Sample Proficiency Exam: PHYS 221
1. (25) Muons are elementary particles with a (proper) lifetime of 2.2 ms. They are produced with very high speeds in the upper atmosphere when cosmic rays collide with air molecules. Take the height of the atmosphere to be Lo = 100 km in the reference frame of the earth.
A. Find the minimum speed that enables an average muon to survive the journey to a laboratory on the earth's surface.
B. What is the thickness of the earth's atmosphere in the reference frame of the moving muon?
2. (25) When sodium metal is illuminated with light of wavelength 4.20x102 nm, the stopping potential is found to be 0.65 V. When the wavelength is changed to 3.1x102 nm, the stopping potential is 1.69 V. Using only these data and the values of the speed of light and the electronic charge, find the work function of sodium and a value of Planck's constant.
3. (25) In order to study the atomic nucleus, we would like to observe the diffraction of particles whose de Broglie wavelength is about the same size as the nuclear diameter, about 14 fm for a heavy nucleus such as lead. What kinetic energy should we use if the diffracted particles are :
A. electrons
B. neutrons
C. alpha particles
4. (25) The situation for a
particle in a finite square well is similar to that of an infinite well,
but the potential has the value Uo for x < 0 and x > L, where we still have U = 0 for 0 < x <
L.
A. Including 6 undetermined constants, write down the wave functions for the three regions x < 0, 0 < x < L, and x > L with the condition that E < Uo.
B. Which of the two coefficients must be set to zero?Why?
C. Keeping in mind the boundary conditions at x = 0 and x = L, sketch the three lowest-energy wave functions and probability densities. Do not attempt to apply the boundary conditions explicitly; just show the expected form of the wave functions. Let the solutions for the infinite potential well serve as a guide for the form of the wave function inside the well.
5. (25) Explain why each of the following sets of quantum numbers (n, l, ml , ms ) is not permitted for hydrogen.
A. ( 2, 2, -1, +1/2 )
B. ( 3, 1, +2, -1/2 )
C. (4, 1, +1, +1/2 )
D. ( 2, -1. +1, +1/2 )
6. (25) Three different rock samples have ratios of 238U atoms to 206Pb atoms of 0.5, 1.0 and 2.0. Compute the ages of the three rocks. The half life of 238U is 4.5x109 y. The other members of the uranium to lead series have half lives much shorter than this.
7. (50) Respond to each of the following questions with a few sentences.
A. What is the most stable nucleus? Why?
B. What are the key differences between particles that obey classical statistics, Bose-Einstein statistics and Fermi-Dirac statistics?