Chem 302

Midterm Exam

Part B

February 28, 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 an open book and class notes close exam, and you are responsible to be sure that your exam has no missing pages (6 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.

No one can make you feel inferior without your consent

- Eleanor Roosevelt -

Honor Statement

I have neither give nor received aid in this examination.

Full signature _______________________________

Problem 1 (25 points)

A positive and a negative electron can form a short-lived complex called positronium. Assume that the Bohr theory of the hydrogen atom could be applied to positronium and calculate

a) its ionization energy

b) the energy levels of its first excited state

c) its radius in the ground state.

Remember to use the reduced mass

in Bohr theory.

Problem 2 (25 points)

Ionization potentials of several atoms and ions are

Li: 5.363 eV	Na: 5.17 eV
Be: 18.12 eV	Mg: 14.96 eV
B: 37.75 eV	Al: 28.31 eV
Ca: 64.27 eV	Si: 44.93 eV
N: 97.4 eV	P: 69.70 eV

Plot the square root of these energies against the corresponding nuclear charge and explain the relation as well as you can in terms of the Bohr model.

Problem 3 (25 points)

Suppose that we are to use Bohr model to describe the motion of the earth around the Sun. What would be the principal quantum number of the earth if the sun's mass is assumed infinite.

Problem 4 (25 points)

The function

is an eigenfunction of the operator

only under certain conditions. What are these conditions, and what is the eigenfunction when they are satisfied? Finally normalized the eigenfunction in the interval .

Bonus (10 points) No partial credit.

Can an irrational number to an irrational power be a rational number?