PH 314 Homework Set #3
Spring 2008

Assigned: Monday 04/14/2008

Due: Monday 04/21/2008 3:00 PM

When writing a solution, you must explain carefully and concisely, and demonstrate that you understand. When writing in English, you must use complete sentences. (A complete sentence has both a subject and a predicate.) When writing in mathematics, you must use complete equations. (A complete equation has a right-hand-side, an equal sign and a left-hand-side). When grading the homework and exams, the points awarded will be broken down into three main categories: 1) translate (translating the problem from English sentences to mathematical equations, drawing a diagram and explicitly converting prefixes), 2) equate (identifying the relevant relationships between the physical quantities) and 3) solve (using algebra, geometry, trigonometry and/or calculus to solve for the unknown quantity or quantities.) For full credit, the answer must include the units and three significant digits. The answer itself is only worth 10 to 20% of the points. How well you write down how you got the answer is worth 80 to 90% of the points.

1) The rms speed of a collection of ten ions at high temperature is 2.50 x 10⁶ m/s. Ions one through five move at 2.40 x 10⁶ m/s and ions six through nine move at 2.55 x 10⁶ m/s. At what speed does the tenth ion move? Give your answer in m/s.

2) Two sources emit identical light waves that have wavelengths of 2.00 nm and are initially in-phase. One source is located at (x, y) = (0, 0) and the other is located at (0, 5.00 nm). Find all points along the positive x-axis where constructive interference will occur.

3) (a) At what rate are photons emitted by a 3.50 mW laser if their wavelength is 645 nm? Give your answer in photons/sec. (b) The light from the same laser forms a cylindrical beam 3.25 mm in diameter. What is the intensity of the laser beam? Give your answer in W/m².

4) Light emitted from a distant star is collected in an astronomer's telescope and undergoes spectral analysis. It is found that the maximum intensity occurs at a wavelength of 125 nm, which is in the ultraviolet part of the electromagnetic spectrum. Assume the star emits light as a blackbody and determine its surface temperature in kelvin.

5) A photon scatters off a proton which is initially at rest. (a) What is the maximum change in the wavelength of the photon? (b) If the photon's final velocity is perpendicular to its initial velocity, then what is the change in the wavelength of the photon?

6) Initially, there are two photons with the same frequency and wavelength moving directly toward each other. They collide and annihilate. In their place, an electron-positron pair is produced. The electron and positron have the same mass. (a) What is the maximum wavelength of the photons for this to occur? (b) If the electron and positron move at one-half the speed of light after being produced, then what was the wavelength of the photons?