solutions 03

# Modern Physics

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PHY251 Homework Set 3 Reading: Chapter 4 Homework: Chapter 4, Questions 3,5,7 Problems 2,8,13,16,32 Hints and Solutions Note: SHOW ALL WORK! Question IV.3 How would you estimate the temperature of a red-hot piece of steel, given that the wavelength of red light is in the neighborhood of 700 nm? What assumption would you have to make for your estimate? Hints: How do you know that the red wavelength is a maximum, and not a tail of the distribution in the visible part of the spectrum? Solution: If it were the tail of a shorter wavelength distribution, the color would be more yellow-blue; it could, however, be the high-end tail of the distribution, with a maximum at the near infrared; the radiation would be weaker ("dull-red") and the temperature would be somewhat less. Assuming we indeed see the maximum at λ = 700 nm, the temperature is simply derived from: λ max · T = 2.9×10 -3 m·K; T = 2.9×10 -3 m·K / 700 nm = 4.1×10 3 K. Question IV.5 Suppose you have a source that emits a beam of light at some frequency f that impinges on a metal plate. What happens to the energy of the photoelectrons that are emitted when you are moving the source closer to the plate? Hints: What happens to the frequency when the source approaches the observer (electron)? Solution: The Doppler effect will make the photon's frequency to the electrons a bit higher, and therefore more energetic. The photoelectrons are thus slightly more energetic on average.

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