ATOMIC SPECTRA
Ken Cheney
6/9/2006
PICTURES:
http://www.paccd.cc.ca.us/physics/teachers/cheney/lab%20manuals/WEB%
20Image%20Folders/Spectra%20Pasco.pdf
ABSTRACT
The spectra of a number of elements and molecules will be observed with a
spectrophotometer. The results for hydrogen will be compared with theory.
Swing of Photo
Detector

Diffraction
Gating
Photo Detector
Diffracted
Light
Slit
Light
Source
Figure 1
Outline of Spectrophotometer
OVERVIEW OF SPECTROPHOTOMETER
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Light from a source is sent through a slit, diffraction grating, and the
resulting spectra is measured to obtain the intensity as a function of angle.
The grating constant is then used to convert the angles of the lines to
wavelengths.
Adsorption can be done by sending the light from a continues spectrum
through a transparent adsorbing medium. See Figure 3.
Axel, Pinion, rotated
by Degree Plate
Measure angles.
Bench, grating:
Fixed
Degree Plate, Arm,
Photometer: Rotate together
Light Source
Figure 2
Angle Measuring System
The arm is rotated by hand to sweep the photometer across the spectrum.
The computer records the output of the photometer and the rotation of the
axel.
---------------------- TO DO -------------------------------1.
2.
3.
4.
Do the calibration of the angle conversion, very carefully!
Find the grating spacing d using the known wave length of Na.
Find spectra for Hg, H, D, two lasers, and two other gases.
If possible do at least two adsorption spectra.
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5. For Na and Hg find the percent errors compared to accepted values for
the wavelengths.
If you can find accepted wavelength values for you last two gases
include those too.
6. For H1 and D compare your measured wave lengths with the wave
lengths you calculate using Eq. (1.6)
D or H2 (one proton, one neutron) has a different reduced mass from
H1 (one proton) hence different energy levels.
Calculate, clearly, what energy photons should be visible within the
400-700 nm range of visible wavelengths.
-------------------------- SET UP -----------------------------Pasco Equipment and Computer Using Data Studio
Hardware setup:
Don’t drag the Light Sensor/Table around by the wires!
Be very sure the small axel is firmly attached to its shaft. Check
the black plastic knob is tight.
Be sure the small axel is rotating with the large table.
To find the conversion factor between the small axel and large table:
You must still determine the ratio between the rotation of the large
turntable and Light Sensor and the small axel that is connected to the
rotation sensor. Usually this ratio is very close to 60:1
Simply rotate the large table as far as possible (it won’t go 360
degrees) and compare the degrees you read on the large table with the
degrees the computer plots for the small axel. Click the “start” icon near the
top of the screen, rotate, click the “stop” icon that the “start” turned into.
The graph will just be a straight line but that is ok for now. Use the curser
icon to find the beginning and ending rotations, subtract, divide by the
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degrees you rotated the large table, repeat for a good average (and standard
deviation of the mean of course).
Software setup:
To use existing software:
Select Data Studio from the desktop.
Select “Open Activity”
Select “Spectra” or the most likely looking file!
This should show you the interface with connections to the Light
Sensor and rotation sensor.
There should be a graph with the y axis labeled “% . . .” and the x axis
labeled “degrees rotation”.
To set up the software yourself (not recommended if it can be avoided!)
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Select Data Studio from the desktop.
Select “Create Experiment”
From “Sensors” drag “Light Sensor” and “rotary motion sensor” to
the interface.
Double click on the Light Sensor, chose the “General” tab, set the
“Sample Rate” to 20 HZ.
From “Displays” drag the graph icon to the Light Sensor.
If the y axis is not labeled “Light Intensity (% Max)” drag, from
“Data” the “Light Intensity” icon to the y axis. You should get a dotted line
around the y axis when you are located properly.
From “Data” drag the “Angular Position” icon to the x axis, stop
when there is a dotted box around the x axis. The x axis should now have
units of degrees.
Caution!! The y axis is reading the rotation of the very small axel that is
rotated by the large table that has degree markings and moves with the light
detector. You must convert the rotation of the small axel to the rotation of
the large table.
----- PROCEDURES TO IMPROVE
RESULTS ---
See Figure 3.
For the brightest lines:
1. Move the light source as close to the slit as possible.
2. Use the bright light produced by the blazed grating on one side.
3. Carefully adjust the first lens (collimating lens) to gather the most
light, “focused” on the slit. See Figure 3.
4. Carefully adjust the second lens to focus the light on the slit in
front of the photometer. See Figure 3.
5. Mask the light source so stray light does not reach the photometer.
6. Mask everything!
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Swing of Photo
Detector
Detector
Slit

Diffraction
Gating
f
Diffracted
Light
f
Photo Detector
First Lens
Light
Source
Slit
Second
Lens
Transparent fluid for
adsorption spectra
Figure 3
More parts of Spectrophotometer
For best results setting the gain
1. There are three levels of gain on the photometer and a software
adjustment of sensitivity.
2. Start with the least sensitive setting on the photometer, then
increase the setting after each run.
3. Last, if necessary, increase the software sensitivity.
For the Sharpest Lines
1. Adjust the first lens to produce a parallel beam, check across the
room with the diffraction grating etc. moved out of the way.
2. Adjust the diffraction grating so as much of the grating as possible
is illuminated.
3. Focus the second lens carefully.
4. Use the smallest slits possible.
For well defined peaks on your plot
1. Move the photometer slowly.
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2. Move the photo detector very slowly when near a peak, it is
possible to move too fast for the computer.
For accurately measured angles
1. Always move the detector in the same direction.
2. Install a stop at the beginning. The angle at the start of each run is
defined as zero. To compare runs you must always start at the
same spot.
3. Start with the light sensor outside the first order spectra and move
it (SLOWLY) past the central maximum and past the first order
spectrum on the other side.
4. Eliminate lines between points and line markers: click on graph
icon at the top of the graph (or left click on any data line), chose
the “Appearance” tab, deselect “connect data points” and “legend
symbols”.
5. Use the software with magnification to measure the angles on the
plots.
Enlarge the peak of the line of interest: make a selection box
around the region of interest by dragging from upper left to lower
right. Click on the “enlarging” icon “small box arrow to large
box” at the top of the graph.
Use the curser icon (crossed doted lines) at the top of the graph to
read the location of the peak of the line.
Find the location of the matching line on the other side of the
central maximum.
Subtract, divide by the conversion factor from small axel to large
table. Divide by two.
If you can’t find the line on the other side of the central maximum
(too dim) use the central maximum as the reference and don’t
divide by two.
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Now you can use sin (angle)= lambda/d to find the wavelength or
grating spacing d.
For accurate angle calculations:
Follow the instructions about calibrating the angle measuring
equipment very carefully. All your measurements use this calibration, so do
a very good job!
For adsorption spectra
Use a DC power supply for the continues light source, I assume the photo
detector will be confused by the varying light produced by an AC source.
-------------------------- THEORY ---------------------------THEORY: DIFFRACTION GRATING: ANGLE AND
WAVELENGTH
n  d sin
(1.1)
n:
The order of the spectra, the number of integer wave lengths
from one slit in the diffraction grating to the next slit.
The wavelength of the spectral line
:
d:
The distance from one slit to the next in the diffraction grating
The angle the light is deflected to the spectral line.
:
THEORY: DIFFRACTION GRATING: RESOLUTION
The resolution of a diffraction grating is a measure of how small a difference
in wavelength can be measured divided by the wavelength:
 1
(1.2)

 nm
 : The smallest wave length difference that can be measured.
The wavelength being used.
:
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n:
The order of the spectrum
m:
The number of slits on the diffraction grating that are
illuminated.
The importance of this here is that we want to arrange the source, slit, first
lens (collimating lens), and diffraction grating to illuminate as much as
possible of the grating.
THEORY: ENERGY LEVELS OF HYDROGEN AND
OTHER SINGLE ELECTRON ATOMS (IONS)
Solving the Schrodinger equation for a Coulomb potential and a single
electron yields three quantum numbers n, l, and ml but, if there are no
external fields, the energy of the electron only depends on the principle
quantum number n:
En 
 Z 2 e4 1
8 0 2h 2 n 2
(1.3)
For H1 this becomes, in electron volts:
En 
13.6eV
n2
(1.4)

me mn
me  mn
(1.5)
The energy of the photon emitted when the electron changes from one
energy level to another is just the difference in the energies of the two levels:
E photon  En  Em
(1.6)
En:
:
Z:
e:
eV:
0
h:
n:
me:
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The energy of the electron with principle quantum n.
This is the energy it takes to remove the electron to infinity,
The energy is negative since energy must be put into the atom
to do this.
The reduced mass, see Eq. (1.5)
The number of protons in the nucleus
The electron charge
Electron volts. 1eV=1.602 10-19J
:Permittivity 8.854 10-12 C2/Nm2
Plank’s Constant
The principal quantum number 1, 2, 3, . . .
The mass of an electron
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mn:
The mass of the nucleus
------------------- CONSTANTS -------------------------SPECTRA:
Lots, with pictures at: http://hyperphysics.phyastr.gsu.edu/HBASE/quantum/atspect2.html
He
Line Number Wavelength Description 1 6678 Faint red 2 5875 Bright
yellowish/green 3 5016 Bright green 4 4922 Faint Green 5 4713 Faint green
6 4471 Bright blue-violet 7 4026 Faint blue-violet 8 3889 Faint deep violet
Hg
mercury lines are at 435.835 nm (blue), 546.074 nm (green), and a pair at
576.959 nm and 579.065 nm (yellow-orange). There are two other blue lines
at 404.656 nm and 407.781 nm and a weak line at 491.604 nm
Na
589.0 nm and 589.6 nm, more accurately the difference is 0.597 nm
Ne
 nm Color
540.1 green
585.2 yellow
588.2 yellow
603.0 orange
607.4 orange
616.4 orange
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621.7 red-orange 692.9 red
626.6 red-orange 703.2 red
633.4
red
638.3
red
640.2
red
650.6
red
659.9
red
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electron mass:
9.109 381 88 (72) 10-31kg
electron charge: 1.602 176 462 (63) 10-19 C
proton mass:
1.672 621 58 (13) 10-27 kg
neutron mass:
1.674 927 16 (13) 10-27 kg
plank’s constant: 6.626 068 76 (52) 10-34Js
speed of light:
2.997 924 58 108m/s exact
Permeability of free space:
0
0
Permittivity of free space:
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1
0 c 2
11