## Class Notes, Spring 2002

 Week of Jan 14 Feb 4 Mar 4 Apr 1 Phy 360 page Jan 21 Feb 11 Mar 18 Apr 15 Jan 28 Feb 18 Mar 25 Apr 22 Feb 25

## Phy 360, Week 8

4 Mar Continue the development of Bohr's model of the one-electron atom. I'm doing the simpler derivation, even though this way the critical step is essentially unmotivated.

After some discussion of the meaning of the various terms, the three equations that I arived at are

k Z e2 / r2 = m v2 / r       E = m v2 / 2 - k Z e2 / r       L = m v r = n h / 2 p

n is an integer. These three equations have the three unknowns v, r, E. It is now straight-forward to solve them.
The orbital radius comes in discrete steps, varying as n2.
The energy is discrete, proportional to - 1 / n2.

6 Mar Restate the equations that lead to Bohr's model. Introduce the fine structure constant, the dimensionless number whose value is approximately a = 1/137. This permeates the subject, and all the results found by solving the above three equations for E, v, and r can be expressed in terms of it. For the hydrogen atom Z = 1, and

E = - a2 m c2 / 2 n2       v = a c       r = ( hbar / m c ) / a

This constant is a = k e2 / hbar c. In the setup equations for the Bohr theory, the charge e always appears as Z e2, where Z is the atomic number of the nucleus. This means that wherever a appears in the result it will have a factor of Z with it.

In order to understand the relation between the graph of potential energy and the idea of binding energy, I went over the interpretation of the motion of a particle in an arbitrary potential energy.

8 Mar The effect of energy quantization on specific heat. Describe the behavior of the specific heat of hydrogen as a function of temperature. It is not constant and appears to have steps. The existence of energy levels will account for the phenomenon. In order to see how this can happen, first review how specific heat can be derived from a simple kinetic model of bouncing molecules.

How did Bohr develop his model? Not the way this book (or most others) say. It was really much more interesting. He assumed the existence of energy levels, an idea motivated by the experimental observation about the combining properties of the frequencies of spectral lines. He then used the idea that whatever the correct atomic theory is, it will reduce in some way to the classical theory when you are dealing with high energy states. I didn't finish this.

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