PH 314 Homework Set #4
Spring 2008

Assigned: Monday 04/21/2008

Due: Monday 04/28/2008 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) Krane, Chapter 3, Problem 30.

2) A neutral pi meson with a mass of 135 MeV/c² moving at 0.800c decays into two photons which are not identical: π⁰ → γ₁ + γ₂. The neutral pi meson moves directly to the right, photon one moves up and to the right, photon two moves down and to the right. Photon one has twice as much energy as photon two. (a) What is the angle between the velocities of the two photons? (b) What are the wavelengths of the two photons?

3) What is the de Broglie wavelength of a 7.25-kg bowling ball moving down the lane at 12.5 m/s?

4) Assume that a baseball is perfectly spherical and has a mass of 0.142 kg and a uniform density of 745 kg/m³. At what speed would its de Broglie wavelength equal its radius?

5) While moving through a nanotransistor, an electron has a de Broglie wavelength of 1.25 nm. (a) What is the electron's wave number? (b) What is the magnitude of the electron's momentum? (c) What is the electron's kinetic energy?

6) Krane, Chapter 4, Problem 17