D IFFRACTION G RATING S PECTROSCOPY :
E MISSION AND A BSORPTION S PECTRA *
A D V A N C E D L A B , U N IV E R S IT Y

OF

S O U T H F L O R ID A

O VERVIEW
You will use a computer-interfaced diffraction grating spectrometer to measure the visible emission spectrum of mercury. The same spectrometer will be used to measure the visible absorption spectra of several solutions, including chlorophyll and food coloring. These emission and absorption spectra will be interpreted and compared to known results. As a pre-lab activity, you will observe the spin-orbit splitting of the famous sodium D-lines.

B ACKGROUND
EMISSION SPECTRA
A brief overview of the background will be provided here. However, you are expected to research other sources (such as your introductory and modern physics textbooks) in order to help you understand this lab. As a starting point, you may want to refer to the following sources:
1. Introductory Physics textbook (any will do); Look up “diffraction grating” in the index.
2. Serway, Moses, and Moyer, Modern Physics, Third Edition, Sections 4.3 and 9.3.
Diffraction Grating Spectroscopy
We will use a transmission diffraction grating to view the visible emission lines from hydrogen and sodium light sources. A diffraction grating is a device with a very large number of closely spaced slits.
The advantage of a grating over a simple double slit is that the lines can be made very close to each other.
As you may recall from introductory physics, this results in the maxima becoming very far apart from each other. The expression that relates the location of the maxima to slit spacing and the wavelength is given by
,
(1) where d is the slit spacing, λ is the wavelength, θbright is the angle at which the maxima can be found
(relative to the central maxima at θ = 0), and m is the order of the maxima. The derivation of this can be found in a typical introductory physics text for scientists and engineers. For our diffraction grating, the spacing d can be calculated by knowing how many lines per mm for the grating; this information will be marked on the grating in lab. We will neglect random uncertainty in this value.
Atomic Emission Spectra
The results of this lab illustrate that atomic energy levels are quantized. When an atom makes a transition from a high energy level to a lower one, light with energy equal to the difference in the energy levels is emitted. Conversely, if an atom makes a transition from a low energy level to a higher one, light is absorbed. (The latter effect results in the famous solar absorption Fraunhofer lines.) A larger energy splitting between levels corresponds to a higher energy of emitted (or absorbed) light. Recall that
E = h f,

*

Written by M. D. Chabot. Last revised in February, 2014.

1

(2)

where f is frequency, E is energy, and h is Planck’s constant. From this, it is clear that the larger energies correspond to higher frequency radiation. Since c = λ f, higher frequency is shorter wavelength.
Spectroscopic Notation for Atoms with One Outer Electron
You will need to understand spectroscopic notation in order to understand the energy levels of sodium and mercury. The usual spectroscopic notation used for atoms with one outer electron is
, where n is the principle quantum number, j is the total angular momentum quantum number, s is the spin quantum number, and L = {S, P, D, F, …} depending on the orbital angular momentum quantum number
(l = 0 is the S-state, for example).1 Recall than n can be any positive integer, while

l

= 0, 1, 2 …, (n-1).

The total angular momentum is the vector sum of the orbital angular momentum and the spin angular momentum. Therefore, allowed values for the total angular momentum quantum number are
(3)
For a single atomic electron, s = ½, so j = ½ for

l

=0. Thus, the ground state of hydrogen would be

written 12S1/2. (Often, the “2s+1” or the “n” terms are left off, so that the ground state is represented by
2
S1/2 or 1S1/2.)
Sodium D-Lines
The sodium spectrum