Chem 302

Quantum Chemistry

Midterm Exam

February 28, 2002

Name __________

Full credit will be given to correct answers only when ALL the necessary steps are shown. DO NOT GUESS THE ANSWER.

This is a closed book and closed notes exam, and you are responsible to be sure that your exam has no missing pages(5 pages).

If you consider that there is not enough information to solve a problem, you have to specify the missing information and describe the problem solving procedure.

But surely this is an old tale you tell, they say;

But surly this is a new tale you tell, other say.

Tell it once again, they say;

Or, do not tell it yet again, others say.

But I have heard all this before, say some;

Or, but this is not how it was before, say the rest

Naqshbandi recital, from The Way of the Sufi, by Idries Shah

Honor Statement

I have neither give nor received aid in this examination.

Full signature _______________________________

Problem 1 (30 points)

For a face-centered cubic (fcc) crystal with a = 3 x 10m, what is the smallest diffraction angle for l = 1.50 x 10m at 300 K.

Problem 2 (30 points)

The wavelength of maximum intensity in the solar spectrum is 0.500 mm. Assuming the sun radiates as a blackbody, compute its surface temperature.

Problem 3 (30 points)

Demonstrate whether or not .the function

is an eigenfunction of the operator

If it is an eigenfunction, determine the eigenvalue.

Problem 4 (10 points)

Consider a one-dimensional particle in a box model of butadiene, H₂C=CH-CH=CH₂ . For the transition

E_Ground-> E_{First Excited}

the absorption occurs at

1/l = 4.6 x 10⁴ cm^-1 .

For this molecule, we assume that the p electrons in move along a quantum mechanical box. If a C=C and C-C bond lengths are calculated to be 1.35 A and 1.54 A, estimate the size of the end of the box, C< .