Homework Problems

For some of these homework problems, you may find it convenient to refer to the diagram of the electromagnetic spectrum shown in section 6.4 of Electricity and Magnetism.
1	Give a numerical comparison of the number of photons per second emitted by a hundred-watt FM radio transmitter and a hundred-watt lightbulb.	√
2	Two different flashes of light each have the same energy. One consists of photons with a wavelength of 600 nm, the other 400 nm. If the number of photons in the 600-nm flash is 3.0×1018, how many photons are in the 400-nm flash?	√
3	When light is reflected from a mirror, perhaps only 80% of the energy comes back. The rest is converted to heat. One could try to explain this in two different ways: (1) 80% of the photons are reflected, or (2) all the photons are reflected, but each loses 20% of its energy. Based on your everyday knowledge about mirrors, how can you tell which interpretation is correct?	[Based on a problem from PSSC Physics.]
4	Suppose we want to build an electronic light sensor using an apparatus like the one described in the section on the photoelectric effect. How would its ability to detect different parts of the spectrum depend on the type of metal used in the capacitor plates?
5	The photoelectric effect can occur not just for metal cathodes but for any substance, including living tissue. Ionization of DNA molecules can cause cancer or birth defects. If the energy required to ionize DNA is on the same order of magnitude as the energy required to produce the photoelectric effect in a metal, which of these types of electromagnetic waves might pose such a hazard? Explain. 60 Hz waves from power lines 100 MHz FM radio microwaves from a microwave oven visible light ultra violet light x-rays
6	The beam of a 100-W overhead projector covers an area of 1 m × 1 m when it hits the screen 3 m away. Estimate the number of photons that are in flight at any given time. (Since this is only an estimate, we can ignore the fact that the beam is not parallel.)
7	The two diffraction patterns were made by sending a flash of light through the same double slit. Give a numerical comparison of the amounts of energy in the two flashes.	√
8	Three of the four graphs are properly normalized to represent single photons. Which one isn't? Explain.
9	Photon Fred has a greater energy than photon Ginger. For each of the following quantities, explain whether Fred's value of that quantity is greater than Ginger's, less than Ginger's, or equal to Ginger's. If there is no way to tell, explain why. frequency speed wavelength period electric field strength magnetic field strength
10	Give experimental evidence to disprove the following interpretation of wave-particle duality: A photon is really a particle, but it travels along a wavy path, like a zigzag with rounded corners. Cite a specific, real experiment.
11	In the photoelectric effect, electrons are observed with virtually no time delay (∼ 10 ns), even when the light source is very weak. (A weak light source does however only produce a small number of ejected electrons.) The purpose of this problem is to show that the lack of a significant time delay contradicted the classical wave theory of light, so throughout this problem you should put yourself in the shoes of a classical physicist and pretend you don't know about photons at all. At that time, it was thought that the electron might have a radius on the order of 10-15 m. (Recent experiments have shown that if the electron has any finite size at all, it is far smaller.) (a) Estimate the power that would be soaked up by a single electron in a beam of light with an intensity of 1 mW/m2. (b) The energy, W, required for the electron to escape through the surface of the cathode is on the order of 10-19 J. Find how long it would take the electron to absorb this amount of energy, and explain why your result constitutes strong evidence that there is something wrong with the classical theory.