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In this lab we will take a look at quantum systems. In these systems the total energy
takes on discrete values that we describe with energy levels. Each level can be labeled
with a quantum number n. Since the energy comes in discrete values changes in energy
are also discrete and correspond to changes in energy level. This means that the energy
emitted or absorbed by the quantum system has to match up with the energy differences
between two levels. This means that photon emitted or absorbed by the system can only
have certain wavelengths. We will look specifically at the Hydrogen atom. Where the wavelengths
of the emitted light are described by the Rydberg equation. We will see that transitions
to the final level of n = 2 correspond to wavelengths in visible spectrum of light.
So in this lab we will measure the wavelengths of light emitted by the excited hydrogen atom
and verify that these wavelengths are predicted by the Rydberg equation. To measure the emitted
wavelengths we will use the spectrometer, which is a tool to precisely measure diffraction
angles from a grating. Recall that the angle of diffraction increases with wavelength as
described by the equation
Let's take a look at the spectrometer. On the input side is a collimating tube, which
has an adjustable aperture so you can control the amount of light that gets through.
The light that gets through the tube is collimated before it hits the diffraction grating, which
is mounted perpendicular to the incoming light.
Light diffracts from the grating, and can be viewed again by a telescope. The angle
between the telescope and the collimating tube is indicated on the platform of the spectrometer.
Before we trust these angle measurements, we will have to calibrate the spectrometer.
So to calibrate the spectrometer you will need to use the mercury source, which has
one brightest wavelength, so it is easy to use as calibration. So, here is the zeroth
order and as I rotate around you can see there is the first order there are two different
lines but one is bright green and you will be able to see that one much more sharply.
The other is a little bit more of a yellow color. So this is first order diffracted beam
for both of those and then as you keep going you will see the second order and you can
see kind of to the left a little bit, the yellow, and they are separated by a little
bit more. So you get higher resolution as you go out to higher orders. Then as you keep
going you can start to see the third order come in. There it is. This is what you will
be doing but you will be making more accurate measurement. To use this you push the spectrometer
directly upto the source. The light from the hydrogen source gets through to the input
of the spectrometer and now if you look through the grating you can see that there is the
source, but we do not want to look directly at it. What we want to do is look through
this telescope at it, so that we can see the diffraction angles. if i move this here and
try to look through the telescope, then we can see that there.
You will adjust the telescope angle so that the cross-hairs are in the center of the band,
and then measure the angle. As you increase the angle of the telescope, you'll see colored
bands of diffracted light corresponding to the different hydrogen transitions.