Measurement of Wavelengths of Visible Hydrogen Spectra
Theory
Wavelengths of visible light emitted by excited hydrogen atoms when they decay to
lower energy levels can be measured with a spectrophotometer. This uses a diffraction
grating to separate the different wavelengths. The wavelengths are determined by the
equation:
nλ = d Sin(Өn)
where λ = wavelength of light deflected through angle Өn
d= the grating spacing
and
n=1, 2, 3, etc. = the order of the deflected light
The three* visible wavelengths of the hydrogen spectrum were first explained by the
Bohr Model (see text.) They are:
Electron Transition
Color
Wavelength
Level 3 to Level 2
Level 4 to Level 2
Level 5 to Level 2
*Level 6 to Level 2
Red
Blue-Green
Violet
Violet
656.1 nm
486.1 nm
434.0 nm
410.2 nm
*The fourth is difficult to see by eye, but may show up on the spectrophotometer scan.
Apparatus
60 cm optical bench
Hydrogen spectrum tube
High voltage spectrum tube power supply
Collimating slits on holder
Collimating lens
Blocks for elevation of optical bench (about 3 to 4 cm high)
Pre-assembled spectrophotometer assembly, consisting of:
Spectrophotometer base and pinion
Degree plate / Light sensor arm
Rotary motion sensor, with its rod clamp
Grating mount
High sensitivity light sensor (Pasco CI-6604)
Light sensor mount
Aperture disk & screen
Threaded post
Diffraction grating (600 lines per mm) and Focusing lens
Screen for blocking stray light
Brief Description of Data Collection
Light from the hydrogen spectrum tube passes through a collimating slit, through a
collimating lens, and falls on the diffraction grating. Light of each wavelength is
deflected into first and second order on both sides of the undeflected central beam.
The light sensor is slowly moved by hand through the angular range enclosing first
order on one side, the central beam, and first order on the other side.
The rotary motion sensor tracks the angular position and inputs it to the computer. The
light sensor inputs the light intensity at each angular position. Then the computer can
graph intensity versus angular position, and on this graph the three (possibly four)
hydrogen wavelengths can be identified in first order on opposite sides of the central
beam.
Zooming in on each wavelength enables a very accurate value of its angular position
to be determined.
Once the first-order angular positions for a wavelength have been recorded, the
following example shows how to calculate a best value of Ө1:
1st order (right) = 155.96°
Central beam = 133.61°
1st order (left) =111.30°
Then
Ө1(right) = 155.96° – 133.61° = 22.35° *
And
Ө1(left) = 133.61° – 111.30° = 22.31° *
*If these differ by more than .20°, recheck your recorded angular positions for mistakes.
So the average Ө1 = (22.35 + 22.31)/2 = 22.33°
This average Ө1 is the best experimental result and is used to calculate the wavelength.
Initial Equipment Set-up
1. Place the collimating slit holder at the extreme left end of the optical bench, with
the slits facing left (away from the bench.) Choose collimating slit #2. Make sure
slit #2 is centered in the larger slit.
2. Make sure the spectrum tube power supply is not initially plugged in. DANGER ----HIGH VOLTAGE and HOT----- THE HIGH VOLTAGE SUPPLY
PRODUCES SEVERAL THOUSAND VOLTS. And THE HYDROGEN
TUBE BECOMES VERY HOT WHEN IN USE. DO NOT TOUCH THE
ELECTRODES OR THE GLOWING TUBE. Place the hydrogen spectrum
tube into the power supply. Then plug in the power supply and turn it on.
3. Elevate the optical bench about 3 to 4 centimeters as necessary to have the
brightest part of the hydrogen tube at the level of the collimating slit. Place the
light source about 1.5 centimeters from the collimating slit (just leave enough
space so the light source doesn’t get bumped.)
4. Place the collimating lens 8 centimeters from the slit.
5. The spectrophotometer assembly should be pre-assembled and clamped to the
right end of the optical bench. Make sure the diffraction grating is in place. Place
the focusing lens within the marked rectangle on the side near the light sensor. Set
the aperture on slit #2 and the light sensor gain on 100.
6. The diffraction grating should be perpendicular to the light beam, and it should
remain at rest when you rotate the light sensor arm. Try this. If the diffraction
grating moves, call your instructor.
7. With the room lights low, move the end of the optical bench near the hydrogen
tube back and forth slightly until the beam falls on the center of the diffraction
grating. A sheet of paper held in front of the diffraction grating makes it easier to
see this At this point you should also see narrow, clearly-focused first-order
beams falling on the aperture slit as you rotate the light sensor arm. Call your
instructor if the first-order beams are not well-focused.
8. Use shielding as necessary so that only light from your collimating slit reaches the
diffraction grating and only light from the diffraction grating reaches the light
sensor.
Computer Set-up
1. Connect the rotary motion interface cable to the Pasco workshop digital channels
1 and 2 (yellow lead to channel 1.) Connect the light sensor cable to analog
channel A.
2. Turn on the Pasco workshop first, and then turn on the computer. After log-in
choose “Data Studio” and “Create an Experiment”.
3. Drag the Light Sensor icon to Analog Channel A.
4. Drag the Rotary Motion Sensor icon to Digital Channels 1 & 2.
5. Double-click on the Light Sensor icon to get the “Sensor Properties” screen. Raise
its sampling frequency to 20. On its “Calibration” page raise the Sensitivity to
High, and then click on OK.
6. Double-click on the Rotary Motion Sensor icon. On the “Measurement” page
select “Angular Position (degrees)”. On the “Rotary Motion Sensor” page select
1440 Divisions/Rotation. Click on OK.
7. Because the 360[degree] wheel’s radius is 60 times greater than the pinion radius,
the rotary motion sensor rotates 60[degrees] for each 1[degree] of the wheel and
light sensor. So you must calculate the “actual angular position” of the light
sensor. Click on “Calculate” on the top tool bar. Drag the words “Angular
Position” from the Data screen to the Calculator screen position marked “Define
Variable x”. This line should then read “x = Angular Position”. Then in the
“Definition” window, change the equation to y=x/60. Then click on “Accept”.
(Now, x is the rotary motion sensor angle and y is the “Actual Angular Position”
of the light sensor.)
8. Drag the “Graph” icon from the Display screen to the “Light Intensity” in the
Data screen. Then drag “y” from the Data screen to the horizontal axis of the
graph. The graph should now show “Light Intensity %” versus “y”.
Collection of Data
1. Move the light sensor arm past the first-order spectral pattern on the side nearer to
the student (about 25° from the central beam for a 600 lines/mm grating.)
2. Start recording data. Slowly move the light sensor arm past first-order, central
beam, and first-order on the other side. The arm should be moved slowly and
steadily in one direction only. Then click on “Stop”.
3. Click on “Scale to fit” (the first graph icon) to display the entire run. Print this.
You should be able to identify the central beam and at least three hydrogen
wavelengths symmetrically located on either side of it.
4. Now zoom in on each wavelength as follows: Click on “Zoom Select” (the fourth
graph icon) and then drag a rectangle enclosing the wavelength profile you want
magnified. Repeat this three or four times until you have magnified the profile
sufficiently. (Remember to hit “Zoom Select” before dragging each rectangle.)
Then print the profile and record the angular position of its center to an accuracy
of .01[degrees].
5. To return to the display of the entire run, push “Zoom Out “ repeatedly and then
use “Zoom Select” to magnify the vertical scale.
6. Repeat step 4 for each wavelength on both sides of the central beam, and for the
central beam also.
Calculations
When the angular positions have been found for all wavelengths and the central beam,
calculate the three (or four) hydrogen wavelengths, as in the sample calculation. Compare
your calculated wavelengths with the standard values.
Additional Data Collection and Calculations
Redo Data Collection steps 1 to 6 enclosing the second order beams in your scan (Start
about 55° on one side of the central beam, and scan to 55° on the other side.) Identify the
wavelengths in second order, magnify them with “Zoom Select” as described above,
record their angular positions precisely, and use them to calculate the three hydrogen
wavelengths. Again compare your wavelengths with the standard values.