Chapter 34 Photons
This chapter begins a transition to Modern Physics. As technology for investigating matter and radiation improved in the latter 1800’s. It was noted that Classical Physics could not explain some experimental results: the emission of certain wavelengths of light from hot gases, the spectrum of light emitted by a blackbody, and the ejection of electrons from a metal by light (the photoelectric effect). This chapter will show how the model of light as a localized package of energy (photon) can be used to explain some of these experimental results.
page 2 Blackbody Radiation
A hot object will emit light at all wavelengths. This is called a continuous spectrum since there is energy present at all wavelengths. A thin, hot, gas emits an emission spectrum that has energy only at selected wavelengths.
*What is a "blackbody?"
Does a "blackbody" always appear to be a black color?
For a blackbody, the wavelength that has the highest intensity (joules/sec/square meters) changes as the temperature of the object changes. This result is summarized by Wien’s Law
Wavelength that has the highest intensity = 2.898 millimeters/T T is the temperature in Kelvins
Calculate the wavelength of the peak intensity for light emitted by your body.
Figure 1 shows the experimental intensity distribution vs. wavelength for a blackbody. The dotted line shows the prediction from Classical Physics. This mismatch is called the "Ultraviolet Catastrophe." Why did this disturb physicists?
page 3 There is a second important difference in the intensity distribution of a blackbody as the temperature is changed. The total energy/second emitted is proportional to the fourth power of the temperature in Kelvin. Suppose that you have two identical blackbodies. Suppose that at a later time temperature of one of the blackbodies doubles. Describe the ratio of the energy emitted per second for the two objects.
Why does the book refer to the 10,000K star as a "blue" star and the 4000K star as a "red" star?
page 4 Planck Blackbody Radiation Law
Max Planck was able to find, by trial and error, a mathematical equation that fit the experimental intensity distribution for a blackbody. After he found the equation he sought to develop a theoretical derivation of the formula. Planck was able to derive the formula if he assumed that the electrons did not emit or absorb light at all possible values of energy but instead emitted or absorbed energy in packages that had a value of energy:
E = hf h is Planck’s constant, f is the frequency of the light
The packets of energy are called quanta.
page 5 The Photoelectric Effect
In 1887 it was noticed that light can enhance the electrical effects in a metal. It is easier to create a spark between two metal rods if light is shining on the negative electrode. A negatively charged electroscope will discharge more rapidly if light is shining on the metal.
Detailed investigations of the Photoelectric Effect showed that
1) when electrons are ejected a brighter light will eject more electrons
2) if the wavelength of light is too large (red) no electrons are ejected
3) there is almost no time delay between the time the light is turned on and the first electron
4) the maximum Kinetic Energy of the electrons is proportional to the frequency of the light.
Classical Physics can only explain observation #1.
Einstein was awarded the 1921 Nobel Prize for his explanation, in 1905, of the Photoelectric Effect.
Einstein’s explanation claims that light is a photon, not a wave, when it interacts with matter. The energy of the photon is E = hf. Einstein’s Photoelectric formula is
KE (max of electron) = hf – W
W is the "work function" of the electron. W describes how tightly the surface electrons are held to the metal.
page 8 Planck’s Constant h
6.64 E-34 Joule-seconds
The value of h can be found using the photoelectric effect. What should be measured to determine h?
It is worth noting that h has the dimensions of angular momentum. This will be important in a future chapter.
page 9 Photon Energies
E=hf c = wavelength * f
We will do some calculations for the Photoelectric Effect.
The work function for Zinc is about 3.1 eV. Calculate the wavelength of light needed to eject an electron from Zinc with a KE of 0 Joules.
page 11 Particles and Waves
What questions do you have on Exercise 8?
What portion of the electromagnetic spectrum exhibits primarily a particle nature for light?
What portion of the electromagnetic spectrum exhibits primarily a wave nature for light?
page 12 Photon Mass
What is the mass of a photon? (Does the question need more explanation?)
How does light differ from matter?
How does the calculation of the energy of a photon differ from the calculation of the kinetic energy of an object?
The neutrino is a particle produced in certain nuclear reactions that has a low probability of interacting with matter. The neutrino does have a small rest mass.
page 13 Photon Momentum
In the previous semester we calculated the linear momentum of a particle using p = mv. Even though the photon does not have a rest mass it does carry momentum. The momentum of a photon is found by combining E = m c-squared with E = hf. The result is momentum = h/wavelength.
Calculate the momentum for a photon of red light.
page 14 In the Compton effect a photon has an elastic collision with an electron. It was observed in 1923 that the photon leaves the collision with a longer wavelength than it had before the collision, and an electron leaves the collision site with kinetic energy. What is your explanation for this result?
In what way does Classical Physics fail to correctly explain the Compton Effect?
page 15 Another way to understand the expansion to the Red Giant state of a star is that the higher temperature of the core leads to more gas pressure on the inside of the star. This increased internal pressure dominates over gravity until the star expands and cools its atmosphere.
The scientific theories of the Big Bang indicate that light played a dominate role in the early universe. Until the universe expanded and cooled, the collisions of light and particles prevented the formation of atoms of hydrogen and helium, not to mention larger objects. After the universe cooled atoms formed. The atoms were more transparent to light (less interactions) and the light "decoupled" from matter.
page 16 Antimatter Start by looking at Figure 7. This photograph is a record of tracks of subatomic particles. The V-shaped tracks show the path of an ordinary electron and a positron (the antimatter electron). There is a magnetic field passing through the region where the particles are moving. By looking at the paths of the two objects describe the charge on the positron.
The equations of Quantum Mechanics predict the existence of antimatter. The general concepts of this prediction are given on page 16. What questions do you have on the material on this page?
page 17 When matter and antimatter of the same type get near each other the mass is totally converted to energy (light). This energy release is enough to allow the starship Enterprise to travel at warp speeds J .
How can antimatter be stored for long periods of time?
Is there much antimatter on the earth? … in our solar system? …. in our galaxy? …. in the universe?
page 18 Interaction of Photons and Gravity
I will give one bonus point to the first person to send me email with a correction to a fact listed in the first column on this page.
Photons do interact with the gravitational field. What would be the gravitational effect on the wavelength of a photon that is leaving the surface of a star and headed towards the earth?
page 19 What does gravitational lensing have to do with the interaction of photons with the gravitational field?
page 20 Why do astronomers believe that the four images in Figure 9 are all related to one, distant, quasar?
page 21 Evolution of the Universe
We have already discussed Hubble’s Law and the expansion of the universe.
page 22 Another View of Blackbody Radiation We will skip this page.
page 23 Models of the Universe
Geologists calculate that the earth is over 4 billion years old. Astronomers calculate that the sun is about 5 billion years old. How is it possible that the sun has been shining that long? (What is the power source for the sun?)
pages 24 – 25 We will skip this.
page 26 - 28 The Big Bang Model What is the evidence supporting the Big Bang?
Copyright© 2001 - 2006 by Greg Clements Permission is granted to reproduce this document as long as 1) this copyright notice is included, 2) no charge above photocopy costs is made, and, 3) the use is for an educational purpose. Editing of the document to suit your own class style and purposes is allowed.