PH 314 Homework Set #6
Spring 2008

Assigned: Monday 05/05/2008

Due: Monday 05/12/2008 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 5, Problem 13.

2) The probability wave function for the first excited state of the harmonic oscillator is where A is the normalization constant and a is another constant. (a) Determine the constant a in terms of the spring constant and the mass of the oscillator. (b) Determine the total energy E of the oscillator in terms of the same two variables.

3) What is the distance of closest approach for an alpha particle moving at 2.50 x 10⁶ m/s directly toward an iron nucleus?

4) Krane, Chapter 6, Problem 11

5) (a) Determine expressions similar to Equation 6.34 on page 191 of Krane for the kinetic and potential energies of the electron in the hydrogen atom. (b) In which quantum state is the electron moving the fastest? (c) In which quantum state does the electron have the greatest amount of potential energy?

6) Repeat problem 5 for ionized helium, which has one electron and two protons. (The number of neutrons is not relevant to this problem.)