which explained the spectrum of the hydrogen atom.

We have said that all particles have a wave nature and deBroglie's hypothesis specifies that wavelength.

For a classical particle, the wavelength is so small that it does not have any measurable effects.

Clicker Quiz Ch 27 Prob. 3

Prob 21

Prob. 41

19.

Hw QuizBlack Body Radiation.Plank's Quantum HypothesisBlack Body Radiation.The Photoelectric EffectThe Wave Theory vs Photon Theory

The Compton EffectPair ProductionAntimatter

3 interactions of a Photon with MatterThe momentum of a photonWave-Particle Duality: the Principle of ComplementarityWave Nature of MatterRutherford ScatteringThe Bohr Model – quantization of angular momentumThe hydrogen atomIonization Energy

The Correspondence priciple

de Broglie's hypothesis applied to atomsStanding waves in a circle.