Physical Chemistry II
Review Set 1
1. A particular wave function is:
Compute the average value of the momemtum squared operator. All space for this wave
function is (-∞,∞).
2. The work function for metallic francium is 3.84eV (1eV = 1.602677·10-19 J). Compute
the KE and speed of and electron hit by a photon of wavelength 170 pm. What if the
wavelength of the photon is 170 m?
3. The Heisenberg uncertainty relation for energy and time is Et ≥ h. It the uncertainty
in the lifetime of an excited state is 10-9s what is the uncertainty in the states energy?
4. Explain black body radiation and why it is so important. Sketch a curve for T = 100K,
1000K and 10000K.
5. A laser emits photons with a wavelength of 1064 nm with a power output of 5106 J/s
a. Compute the energy form a 210-8 s pulse.
b. Compute the energy of one photon from this laser
c. Compute the number of photons in 10 pulses.
6. True/False:
a. A probability density can never be negative
b. The state function can never be negative
c. The state function must always be real
d. The integral of the wave function over "all space" = 1.
7. For a harmonic oscillator:
a. Sketch the ground state.
b. Sketch the 3rd excited state.
c. Qualitatively, what do you know about the derivative of the probability density where
it is maximum?
d. Sketch the density for the 4th excited state and label the most/least likely places to find
the particle.
8. For PIAB wave functions:
a. Sketch the ground state.
b. Sketch the 3rd excited state.
c. Sketch the 2nd excited state probability density.
d. Given a 1D “box” of length L = 3nm, evaluate x
for the 1st excited state. What is counterintuitive about the result given what you know
about the wave function and/or the probability density of this state?
9. Evaluate p̂y for (x) particle in a box. Is (x) an eigenfunction of the momentum
operator?
10. For a particle in a 1D box:
a. What is the quantum number of the state below?
b. Where are you most likely to find the particle for the state below?
c. What is the value of the integral of * over the length of the box?
11. Using the PIAB eigenvalue formula as a rough model for the valence electronic
energy levels of 1,3-propene, sketch what you would expect the spectrum to look like if
the source’s photons could excite the valence electron into the first five available energy
levels.