Name                                                                                                                                  

                                  Modern Physics Final                           150

                                                          10 May 2007, 11:00 AM

 

You are only required to do 5 out of the 6 problems.

 

Show all your work. Be as complete as possible.

 

1. Two rockets are leaving their space station along perpendicular paths, as measured by an observer on the space station. Rocket 1 moves at 0.60c in the +x direction and Rocket 2 moves at 0.80c in the +y direction both measured relative to the space station.

a. (15 pts) What is the velocity in the x direction of Rocket 2 observed by Rocket 1?

          b. (15 pts) What is the velocity in the y direction of Rocket 2 observed by Rocket 1?

 

2. (30 pts) The data below are from the high temperature (light bulb) investigation of black body radiation. How does the Rad (assumed proportional to the incident radiation) depend on T? Support your conclusion with calculations and a graph.

 

                        Rad                  T (K)

                        0.20                 754

                        1.22                 1121

                        2.99                 1385

                        5.25                 1610

                        7.95                 1798

                        26.52               2468                                                                                                                                                                           

 

3. a. (15 pts) What is Ψ320 for the electron in the hydrogen atom? 

b. (15 pts) Set up the integral to find <r> for the Ψ320 state of hydrogen?

 

4. (30 pts)   

 

 

 

a. (20 pts) Assume Ψ(r, φ) = R(r) Φ(φ) and find the solution for Φ(φ).

b. (10 pts) Interpret the solution.                                                                                                          

 

5. a. (20 pts) Use the binding-energy formula (16-30) to predict the binding energy of 40Ca.

b. (10 pts) Compare your answer with the actual binding energy found from the masses listed in Appendix D.

 

 

6. A semiclassical approach: From the reference frame of the electron in a hydrogen atom with orbital angular momentum the proton revolves around the electron generating a current. The current will produce a B field. The B field at the center of a circular loop of current is B = μoI/2r.

a. (15 pts) Show that

                                     B = μo  eL

                                 4πmer3

where L is the electron's orbital angular momentum.

 

b. In the Bohr model for the n=3 orbital, L =3 h/2π and r = 9aB. Calculate the B field experienced by the electron (10 pts) and the splitting of the two spin levels due to this magnetic field (5 pts).