Chem 302

Midterm Exam

Part A

April 13, 1995

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.

Barth's distinction

There are two types of people: those who divide people in two types, and those who did not

Honor Statement

I have neither give nor received aid in this examination.

Full signature _______________________________

Problem 1 (25 points)

Set up the Schrödinger equation for a particle of mass m in a three dimensional box with sides L,Land L. Show that the wave function is defined by three quantum numbers, and that the Schrödinger equation is separable. In the case of a cubic box of side L write down the energies of the ground state and the three first excited states. Express these energies in terms of m, L and physical constants. Also give the degeneracy, if any, of the four levels.

Problem 2 (25 points)

Calculate the fundamental vibrational frequency of carbon monoxide, CO, considering it to behave like a harmonic oscillator with force constant 1902.5 N m. By how much will this frequency change if the molecule contains the isotope C instead of the more abundant C ?

Problem 3 (25 points)

Calculate the expectation value of xs|2>.

with

.

Problem 4 (25 points)

For the 1s orbital of the hydrogen atom calculate the probability of finding the electron within a distance afrom the nucleus.