Physics 204, Spring 2011

Atomic Spectra

It came as a surprise to Bunsen and Kirchoff that atoms in flames emit light at sharply defined frequencies, what came to be called spectral lines, for reasons that we will soon see. These frequencies (or, equivalently, wavelengths) could be accurately measured, and their study was the beginning of spectroscopy.

Atomic spectra are beautiful to see. You can use a hand-held diffraction grating to look at the spectra of helium, neon, and mercury. They are very distinctive – you could certainly recognize them again if they were presented to you again in an unexpected setting. Thus for purposes of identifying a light source you don’t really need to understand them. And for a long time this was their main use, as a means of identifying chemical elements.

Of all the atoms, hydrogen turns out to be the only one with a spectrum that is simple to understand, and that one tells us an amazing story – the atom looks, in some sense, like Bohr’s model. You know all the peculiar features of this theory by now: how the frequencies f satisfy

Here n and m are integers (quantum numbers), h is Planck’s constant, and the energies are

Here c is the speed of light, and R is the Rydberg constant. Its value is such that

1/R=91.14 nm.

The Bohr scheme of energy levels and transitions between them is illustrated below.

Use a spectroscope with a diffraction grating to locate the diffraction maxima of light in the Balmer series of the hydrogen atom spectrum and thus measure the wavelengths of these lines. Convert to frequency and plot versus 1/n^2, assuming that the lines belong to n=3, 4, 5, and 6. (You may not be able to see n=6.) Interpret the slope and intercept – what are they telling you?