Download Physical Chemistry II Review Set 1

Physical Chemistry II
Review Set 1
1. A particular unnormalized wave function is


 32x5  160 x3  120 x e  x

2
/2
.

Give a simplified symbolic expression for N, the normalization constant in terms of an
integral. All space for this wave function is (-∞,∞).
2. Solve the differential equation for the unknown function y(x): 𝑦 ′′ + 25𝑦 = 0
3. What must the potential energy of an electron, initially at rest, be so that wavelength is
1Å when moving.
4. 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?
5.
a. Explain black body radiation and why it is so important. Sketch a black body curve.
Label the axes.
b. Explain the significance of the double slit experiment for electrons
c. Explain the significance of the photoelectric effect.
6. 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.
7. 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.
8. For a particle in a box of length 1nm:
a. Sketch the ground state.
b. Sketch the 3rd excited state.
c. Using the principals of calculus, state qualitatively what 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.
10. Define and give an equation for:
a. x
b. p
c. T̂
11. Evaluate p̂y for (x) particle in a box. Is (x) an eigenfunction of the momentum
operator?
12. 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?