This lecture covers selected parts of sections 1-6 through 1-9 of McQuarrie:
The spectra of one-electron atoms consists of a several series of lines. For the visible line of the hydrogen, Balmer found a remarkably simple formula that could account for the wavelengths of the lines. His formula requires one to assign an integer to each line. For the visible series, the longest wavelength line at 6563 A is assigned the integer three, the line at 4862 A is assigned 4, etc. Later Rydberg generalized the Balmer formula to account for all of the series over all spectral regions. This formula involved a constant, R, the Rydberg constant.
MATLAB is a convenient tool to discover the Rydberg line. We can show that only a plot of spectral line frequency vs inverse integer squared is linear. Moreover, it is linear only if the integers are specific values. Thus, we can rule out a series of alternative models that predict the position of spectral lines.
Niels Bohr was the first to account for the Rydberg formula in terms of the structure of the and microscopic behavior of the motion of the electron as it moved around the nucleus. The Born atom is subject to three fundamental equations. The first two are from classical physics and describe (a) the total energy as the sum of the classical kinetic energy and Coulombic potential energy of the electron in a circular orbit around the nucleus. The third equation is unprecedented and states that the angular momentum is restricted to specific values (quantized).
From his three equations, Bohr was able to derive the Rydberg formula. In addition, the Rydberg constant was determined entirely by other more fundamental constants (electron mass, electron charge, epsilon and h.
Click here to view a copy of the M-file for this Leccture. This m file and all of the others have line breaks missing. Do not "save" the file. Instead, highlight the entire text and copy and paste it into the MATLAB editor (select a new M file in the File menu of MATLAB first). Now the script will have line breaks and you can do a " save as" to save it as a named file.