Lab: Emission Spectra
In this lab you will observe the spectra of hydrogen, helium, and mercury (as gases under
low pressure) from which you will gain an understanding of how spectra can be used to
identify substances anywhere in the Universe. You will also determine the energy and
wavelength associated with photon emission.
THEORY:
When a substance absorbs energy (from heat or high voltage applied to a gas discharge
tube, or photon absorption, etc.) electrons are raised to higher energy state. When they
drop back to their original levels, the absorbed energy is released as photon emission
(visible or invisible light). The frequency, (thus the color) of this light is directly
proportional to the energy difference between the initial and the final energy levels. The
energy, with respect to the nucleus, of each energy level (n) in the hydrogen atom can be
determined from the following equation:
En = -13.6 eV (1/n2)
This quantity En is the energy level of orbit n. For example, an electron in orbit n = 2
requires energy E2 = 3.4 eV to be separated from the nucleus, while an electron in orbit
n = 3 requires only E3 = 1.51 eV; thus, orbit n = 3 is less tightly bound to the nucleus than
orbit n = 2. When an electron jumps down from orbit n = 3 to orbit n = 2, it gives off
energy E = E2 - E3 = 1.89 eV. This is exactly the energy of the photons which make up
the red line of hydrogen in Fig. 2. Likewise, electrons jumping from orbit n = 4 to orbit
n = 2 produce the blue-green line, and electrons jumping from orbit n = 5 to orbit n = 2
produce the deep blue line. When an electron jumps from a high-numbered orbit to a lownumbered orbit, the atom emits a photon.
Fig. 3. Energy levels (horizontal lines), and downward jumps (arrows) of
hydrogen. The wiggly arrows in color represent the photons produced
when an electron jumps down from one orbit to another. To save space, the
lowest level (n = 1) is not shown.
What happens when an electron in a hydrogen atom jumps up to a higher orbit? This
takes energy, which has to come from somewhere. One way to supply the energy is with
a photon, but the photon has to have exactly the right amount of energy -- no more, and
no less. For example, an electron in orbit n = 2 can jump up to orbit n = 3 if it absorbs a
photon with energy E = E2 - E3 = 1.89 eV.
Since the structure of atoms differ from element to element, the possible transition
between energy levels (E) within atoms of each element is also distinctive. Thus, each
element is capable of displaying a characteristic array of colors, or spectrum. These
colors are determined by the wavelength and frequency of the light emitted:
E = hc/
OR
E = hf
Gases under low pressure emit characteristic bright-line spectra, which are like fingerprints for that element. This can be seen for several elements below:
Hydrogen: a simple atom with a
simple spectrum. Besides the
three lines shown here, you may
be able to see another in the blue
near 410 nm.
Helium: slightly more complex
than hydrogen, with one yellow
line and a number in the blue.
Mercury: the strongest line, at
546 nm, gives mercury a
greenish color.
Fig. 2. When heated in a electric discharge tube, each element produces a unique pattern of spectral `lines'.
MATERIALS:
Diffraction gratings
high voltage source
hydrogen, helium and mercury discharge tubes
PROCEDURE:
1. Position the light source approximately1.00 m (L) from the diffraction grating as
shown below:
2. Measure and record the position of the bright lines which are visible to you (each
“line” will have a corresponding “x” value. (Be careful to keep the grating facing
the lamp, and keep all distances “L” and “x” perpendicular to each other. Move
your eye position, not the grating, to see the lines to the side of the lamp.)
3. With a meter stick just behind the lamp, as shown, measure the x-positions of
each of the 3 or 4 lines as accurately as possible for the hydrogen lamp.
4. Repeat this process for the mercury and then for the helium lamps, recording all
colors, “x,” and “L” values for each line seen.
RESULTS/CALCULATIONS:
1. With your measured L and x values, compute the angle  of each of the first-order
lines for each lamp. Make a table of your results in your lab book. Leave space for
extra columns to add the further calculations below. Show your work for your
calculations below the table.
2. The number of lines per mm is marked on the grating. From this, you can
compute the spacing d of the grating. Find this value and record it in your lab
book.
3. Using your computed  's and computed d, compute the wavelengths of each of
the three (or four) most prominent lines for each lamp using the following
equation:
 = d sin 
4. Using the equations from the “theory” section, calculate the energy change
associated with the emissions from each gas tube. Based upon the energy values,
determine the energy level transitions in the hydrogen atom responsible for the
colors you see.
INTERPRETATIONS:
1. Discuss the agreement between what you observed (colors seen) and the
calculated wavelengths. Using the chart on the top of page 686, compare the
colors you saw with the calculated wavelengths.
 Did they all agree?
 What might cause the values to differ?
2.
Discuss and explain what is happening to electrons inside the atoms and how this
causes the line spectra that you observed.
 How can hydrogen, with only one electron, produce several lines?
3. The energy changes taking place within an atom can have many values. These all
correspond to different wavelengths and frequencies of electromagnetic radiation
which are emitted. Discuss why you see only a few lines when there are so many
possible energy transitions taking place.
4. Discuss two sources of error in this lab. For each of these, specifically explain
how this source of error would affect your results. Don’t just randomly list
sources of error, but rather do an analysis of error sources and tie them into your
results for this lab.