a) a 1.00 g bullet with a velocity of 300.0 m s-1.
b) a 1.00 ´ 10-6 g particle with a velocity of 1.00 ´ 106 m s-1.
c) a 1.00 × 10-10 g particle with a velocity of 2.00 ´ 108 m s-1.
d) an H2 molecule with energy equal to 
at T = 20
K.
Tarleton State University
Department of Physical and Environmental Sciences
Chem 3244 Spring 1999 Physical Chemistry
Problem Set 1
Due Date: Tuesday, January 19, 1999
Please hand in the answers to the following problems showing all work needed to obtain the answer. All work must be done in legible fashion. Remember to show all your work. No credit will be given for just the numerical answer or an answer with no explanation (for example, true and false answers must be accompanied by an explanation of your choice). Also remember to keep track of significant figures and units. All numerical answers must have the correct number of significant figures and must have the appropriate units attached. Assume all gases are perfect unless otherwise stated.
1. a) Calculate the fraction of radiant energy density emitted by a black body in the wavelength region between 7800 Å and 8000 Å at a temperature of 727°C.
b) Repeat this calculation at a temperature of 2227°C.
2. At what wavelength does the maximum in radiant energy density distrubution occur for a temperature of: a) 300 K?; b) 500 K?
3. The work function for potassium is equal to 2.2 eV and that of nickel is equal to 5.0 eV (where 1 eV = 1.602 ´ 10-19 J).
a) Calculate the threshold frequencies and wavelengths for these two metals to start ejecting photoelectrons.
b) Will violet light of wavelength equal to 400.0 nm cause the photoelectric effect in any or both of these metals?
c) Calculate the maximum kinetic energy of photoelectrons in these metals from part (b).
4. Calculate the de Broglie wavelengths of the following particles:
a) a 1.00 g bullet with a velocity of 300.0 m s-1.
b) a 1.00 ´ 10-6 g particle with a velocity of 1.00 ´ 106 m s-1.
c) a 1.00 × 10-10 g particle with a velocity of 2.00 ´ 108 m s-1.
d) an H2 molecule with energy equal to
5. For a particle in a one-dimensional box (or restrained between x values of 0£ x£ a, where a is a constant), the ground state wavefunction is:
a) What is the probability that the particle in the ground state can be found in the right half of the box?
b) What is the probability that the particle in the ground state can be found in the middle third of the box?
6. What are the results of operating on the following
functions with the operators 
:
a)
b)
c)
d) Which of these functions are eigenfunctions of the particular operators?
e) For the eigenfunctions, what are the corresponding eigenvalues?
