Planck’s Constant Activity
AP Physics
Name:
Period:
In this activity, we will look closely at the spectrum produced by energized hydrogen atoms. The
spectrum produced is quite different from the spectrum of a blackbody and those differences tell us a lot
about how atoms work: To capture the spectrum, we will use a diffraction grating. Remember that a
diffraction grating has multiple slits that allow incoming light waves to pass through and spread out on
the far side. As the spreading waves from different slits meet, they interfere – most of the interference is
destructive, but if you look at the right angle the waves undergo constructive interference and you will
see a light wave with a particular wavelength at that angle.
Materials:
Hydrogen Spectrum Tube
Spectrum Tube Power Supply
Diffraction Grating & Mount
Meter Stick
Procedure:
1. Place the Spectrum Tube at one end of your table. Align
the diffraction grating mount so that it points at the spectrum
tube – the end with the diffraction grating should be the far end from the spectrum tube and the end with
the meter stick should be close to the spectrum tube.
2. On the diffraction grating, read the density of the lines – the number of lines per meter or the number
of lines per centimeter – and record the value. Then convert that number to the line spacing – the
distance between adjacent lines, d, and record that value.
3. Measure the length of the diffraction grating mount – from the grating itself to the meter stick where
you will measure the lines you see. Record that value as the length, L, between the grating and the line.
4. Turn on the spectrum tube and look through the diffraction grating, down the length of the diffraction
grating mount at the tube. Adjust the diffraction grating mount so that you see the spectrum tube at the
50 cm mark on the mount’s meter stick.
5. Moving your eyes, not your head, look to either side of the 50 cm mark and you should see four
distinct lines of color that are parallel to the spectrum tube – those lines are the spectra produced by the
energized hydrogen gas. In order away from the tube, you should see a dark violet line, a blue violet
line, a blue-green line and a red line. (The dark violet line is the hardest to see.)
6. Start with the lines to the right of the spectrum tube. Measure how far out it appears to be from the
center of the meter stick – the x value. If you can see the meter stick clearly enough, simply read off the
distance from the 50 cm mark. If you can’t see the meter stick, have a partner slide a piece of paper
along the meter stick until the edge matches the line and then your partner should be able to read the
distance from the 50 cm mark.
7. Repeat step 6. for the lines to the left of the spectrum tube. Ideally, these measurements will be the
same as those you just took. If they are not, then your diffraction grating mount is slightly angled.
Don’t worry about the angle, by taking the data on both sides, we will average away any measurement
errors.
8. Switch positions with your partner and repeat the measurements in step 6. and 7. Record these new
measurements as trial 2.
9. Take the average of all your measurements for the position of each line. Use the average value for all
of your calculations from this point forward.
Planck’s Constant Activity Data
line density:
line spacing, d:
Grating to line distance, L:
Line Color
Trial 1
(right)
Trial 1
(left)
Trial 2
(right)
Trial 2
(left)
Mean Value
(x)
Dark Violet
Blue-Violet
Green-Violet
Red
Analysis:
Part I: Light Waves
Our first task is to find the wavelength and frequency of the light waves that
make up the hydrogen spectrum. This involves applying our understanding of
diffraction. We are looking for constructive interference between waves
spreading out after they pass through the slits in the diffraction grating.
Constructive interference means that the crest of the wave
coming through one slit meets the crest of the wave
coming through the other slit (or, equivalently, the trough
of one wave meets the trough of the other). Because the waves are moving the
same speed, this means that one wave has to travel a distance that is exactly one
wavelength further than the other wave travels (it could be two wavelengths or
any integer number, but we are looking at the first order maximum). Although
the two waves coming through different slits do have to travel at slightly
different angles to be able to meet up, the difference is so small that we can
consider the two waves to be going parallel. This makes it easy because then the
extra distance that one wave travels just depends on the distance between the
slits and the angle (see picture).
To meet up just right for constructive interference, the extra distance that one
wave travels (which equals d·sin) has to be equal to a single wavelength, so  =
d·sin. Use this fact and some basic trigonometry (see the picture at the top of the page) to fill in the
following table:
Diffraction Results
Line Color
Dark Violet
Blue-Violet
Blue-Green
Red
Angle ()
Wavelength ()
Frequency (f)
Part II: Bohr’s Theory
When people originally observed the bright line spectra given off by excited gases, they were baffled
by them. They very quickly understood two important ideas: 1) light to come from vibrating charges
(which is not wrong); and 2) in order to emit a light wave, the atom had to lose energy by moving its
electron into an orbit closer to the nucleus. However, neither of those ideas put any limits on what kind
of light waves could be created by the atom.
It wasn’t until Planck and Einstein brought the idea that light was quantized into view, that anyone
made progress on the question of the hydrogen spectrum. Niels Bohr took the idea of quantization to
heart, realizing that if light was quantized into photons, a hydrogen atom only emitting particular
wavelengths of light meant that the hydrogen atom could only emit photons with certain amounts of
energy. Since the energy came from the electron in the hydrogen atom moving into orbits that were
closer to the nucleus, that suggested that only certain orbits were allowed and the lines we see as the
hydrogen spectrum come as the electron jumps from one allowed orbit to another allowed orbit – losing
just the right amount of energy to produce one of colors of the spectrum. Bohr’s analysis suggested that
the electron’s energy in any orbit had to be:
-13.6 eV 2.176 x 10-18 J
En =
=
n2
n2
We will apply Bohr’s theory to our data. The visible part of the hydrogen spectrum is produced by
the electron jump from a higher orbit (third through sixth) into the second orbit. Use your knowledge of
how photon energy varies with frequency to deduce which line is produced by an electron starting in
which orbit. Fill in your results in the table below.
Once you know which orbits are involved, use Bohr’s formula to calculate the amount of energy that
the electron has in each orbit and fill in your values in the table below. The find the amount of energy
that the electron loses as it drops from a higher level orbit into the second orbit. Record your results in
the column labeled Ejump.
All of the energy lost in the jump must go into the photon produced and the energy of the photon is
equal to Planck’s constant multiplied by its frequency (Ephoton = hf). Solve for the value of Planck’s
constant that fits the data for each line and record the result. After solving for the individual values from
each individual line, take the mean value your data gives for Planck’s constant.
Applying Bohr’s Theory
Line Color Frequency
(Hz)
Dark Violet
Blue-Violet
Green-Violet
Red
Average
ni
nf
Ei
Ef
Ejump
h
2
2
2
2
.
Questions:
1. a) Make a graph of the energy the electron gives up against the frequency of the light emitted. Find
the equation for the graph’s line of best fit.
b) Where do you find Planck’s constant in the equation for the graph? Why?
c) What value does your graph give you for Planck’s constant?
2. a) Find the percent error for the two values of Planck’s constant you have found: the one from the
average value in the data table, the other from the equation for your graph
b) Which method gave you a more accurate value for Planck’s constant, taking the average of
individual points or graphing them?
3. What are the biggest sources of error in this experiment?
4. How do you calculate the energy of any spectral line?
5. Why does the hydrogen spectrum contain so many visible lines (called Balmer lines) even though the
hydrogen atom only contains one electron?
6. As the wavelength decreases, what happens to the distance between the Balmer lines? Why?