Physical Chem. HW

CHEM402 Spring 2023Homework 2
Due 2/7/2023
Answers to the following problems must be uploaded to Blackboard before 12 pm on the date due.
You may work with others, but individual assignments must be submitted. Please include short verbal
explanations along with your math and reference any math tools used such as integral/ derivative
calculators etc.
1. Calculate the probability that a particle in a box of length L will be found between 0.65 L and
0.70 L when the particle has a principal quantum number of n = 2.
2. A nitrogen molecule is confined in a cubic box of volume 1.00 m 3. Assuming that the molecule
has an energy equal to 3/2kBT at T = 300 K, what is the value of n = (nx2 + ny2 + nz2 )1/2 for this
molecule? What is the energy separation between the levels n and n + 1?
Bonus: What is its de Broglie wavelength?
3. Calculate the wavelength of a photon needed to excite a transition between neighboring energy
levels of a harmonic oscillator with the effective mass equal to that of an oxygen atom (15.9949
u) and force constant 544 N/m.
4. The particle on a ring is a useful model for the motion of electrons around the porphine ring, the
conjugated macrocycle that forms the structural basis of the haem group and the chlorophylls.
We may treat the group as a circular ring of radius 440 pm, with 22 electrons in the conjugated
system moving along the perimeter of the ring, see below. We assume that in the ground state
of the molecule quantized each state is occupied by two electrons. Calculate the energy and
angular momentum of an electron in the highest occupied level. Calculate the frequency of
radiation that can induce a transition between the highest occupied level.
Highest occupied electronic level: ml quantum number