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V0.61
LAB EXERCISE COTR – L3
DIFFRACTION SPECTROSCOPY AND QUANTUM MECHANICS
Lab format: This lab is performed with the lab kit and the RWSL Spectrometer.
Relationship to theory: This lab exercise explores the spectrometer and the spectra of various elements.
It then focuses on the hydrogen and helium spectra and the quantum-energy changes these reflect.
OBJECTIVES




Build a makeshift spectrometer and calibrate it with the mercury lines in a fluorescent light.
Calibrate the RWSL Spectrometer with Sodium D-Lines or the yellow mercury doublet;
Using the RWSL Spectrometer, measure the wavelengths of light emitted by hydrogen and
helium.
Calculate quantum-energy changes in hydrogen and helium electron transitions.
EQUIPMENT LIST
Lab Kit
 Cornell Slit-film (from Lab Exercise L1)
 Make-shift Spectrometer Template
 Neon bulb (that fits into the night light socket)
 Set of 4 ‘bulldog’ paperclips (from Lab Exercise L1)
Student Supplied
 ‘Night light’ with incandescent bulb
 Desk lamp with fluorescent bulb
 Cardboard Box (large enough to cover the desk lamp lying on its side)
 Table
 Masking Tape
 White Card (3x5 or better 5.5x8.5)
 Headlamp with red LED (Optional, but recommended)
 For RWSL Access:
o Computer: PC running Windows Vista or later
o Browser: Internet Explorer 8 or later
o Internet: 5 Mb/s or faster Internet connection
RWSL
 Access to RWSL Spectrometer with
o Sodium (Na) or Mercury (Hg) spectrum tube
o Neon (Ne) spectrum tube
o Hydrogen (H) spectrum tube
o Helium (He) spectrum tube
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INTRODUCTION
In spectroscopy an atom demonstrates quantum theory in the pattern of the wavelengths of light
(colours) it emits. The wavelengths of the emitted light depend on the different energy level transitions
of orbital electrons in its atomic structure. The energy level diagram for hydrogen is shown in Figure 1
below.
WARNINGS
 Don't get fingerprints on the diffraction grating or the Cornell Slit-film or their function will be
compromised. Handle them only by their edges. DO NOT clean them with Windex or a similar
product because the ammonia dissolves the film gelatine! If you must clean them use a dry soft
cotton cloth and don’t rub too hard.
THEORY
A. The Balmer Series of Atomic Hydrogen:
•
•
α

•
|
|
ß

•
|
|
|
|
γ

E6
|
|
|
|
|
|
δ

E5
E4
E3
E2
_____________
E1
Figure 01: Balmer Series
Hydrogen emits a photon of visible light when an electron transitions from higher energy levels down to
the E2 level. In 1885 Johann Balmer started with the red line and identified these lines by the letters of
the Greek alphabet: red H-α light is emitted when the electron falls from E3 to E2. Blue-green H-ß light
when it falls from E4 to E2, and blue H-γ light when it falls from E5 to E2. He matched them to an
empirical formula to within 0.1%:
k
n2
;
n 2  22
EQ L3.01
where k = 364.56 nm and n = {3,4,5...} with n = 3 for H-α, n = 4 for H-ß etc.
In astronomy the H-αlpha red glow is seen in the hydrogen gas of nebulae. Ultra-violet light energy
from superhot O and B-type stars excite the hydrogen electrons to higher energy orbits. When they fall
to a final E2 energy level within the Balmer series, the transition will produce photons of visible light.
The red background glow behind the Horsehead Nebula is a good example of this.
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Absorption Lines:
This process works both ways: it can emit or absorb energy. If an electron absorbs energy to transit
from E2 to E4 then it absorbs this one colour. A dark line would appear in any white light background
spectrum.
Outer electrons in an atom are normally in the state of lowest energy, called the ground state (level E1 in
Figure 1). But in ionized gases (produced for example in electric arcs) some of the atoms are excited to
the higher levels E2, E3, ... E by collisions with free fast-moving electrons. (Here E represents the singly
ionized state where one electron is removed from the atom.)
An atom in one of the excited levels can make a spontaneous transition to one of the lower levels with
the emission of a light quantum. The fundamental law of quantum theory is that the frequency of the
light is proportional to the energy change. Thus if an atom initially in the state E2 makes a transition to
the ground state E1, the energy change is governed by:
E  E2  E1  hf
Where h is Planck's constant ( 6.626 10
EQ L3.2
34
J  s ).
In optical spectroscopy we measure wavelength λ and convert that to frequency f. For any wave
motion, the frequency and the wavelength are related by:
f 
c
EQ L3.03

Here c is the velocity of the wave in the medium.
Since we are dealing with wavelengths in air, c is to be interpreted as the velocity of light in air for this
experiment (2.9970476 108 m/s). (The distinction is small but a green light wave of 500 nm in dry air
@15C becomes 500.1301 nm in vacuum--although the frequency and thus the colour stays the same.)
The energy difference can now be expressed in terms of the wavelength:
E 
hc
EQ L3.04

Note – You may come across wavelength measured in Angstroms (Å) (1Å= 110-10 metres or 0.1 nm:
where a nanometre is 110-9 m). If you need to convert, use 1nm = 10Å.
A joule is too big a unit for measurements taken at the atomic level, so the energy difference is
measured in electron-volts (where 1 eV is the energy gained by an electron accelerated through a
potential difference of 1 volt). The amount of energy in joules for an electron falling through 1 volt is:
E  qV  1.602 1019 C  1V   1.602 1019 J ; (Remember 1V  1
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J
)
C
EQ L3.05
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To convert to eV  nm convert joules to eV and metres to nm:
m

J  s   2.997  108 
s

hc 
 1.240 103 eV  nm

19 J 
9 m 
1.602 10
110

eV 
nm 

 6.626 10
34
EQ L3.06
Therefore the relationship between the energy difference and the wavelength can be written as:
E 
1240eV  nm


1.24eV 106

m
EQ L3.07
Note – If you are working with Å the and have units of (eVÅ) then convert joules to eV and metres
to Å:
m

J  s   2.997 108 
s

hc 
 1.240 104 eV  Å
J
m



19
10
1.602 10
110

eV
Å


 6.626 10
34
EQ L3.08
and
E 
12400eV  Å


1.24eV 106

m
EQ L3.09
Energy Range of the Visible Spectrum:
The visible spectrum extends from around 390 nm in the violet to 720 nm in the red. (The actual limit
depends on the intensity and on the observer.) To what range of ΔE does this correspond?
VISIBLE CONTINUOUS SPECTRUM
^380 nm
750 nm^
Hydrogen Line Spectra:
brt= 2
3
410.2
434.0
8
486.1
12,18
656.27,656.29 λ(nm)
FIGURE 02: Continuous Spectra and Characteristic Line Spectra
The pattern of energy levels is characteristic of the atomic species, so that each atom emits its own
characteristic spectrum. For a low pressure discharge the energy levels are sharp and the transitions
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between these levels produce a line spectrum - lines of definite wavelength. From these wavelengths
we can find immediately the energy differences ΔE and (after a complicated analysis) also the energy
levels. Of course the zero energy in the energy level diagram is arbitrary; usually the zero is chosen at
the ground level. For the incandescent filament of an ordinary light bulb there are no sharp energy
levels and we observe a continuous spectrum.
Forbidden States and Selection Rules:
Suppose that we have some excited atoms in the state E3. From this state two transitions are
energetically possible. Some atoms may make a transition to E2 while others may go directly to the
ground state E1. Under these circumstances we would therefore get two spectral lines originating from
the level E3. But because of the structure of a particular atom it may happen that a transition that is
energetically possible nevertheless does not occur. For example, it may happen that the transition E3 to
E1 does not occur, so that the corresponding spectral line is missing. In this case we say that the
transition is forbidden by a selection rule. These selection rules eliminate many of the energetically
possible transitions. For our hypothetical atom we have assumed that the transition E2 to E1 is in fact
allowed but for some atoms the corresponding transition may be forbidden. For example for both
helium and mercury the transition from the first excited state is forbidden.
THE DIFFRACTION GRATING EQUATION:
Figure 3: Constructive Reinforcement
A diffraction grating can be used to measure the wavelengths of the colours emitted.
The diffraction grating consists of a square of photographic film mounted in a slide holder. The film has
many parallel rulings. The one in your lab kit could have 500, 600, or another number of rulings per
millimetre. Be sure to check.
When parallel light rays shine perpendicularly on such a grating, the spectrum is observed diffracted
through an angle θ. If d is the distance between successive rulings, the path difference between
successive rays is d sin  . For reinforcement this path difference must be an integral number of wavelengths so the Grating Equation is:
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d sin   n
EQ L3.10
Here n is an integer called the order of the spectrum. For the zeroth order (where n=0) part of the light
passes straight through the grating, so we have sin   0 , so that   0 for all wavelengths. For n=1 we
get the first-order spectrum, for n=2 the second-order spectrum and so on. Note that the grating really
measures nλ, and the order n has to be determined by inspection. In the visible spectrum λ varies from
about 400 nm (violet) to about 700 nm (red). Thus 2λ varies from 800 to 1400 nm and 3λ from 1200 to
2100 nm. Hence the violet end of the third-order spectrum overlaps the red end of the second-order
spectrum.
Fig 4: Overlapping Spectral Orders. The Visual Spectrum from 400 to 700nm Graphed According to Diffraction
Angle of a 600 line/mm Grating. Note the wider spread of the second-order spectrum allows better accuracy when
measuring the angle θ with the spectrometer.
The grating equation assumes the incident beam is perpendicular to the grating: but if it is not, then an
error correction is applied:
n  d  sin   sin  
EQ L3.11
where  is the incident angle.
Thus care should be taken that the grating is aligned perpendicular to the incident beam or this error
would be introduced.
THE SPECTROMETER:
The Principle of the Spectrometer:
The spectrometer measures the angle of diffraction of the spectral lines in order to calculate it's wavelength with the grating equation.
Figure 05.1: Spectrometer Optics (Classic Spectrometer)
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The classic spectrometer (See Figure 5.1) has a central table on which the diffraction grating is mounted,
a collimator (the tube with the slit at the outer end) and a telescope (the tube with the eyepieces at the
outer end).
The light being studied passes through the slit of the collimator, and the rays are made parallel by the
collimator lens. This makes the source appear to be at infinite distance. The grating table is carefully
positioned so that the collimated light rays strike the diffraction grating as perpendicular as possible
(both up-down and left-to-right). The diffracted rays are focused by the telescope onto its cross hairs,
and the spectrum can be observed through the eyepiece. As the telescope is swung left or right, a
pointer shows it's angle θ from 0 to 360.
Figure 05.2: The “Make-shift” Spectrometer
Since quality spectrometers are very expensive it is not possible to include one in your lab kit. Hence, in
this lab exercise you will construct an approximation of the classic spectrometer to get the feel for what
this kind of instrument is like. (See Figure 5.2) Then you will use the high quality on-line RWSL
Spectrometer for accurate measurements.
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PROCEDURE
Part I: Constructing a Make-shift Classic Spectrometer
1. Clear a table in a room where you can eliminate all (preferably) sources of light. Tape one of the
“Make-shift Spectrometer Templates” provided in your lab kit to the table one end of the table
as shown in Figure 6.1.
Figure 06.1: “Make-shift” Spectrometer Template Placement
Figure 06.2: Cornell Slit-film Taped in Box
2. Place an incandescent lamp in the nightlight socket such that its light will travel along the centre
line of the Make-shift spectrometer template. (See Figure 6.1.) Cut a small rectangle approx. 1
cm wide and 3 cm tall from the end of the box. Use masking tape to attach the Cornell Slit-Film
so that only the 0.13 mm slit will allow light to pass out of the box. (See Lab L1 Appendix A for
the details of the Cornell Slit-film and Figure 6.2 for the details of attaching it to the box.) Be
sure to attach the masking tape only to the edges of the slit film so it won’t be damaged. You
may need to cover the slits you don’t want to pass light with some paper. Then place the box
upside down over the nightlight so that the light from within the box will shine out through the
0.13 mm slit along the centre line of the Make-shift spectrometer template.
NOTE – Be careful not to get fingerprints on the Cornell Slit-film. Handle it only by its edges. Should it
become necessary, use a clean dry soft cotton cloth to clean it and don’t rub too hard.
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Figure 07: Diffraction Grating Placement
3. Place the diffraction grating at the centre of the diffraction grating at the centre of the “Makeshift Spectrometer Template as shown in Figure 7. Adjust the alignment of the night light, slit,
and diffraction grating so that you see the vertical white line from the slit through the diffraction
grating when you view from the 0° position. When you hold a white card at the 0° position you
should see this line projected onto the card. If you don’t, then line it up so it does by sliding the
box left or right. This is called the zeroth-order line and it consists of light that is not diffracted,
but travels straight through the diffraction grating.
4. You will probably want to darken the room you are working in at this point or the spectrum you
are trying to see may not show up. Use a headlamp with a red LED from now on when you need
to see, so your eyes can adjust to the dark and you won’t have to keep turning the overhead
lights on to see. Red light will not compromise your night vision and some of the spectra you
are trying to observe might be very dim.
5. The diffraction grating will refract the light in 2 directions. Choose the brightest part of the
continuous spectrum that appears when you move the card left or right to see it. If one side of
the spectrum appears higher than the equivalent spectrum on the other side of the 0° position
then the grating is tilted one way or the other. Make sure it is vertical so the first order
spectrum on either side of the 0° position appear at the same height from the table. Now check
to see if the first order refraction appears in the same angular position left and right of the 0°
position. The first-order spectrum will be about 15 either side of the centre line and look like a
continuous rainbow band of colours.
6. Now move the card further left and right until you see the Second-order spectrum at around
30 either side of the 0° position. The colours should repeat a second time. How many orders
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of refraction can you see? Which orders of refraction overlap? Do the colours appear in the
same sequence or a different sequence on either side?
7. RESULTS: Make a brief sketch to show what colours you saw at about what angle. Include the
position of the zeroth order and indicate where the first order and second order appeared.
Were the colours left-right symmetrical? What sequence were they in? (Don't spend too much
time on this).
┌────────────────────────────────────────────────────────────────────┐
│
│
│
│
└────────────────────────────────────────────────────────────────────┘
8. If it is included in your lab kit replace the incandescent bulb in the nightlight with the neon bulb
and repeat steps 1 through 7. Otherwise go to step 9. The neon bulbs are usually designed to
flicker and they are not as bright as the incandescent bulb as they are intended to be decorative
so this may be more difficult. Record what you observe here and make note of the differences
in the neon spectrum with respect to the incandescent spectrum.
┌────────────────────────────────────────────────────────────────────┐
│
│
│
│
└────────────────────────────────────────────────────────────────────┘
Part 2:
CALIBRATION OF THE GRATING
9. The fluorescent lamp is our calibration light source. Mercury is contained in fluorescent lights.
It emits bright double line at 579 and 577 nm. The diffraction grating is marked as 600, 500, or
some other number of lines/mm. Check it and record the number of lines/mm that is marked
on the grating. The number of lines/mm can vary by up to 5% due to film shrinkage or swelling
from humidity. Here we will attempt to measure its actual value, but this will be difficult with
the makeshift spectrometer as the diffraction angles are difficult to measure precisely. Do the
best you can.
Figure 08: Spectrum of Mercury
Note - The fluorescent bulb spectrum will have other spectra superimposed on the mercury spectrum,
but you will still be able to see the double yellow line at 579 and 577 nm.
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Figure 09: Desk lamp with fluorescent bulb installed and the aluminium foil in place
10. If you have marked the Make-shift spectrometer template to help with the measuring of the
angles above, then tape a fresh unmarked template to the table. Place the fluorescent bulb in
the desk lamp. Cover the desk lamp with aluminium foil and cut a narrow slit in the foil on the
side that will be laying on the table as shown in Figure 9. Lay the desk lamp on the table where
the box will fit over it and turn it on.
11. Place the box with the mounted Cornell Slit-film over the desk lamp so that the 0.13 mm slit is
immediately in front of the aluminium foil cut-out. Carefully repeat the alignment you did in
step 3 making sure the zeroth order beam is passing through the 0° position.
12. Locate the double line at 579 and 577 nm and measure the angle to the first order 579 nm line.
Now use EQ L3.10 to calculate the value of d. See if you can repeat this step for the second
order spectrum.
13. Report your results in your lab report. Now you would be ready to measure the wavelengths of
the lines in various other spectra with your make-shift spectrometer. However, it DOES leave
something to be desired when it comes to obtaining precise angles for sensitive spectroscopy
work so for this reason we will use the RWSL Spectrometer for the rest of this lab exercise. This
is a high quality on-line spectrometer that you can control from your browser. It also removes
the tedium of measuring angles to determine wavelengths.
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Part 3: Using the RWSL Spectrometer
14. Review Appendix 1: The RWSL Spectrometer
15. Schedule a lab session on the RWSL Spectrometer. Your instructor will have the dates when it
will be available as well as scheduling instructions.
16. Make sure your computer system is certified for RWSL access as described in Appendix 1. If it
can’t be, find a system at your local educational institution or somewhere else that can be
certified.
17. A few minutes before your scheduled lab session access the RWSL and, if you have lab partners
contact them on the back-channel you agreed to. (See Appendix 1.)
18. Contact the RWSL Tech you will be working with on the same back-channel.
19. At the appointed time of your session, one member of your lab group should request control of
the spectrometer. Try to give all members of your lab group a chance to control the
spectrometer and take data. See Appendix 1 for instructions on how to do this.
20. Each member of the lab group should take a turn running through the spectrometer virtual
instrument (VI) controls so everyone is familiar with them and can take data. See the
“Experimental Operation” section of Appendix 1 for a review of these controls and instructions
on acquiring a spectrum.
21. Practice using the Neon spectrum. Does the RWSL graph look anything like the Neon spectrum
you were able to see with the make-shift spectrometer? Remember the RWSL Spectrometer
returns an intensity vs wavelength graph, while you were looking at the neon spectrum directly
with your eye in Part 1 so you’ll have to think about this question a little.
22. Calibration of the RWSL Spectrometer: The RWSL spectrometer should already be calibrated,
but it doesn’t hurt to check this and if it is off, you need to know it. You may be using either
sodium or mercury for this part depending on which source is available at the RWSL lab.
Whichever substance you are using it will be our calibration light source. You will locate double
lines in one of these spectra to check the calibration of the RWSL spectrometer.
Figure 10: Typical RWSL Spectrum (Mercury)
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a. Sodium: Sodium emits a pair of bright yellow lines, very close together in wavelength,
called a doublet around 588.995 and 589.592 nm. (This particular doublet is often
referred to as the sodium D lines, a term introduced by Fraunhofer.)
b. Mercury: Mercury emits a pair of bright yellow lines, very close together in wavelength,
called a doublet around 577.119 and 579.226 nm.
You can read the wavelength in nm of each spike and you can see the relative intensities of each
line on the vertical scale (The units of intensity are counts, so this is a measure of how many
photons per time unit at each wavelength impacted the CCD chip in the spectrometer.) You can
also use the analysis tools provided to ‘zoom’ in on a particular line (spike) and see its details.
23. Now select the sample containing the calibration substance (sodium or mercury) by clicking on
the appropriate sample selector button. (A, B, C, or D) The slider will move the spectrometer’s
fibre-optic cable to spectrum tube you selected. You have 30 s to collect your data, but give the
spectrum tube 15 to 20 s to warm up then click the Pause button to freeze the spectrum.
Download the image of your entire spectrum for inclusion in your lab report.
24. Now locate the doublet lines and expand your view of these lines so you can see what
wavelengths they are at. It will look something like figure 11.1 below.
Figure 11.1: Doublet lines with default settings
Figure 11.2: Doublet lines accentuated (Mercury)
Use the analysis tools to more easily read the peak wavelengths. You can change the
‘Integration’ value and ‘Boxcar Width’ to obtain something like figure 11.1 above where you can
more easily read the wavelength of each peak. Record the images you obtained and include
them in your lab report. Are the doublet lines showing at the correct wavelengths? If not,
record the wavelengths they are appearing at and calculate the offset. You should not find this,
but if you do it means the scale is not aligned properly and all lines you record will be off by this
amount. Use this offset to correct all subsequent data. Also if they are not at the correct
location, report this information to the RWSL tech so this can be corrected for future students.
25. Record the calibration substance you viewed (sodium or mercury), the wavelengths the doublet
lines should be found at, the wavelengths you found them at, and what the offset is if there is
one in your lab report.
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Part 4: THE HYDROGEN SPECTRUM:
The hydrogen spectrum is important since it is the basic spectrum and its study led to the discovery of
quantum mechanics. Bohr's theory of the atom predicts that the energy levels of hydrogen are given by
the formula:
1

En  13.60eV  1  2  ; n  1, 2,3,...
 n 
EQ L3.12
Note that we have written the formula in such a way that E1 = 0. (See Appendix 3 for a derivation.)
WHAT IS THE IONIZATION ENERGY OF HYDROGEN?
Hydrogen Line Spectrum:
Figure 12: Hydrogen Spectrum (Top line spectrum/Bottom RWSL line intensity spectrum)
26. Now select the Hydrogen spectrum tube. You should see strong red, blue-green and violet lines
and may also see a second violet line. See Figure 12.
27. Use the RWSL analysis tools to zoom in and record accurate measurements of the wavelengths
of the red Hα line, the blue-green Hß and the violet H lines. If you found an offset when
checking the calibration of the RWSL spectrometer then apply this offset to your data.
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Analysis:
28. Calculate the hydrogen quantum level energies for n = 1 to 6. Draw an energy level diagram,
including the ground level and the ionization energy. Calculate energies in "eV".
29. Construct a matrix of possible transition energies ΔE of the electron between the energy levels.
Only fill out the top left corner of the matrix. Put a * beside the transitions that should be
visible.
30. Calculate your measured wavelengths as energy changes, using EQ L3.07 in eVnm. Examine
your energy level matrix and find which levels are separated by the measured energy differences. Show the transitions you observed: eg. E61.
Part 5: THE HELIUM SPECTRUM:
A neutral helium atom has two orbital electrons. Each electron is attracted by the nucleus and repelled
by the other electron. Thus energy levels depend to some extent on the angular momentum of the
outer electron. (Recall that in hydrogen the energy only depends on the principal quantum number n.)
The angular momentum quantum number is usually indicated by the letters s, p, d, f, etc. (which
indicate values of 0,1,2,3...). For this experiment these letters can be regarded merely as convenient
labels on the energy levels. Thus we get energy levels 1s, 2s, 2p, 3s, 3p, 3d, etc.
The helium spectrum is further complicated by electron spin. Quantum theory shows that the levels can
be divided into triplet and singlet levels. The spins of the two electrons are strongly coupled and can
exist in only two states--parallel and antiparallel. In effect, there are two sorts of helium atoms corresponding to these two states: there is the singlet helium atom with the spins opposed (and this includes
the ground state) and the triplet helium atom with the spins lined up. Triplet levels, as the name indicates, are actually three levels (in general) very close together. Triplets correspond to states where the
spins of the two electrons are aligned. Singlet levels correspond to states with the spins opposed. The
terminology comes from magnetic effects: in a magnetic field the triplet level splits into three different
energy levels while the singlet is not affected because the magnetic effect of the two opposed spins
cancel.
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SINGLET
24
TRIPLET
5d
5s
23.94
4s
4d
23.37
23
23.87
4d
23.49
3d
22.93
3s
23.94
4s
23.63
3p
5d
23.63
3p
22.97
3d
22.91
22.97
3s
22.82
22.62
22
21
2p
2p
21.13
20.87
2s
20.53
20
2s
19.73
Figure 13: Energy Levels for Helium
Singlet and triplet levels are indicated by the superscripts 1 and 3. In Hg transitions are observed
between the triplet and singlet levels, but in He such transitions are forbidden. Thus the spectrum can
be divided into singlet and triplet lines. We are in effect dealing with the superimposed spectra of two
types of He atom, the singlet and the triplet atom. In general the triplet line will be brighter than the
corresponding singlet line.
The energy levels for He are shown in Figure 13. In this diagram the singlet and triplet levels have been
separated, so that it has not been necessary to indicate the type of level by a superscript. It is
convenient in such an energy level diagram to separate horizontally the s, p, and d levels. The ground
state (at zero energy) is not shown on the diagram; note that the ground level is the singlet level 1s.
One selection rule states that transitions occur only between s and p states or between p and d states.
Thus for example, the transitions [3s - 2p], [3p - 2s] and [3d - 2p] are allowed, while the transitions
[3s - 2s], [3p - 2p] and [3d - 2s] are forbidden.
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Helium Line Spectrum:
Figure 14: Helium Line Spectrum (Top line spectrum/Bottom RWSL line intensity spectrum)
31. Now select the Helium spectrum tube. Find the wavelengths of the four brighter lines: the red,
orange, green and blue lines. If possible, find the wavelengths of the faint red line and the faint
violet line. See Figure 14. Record these wavelengths. If you found an offset when checking the
calibration of the RWSL spectrometer then apply this offset to your data.
Analysis:
32. Draw your own energy diagrams for the singlet and the triplet states. On each diagram indicate
the allowed transitions that are visible by connecting the levels with straight lines. Recall that
you have calculated the range for ΔE corresponding to the visible spectrum. For each of the
transitions indicate the energy difference.
33. Calculate the energy difference for each measured wavelength. MATCH THIS ENERGY WITH THE
ENERGY DIFFERENCES IN YOUR ENERGY LEVEL DIAGRAM. Show the measured wavelengths on
the transition lines in your diagram.
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ANALYSIS AND/OR QUESTIONS
Part 1
1. The visible spectrum extends from around 390 nm in the violet to 720 nm in the red. (The
actual limits depend on the intensity and on the observer). To what range of E does this
correspond? (You'll need this for H & He analysis later).
____ eV  E  ____ eV
Part 2
2. The Mercury Calibration Spectrum (using the makeshift spectrometer):
Known Wavelength of mercury double lines: 579 and 577 nm nm
Zeroth Reference Angle: _______
Which line? ______________
Angle
(right)
Angle
(left)
Average
Angle
Grating Line
Spacing (d )
1st Order Mercury
________
_______
_______
________
2nd Order Mercury
________
_______
_______
________
Angle between the first order 579 nm and 577 nm lines: dθ = __________
Calculated Diffraction Grating Constant (lines/mm): _________
How accurately can the make-shift spectrometer measure wavelength?
Part 3
3. Calibration of the RWSL Spectrometer:
Calibration Substance (circle one): Sodium / Mercury
The Doublet lines should be at ______ nm and ______ nm
The measured Doublet lines were at ______ nm and ______ nm
The offset from what the lines should be are ______ nm and ______ nm
(Remember to report a non-zero offset to the RWSL tech.)
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Part 4
4. The Hydrogen Spectrum:
a. Calculate Energies for Levels 1-6 using EQ L3.12.
E1 =
eV
E2 =
eV
E3 =
eV
E4 =
eV
E5 =
eV
E6 =
eV
b. Calculate Energy Level Differences: put a * beside the transitions that should be visible.
If we call E62 the energy level difference between E6 and E2, calculate:
n
6
5
4
3
2
Series
1
Lyman
2
Balmer
3
Paschen
4
Brackett
5
Pfund
Colour
c. Measured wavelengths for Hydrogen:
Order
λ
(N)
(nm)
ΔE
(eV)
Transition
RED
BLUE-GREEN
VIOLET
FAINT VIOLET
Identify the observed spectrum lines with the aid of your matrix in (b) and enter the transition result in
your table: eg. E61.
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Part 5
5. The Helium Spectrum:
d. Draw your own energy level diagrams for the singlet and triplet states. Allowed
transitions (ΔE in eV)
TRANSITION
SINGLET
EXPECTED
COLOUR
TRIPLET
EXPECTED
COLOUR
[5d --> 3p] =
eV
eV
[5d --> 2p] =
eV
eV
[4d --> 2p] =
eV
eV
[3d --> 2p] =
eV
eV
[5s --> 3p] =
eV
[5s --> 2p] =
eV
[4s --> 2p] =
eV
eV
[3p --> 2s] =
eV
eV
[3s --> 2p] =
eV
eV
Colour
e. Measurement of Spectral Line Wavelengths. (Use an s to indicate singlet)
Order
λ
ΔE
Transition
(N)
(nm)
(eV)
RED 1
RED 2
ORANGE 1
ORANGE 2
GREEN
CYAN(dim)
BLUE
VIOLET
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f.
Draw an energy level diagram for the singlet and triplet states showing the transitions
you were able to measure.
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REFERENCES
Original references:
1. Lide, D, CRC Handbook of Chemistry and Physics, 72nd ed. Section 10
2. Matthews, P.W., UBC Physics 115 Lab Manual, 1974, Lab #10.
Original Lab Manual by Rick Nowel, E. Tech, COTR
Adapted for Remote Delivery by Ron Evans, MSc
Under the Remote Science Labs for Second Year Physics Project funded by BCcampus
2012 - 2013
Public domain images in Figures: 01, 03, 04, 05.1, and 13
were imported from the original lab manual that was produced by COTR.
Images or portions of images in Figures: 02, 08, 12, 14, and A1.1
were taken from public domain internet sites
or from the CC licensed NANSLO RWSL Spectrometer Manual.
All other images were produced by Ron Evans
and are covered by the CC license of this document.
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Appendix 1: The RWSL Spectrometer
The Remote Web-based Science Laboratory (RWSL) is a robotic and software interface designed to
enable the student to access and use science lab equipment over the internet and collect authentic realworld data in real-time. This document provides information about using the RWSL spectrometer.
INTRODUCTION TO THE RWSL SPECTROMETER
Like all spectrometers, the RWSL spectrometer can be used to separate a light sample into a spectrum
representing its constituent wavelengths. It can analyze either an emission or an absorption spectrum
to identify various elements by themselves or in compounds and mixtures. The student can view the
entire spectrum from the near infrared (~890 nm) to the soft UV (~190 nm) or focus on one small range
of wavelengths to see relative or absolute intensities of the various bright or dark lines.
CERTIFYING YOUR COMPUTER SYSTEM AND CONNECTING TO RWSL
Before you can connect to the RWSL spectrometer, you must ensure that your computer is certified for
RWSL participation. This will ensure that your particular computer configuration will perform the
experiment without causing you undue frustration or cause server problems with the RWSL computer
interface.
Your instructor will provide you with information on how to certify your system. When this process is
completed the RWSL technician will tell you when the RWSL will be ready for you to access and give you
the required URL and instructions for connecting.
COMMUNICATING WHILE USING RWSL LABS (THE COMMUNICATIONS “BACK-CHANNEL”)
It is important that your lab group is able to communicate during the lab session and with the RWSL
technician should unexpected issues arise. Your instructor may also want to ‘look in’ on your progress
during the RWSL Lab session. There are a number of possible communications services to choose from,
but the service you adopt must:
1) allow multiple participants
2) be agreed upon by all participants ahead of time
3) use minimal bandwidth so as not to degrade the connection to RWSL.
Although video chatting might be desirable when talking to each other before and after the lab session,
it’s important to remember that a streaming video connection requires a great deal of bandwidth. When
connectivity is limited, this extra video connection could significantly degrade the connection to RWSL.
For this reason you should probably not use video to communicate with each other during the actual
RWSL connection. Audio is important as it is the most efficient way to convey information among lab
group participants, the RWSL tech, and your instructor. An audio connection requires significantly less
bandwidth than video, and while it may degrade the RWSL connection when bandwidth is marginal, this
is not so likely. Typing into a chat window uses the least bandwidth of all. Consequently your
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communications set-up should include a text chat feature in case the audio fails or one member of the
group doesn’t have the necessary equipment to support audio communication.
The RWSL development team has used Google+ for back-channel communications, but other services,
such as Skype, MSN, and others, are also good choices.
When choosing and implementing a communications back-channel arrangement, the following process
is recommended:
1. Taking into account the bandwidth implications, comfort level and communications preferences
of everyone involved, select one or two possible back-channel communications service options.
2. Consult with your instructor and the RWSL techs to determine/confirm which communication
arrangement will best serve everyone involved. Your instructor may ask you to use a particular
service.
3. Everyone should set up the necessary accounts and practice using the chosen back-channel
before the scheduled RWSL lab session.
4. Contact each other and the RWSL tech on duty about 10 or 15 minutes before the lab session is
due to begin. This arrangement allows time for everyone to become connected and configure
audio settings. If problems arise, all participants will be aware and not left wondering what
happened. The RWSL tech will give the word for you to begin.
Once the lab session is over, the RWSL tech will drop out of the back-channel, but you and your fellow
lab group partners can carry on discussing the lab exercise with each other if you want to.
APPARATUS
The RWSL spectrometer is a high quality Jaz
spectrometer manufactured by Ocean Optics. This
spectrometer uses a diffraction grating to provide a
high resolution spectrum of any sample. Light from
the sample is transmitted to the spectrometer
through a fibre-optic cable (not shown here) where
it is resolved into its constituent wavelengths to
produce the spectrum. The spectrum is projected
onto a CCD chip within the spectrometer that can
sense light from down into the infrared (~890 nm),
through the visible region of the EM spectrum, and
up into the ultraviolet parts of the EM spectrum
(~190 nm).
When the spectrometer is set up to observe
emission spectra, the open end of the fibre optic
cable is mounted on a slider. You can control which spectrum tube is observed and activate the
spectrum tube the fibre optic cable is pointing to. Currently a maximum of 4 spectrum tubes can be set
up for observing at any one time.
Fig. A1.1: Ocean Optics’ Jaz Spectrometer
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THE RWSL SPECTROMETER VI
When you first access the RWSL spectrometer, you will see the entire RWSL Spectrometer Virtual
Instrument (VI). It will look like this (but the substance labels will be different):
Fig. A1.2: The initial view of the RWSL Spectrometer VI
Gaining control of the spectrometer
When you are ready to gain control of the RWSL spectrometer, right click on the VI and request control.
After you request control of the VI you may have to wait several minutes before you actually receive
control. Be patient and occasionally click on the ‘Pause’ or ‘Start’ button. When you have achieved
control, these will toggle from one to the other. If waiting for control seems to be taking too long, right
click on the VI and request control again.
[At this time, there is no graphical indicator to confirm that you have control of the VI: your only
confirmation that you actually have achieved control of the spectrometer is when the buttons respond
to your clicks. It can take a couple minutes to connect, so be patient. If it takes more than a couple of
minutes, contact the RWSL tech on the communications ‘back channel’.
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RWSL CAMERA CONTROLS
In Fig. A1.3 (below) you can see the camera image as it appears for the spectrometer set-up.
Fig. A1.3: RWSL Camera Controls
As you experiment with the various camera controls, the image above the Camera Controls will
change in some way depending on which camera control you are using.
Camera Selection:
RWSL supports up to 4 different cameras. These are selected by clicking on
the button that corresponds to each camera. You can confirm that this
image currently has camera 1 selected because the left most button is lit up and appears bright
green. If camera 2 were selected then the second button from the left will appear bright green
and the first button will be unlit and appear dark. Cameras 3 and 4 are selected using the 3 rd
from the left and the right most buttons respectively. Not all RWSL lab exercises utilize all four
cameras. If a lab does not use all the available cameras, buttons which do not map to a camera
will simply not respond.
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Camera Presets:
Each camera can be preset with up to 6 different positions as indicated by
the rectangular buttons in the Camera Controls. After selecting the
camera you want to use, you can select the pre-set positions for that
camera. If the camera has been configured with fewer than 6 presets, the rectangular button
corresponding to an undefined preset position will simply not respond.
“Inukshuk” Controls (Pan, Tilt, and Zoom):
The “Inukshuk” control on the left side of the Camera Control area allows you to
pan (move left and right), tilt (move up and down), and zoom (as with a handheld digital camera) the selected camera. The selected camera must have these
functions built in for these controls to work. Please refer to the camera
instructions specific to the lab you are working with for these details. Because
the “Inukshuk” controls are so familiar, you will probably find them relatively
intuitive to use. Play with them and you will see what each of the oval buttons does.
Camera On/off Button:
The circular green button in the middle of the 4 directional control buttons of the Inukshuk
Control is a toggle that will turn the selected camera off and on.
When you are done exploring the camera controls, you can restore the initial camera view for
the lab apparatus by selecting camera 1 (the left most camera button) and pressing preset 1.
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RWSL CAMERA CONTROLS PECULIAR TO THE RWSL SPECTROMETER
The camera controls for the spectrometer lab are similar to those just described above.
Fig. A1.4: the camera controls
The variations specific to the spectrometer camera controls are as follows:
Camera selection: When the RWSL spectrometer is set up for emission spectra observation, only one
camera will be available with pan-tilt-zoom capabilities, so you must keep camera 1 selected (the left
most camera selection button should be selected.) Additional cameras may be added in the future.
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Camera pre-sets: When RWSL spectrometer is set up for emission spectra observation there will be only
5 presets defined for camera 1:
1) Preset 1: will show the whole apparatus. This is the starting view.
2) Preset 2: will show Sample A
3) Preset 3: will show Sample B
4) Preset 4: will show Sample C
5) Preset 5: will show Sample D
“Inukshuk” control: The “Inukshuk” controls will function in the usual fashion.
EXPERIMENTAL SETUP
The left side of the RWSL screen is dedicated
to the control of whatever piece of lab
equipment is in the RWSL at the time you
access it: in this case, the spectrometer
controls. (See Fig. A1.5)
The upper left panel displays a graphic
representation of the spectrum you are
viewing. The horizontal axis is scaled in
nanometers (nm). The vertical axis indicates
the number of photons that strike the CCD
chip within a sampling period and is measured
in counts. This can be treated as a relative
intensity scale, but where absolute intensity is
important the number of counts is an
indicator. In the case of emission spectra, the
brighter a line at a given wavelength is, the
taller the ‘spike’ in the graph at that
wavelength.
When the spectrometer is set up to observe
emission spectra with the spectrum tubes, be
aware that the spectrum tubes have a limited
lifetime, so on manufacturer’s
Fig. A1.5: RWSL Spectrometer Controls (off) Configured recommendation they have been limited to a
for Emission Spectrum Observation
30 s burst. Following the burst, the apparatus
must cool for another 30 s before you can
again view a spectrum. The A, B, C, and D buttons are grayed out during this period. When they are not
grayed out you can acquire a spectrum by clicking on one of them.
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EXPERIMENTAL OPERATION
Displaying an emission spectrum
The Spectrum Status light in the lower right corner of the Spectrometer Controls tells you that you are
‘Ready’ to acquire a spectrum, the sample tube is ‘On’, or that the apparatus is ‘Cooling’. This must
display “Ready” before you can start acquiring a spectrum. If it is ‘On’ the sample tube is lit and you can
acquire your data. If it is ‘Cooling’ you must wait until it turns back to ‘Ready’ to acquire your next set of
data.
Fig. A1.6: RWSL Spectrometer Controls (on, active)
Fig. A1.7: RWSL Spectrometer Controls (on, paused)
To acquire a spectrum:
1. Make sure the yellow ‘Pause’ button is showing. (See Fig. A1.6) If it is not, there will be a green
‘Start’ button in its place. (See Fig. A1.7) Click on this ‘Start’ button and it will change to the
yellow ‘Pause’ button.
2. The samples for analysis will be displayed in the upper right quadrant of your screen. They will
be labeled according to your instructor’s specifications. Click on the button that corresponds to
the sample you intend to observe.
3. The various control buttons will temporarily grey out and in the camera view you will see the
fibre optic spectrometer head move to the sample tube that corresponds to your selection.
Then the selected sample tube will light and a graph of the spectrum will appear in the upper
left quadrant. (See Fig. A1.8)
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4. Clicking the ‘Pause’ button will freeze the spectrum graph and the ‘Pause’ button will be
replaced with a green ‘Start’ button. Now you can begin to analyze what you have.
Fig. A1.8: RWSL Spectrometer in action
Recording your spectrum
When a spectrum is being displayed that you want to record, follow these steps:
1. Press the ‘Pause’ button to ‘freeze’ the graph. This enables you to analyze your spectrum at
your leisure and download your data without worrying about the 30 second burst ending at an
inopportune moment.
2. To save the graphical image, select “Graph Image”, press ‘Export to Clipboard’ The data is saved
on the clipboard and can be pasted into an Excel spreadsheet or a Word document (or any
document that accepts graphic or numeric data for that matter).
3. The same process can be followed to save numeric data. Click on the drop-down menu beside
“graph Image” and select “Graph Data”. Your data will be stored in the clipboard and can be
pasted into a spreadsheet or word processing document. Your instructor will give you the
information you will need to interpret your data based on the curriculum you are studying.
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ANALYZING DATA
Clicking on the dark green cursor button under the spectrum display will turn it to a bright green
and display the wavelength and intensity of the cursor position. To move the cursor,
click on the left most of the 3 buttons below the right-hand corner of the spectrum graph.
You can then drag the cursor to a new position.
Spectrum display options:
 The right button (in the 3-button group below the right corner of the spectrum graph) changes
your mouse pointer to a hand that allows you to drag the spectrum graph left, right, up, and
down providing you do not have the entire graph showing.
 The centre button (in the 3-button group
below the right corner of the spectrum graph)
opens up a menu of 6 buttons. (See Fig. A1.9)
 The lower left button will adjust the
spectrum graph so that the highest peaks will be
almost the full height of the graph. This button
should be pressed right after you start taking a
spectrum in order to fit the graph entirely within
the display. If this button is pressed when no
spectrum data is showing, the background noise to
Fig. A1.9: Spectrum Display Options



fill the whole graph. A subsequent spectrum will
be entirely off scale until you press this button
again.
The lower middle and lower right buttons are zoom-in and zoom-out buttons. Experiment with
them to see how they affect the spectrum graph and then press the lower left button to return
to the full spectrum graph.
The upper left button allows you to select a rectangular region of the spectrum graph to display.
The upper middle button allows you to select a certain range of wavelengths and the upper right
button allows you to select a certain range of intensities to display.
Again to return to a full spectrum display, click the lower left button.
The graph can be exported to your computer by selecting “Graph Image” and
clicking on Export. You can then paste it into your document (spreadsheet, wordprocessor, etc) as
required. Similarly if
spectrum can be exported to your document.
“Graph Data” is selected, the numeric data for your
To tell what wavelength a bright line is on click on the middle button in the group
at the lower right corner of the spectrum graph and then select the top middle button from the menu
that appears. You can now drag the cursor from just left of a spike to just right of a spike. When you
release the mouse button the display will zoom in to include the domain you selected. It will look
something like:
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Figure A1.10: zoomed in on a ‘bright’ spectral line
Now it is easy to tell that this bright line (spike) occurred between 588 and 589 nm, so you would
probably report this example as a bright line at approximately 588.5 nm.
To determine the wavelength of other bright lines you would then go back to the full spectrum by
pressing the lower left button in the spectrum display options and then use the same method to select
the next spike and find its wavelength. It would probably be best to work from left to right (which is
from shortest to longest wavelength) or from right to left so an important bright line is not missed.
Wrapping up the experimental session
Finally, when your turn is over, make sure you right-click on the VI and select “Release the VI”. .
(Reminder - Do not release the VI until the Spectrum Status reads ‘Ready’!) Other group participants will
not be able to get control of the spectrometer until the VI is released.
A few pointers:
 In the emission spectrum graph, bright lines have the tallest spikes and not so bright lines will
have shorter spikes. There is background ‘noise’ that makes the lower jagged line along the
bottom. You are interested in the bright lines that are more intense than the background noise.
 You must start their spreadsheet or Word document before collecting data so that the
document is ready to accept data for recording while the experiment is in progress.
 A lot of data is generated for each spectrum, so you must be sure to leave room in your
documents or better yet save your data into a special document meant for your raw data. Then
you can copy and paste from this document into your lab report as required.
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Appendix 2: SPECTRAL LINES OF COMMON ELEMENTS IN AIR
Excerpted from Section 10 of Handbook of Chemistry and Physics 72nd ed., section written by J. Reader & C.
Corliss of the National Bureau of Standards.
Spectral lines given are taken in air over a visual wavelength of
4000 to 8000 angstroms for neutral and singly ionized atoms.
ionized.
P stands for perturbed by a close line.
Where State I is neutral, state II is singly
Intensity is a linear estimate of relative line brightness.
All Measurements here are given in Angstroms (Å) so you will have to divide by 10 to get nanometres (nm).
HYDROGEN (H Type I)
Inten Wavelength State
15
30
80
120
180
4101.74
4340.47
4861.33
6562.72
6562.852
I
I
I
I
I
HELIUM (He I and II)
Inten Wavelength State
50
12
200
25
30
30
20
100
500
100
100
200
30
50
4026.191
4120.82
4471.479
4471.68
4685.7
4713.146
4921.931
5015.678
5875.62
5875.97
6678.15
7065.19
7065.71
7281.35
I
I
I
I
II
I
I
I
I
I
I
I
I
I
MERCURY Hg I and II (natural)
Inten Wavelength State
1800
150
40
250
400
4000
100
90
80
80
20
40
100
20
20
60
30
1100
30
160
240
100
280
140
60
60
20
20
1000
30
80
160
250
250
200
40
100
20
100
4046.56
4077.83
4108.05
4339.22
4347.49
4358.33
4398.62
4660.28
4855.72
4916.07
5102.70
5120.64
5128.45
5137.94
5290.74
5354.05
5384.63
5460.74
5549.63
5675.86
5769.60
5789.66
5790.66
5803.78
5859.25
5871.73
5871.98
6072.72
6149.50
6234.40
6521.13
6716.43
6907.52
7081.90
7091.86
7346.37
7485.87
7728.82
7944.66
I
I
I
I
I
I
II
II
II
I
I
I
II
I
I
I
I
I
I
I
I
I
I
I
I
II
I
I
II
I
II
I
I
I
I
II
II
I
II
NEON (Ne) Ne I and II
Inten Wavelength State
SODIUM (Na I and II)
Inten Wavelength State
150
100
120
120
70
150
100
200
150
150
100
100
100
100
150
150
120
100
100
15
15
25
20
60
80
40
500
100
100
60
60
100
100
100
120
80
100
100
80
60
100
120
250
150
150
60
100
120
200
150
60
150
70
90
20
100
90
100
50
80
100
150
150
100
150
40
90
100
150
80
60
100
120
300
120
400
700
2000
2000
300
250
250
250
20
250
250
250
250
250
30
40
250
250
200
200
200
40
250
60
200
200
200
200
200
200
200
200
200
200
200
60
100
200
200
200
200
200
200
160
120
200
160
160
160
30
160
100
200
400
40
80
100
80
70
90
280
70
560
80000
40000
120
240
60
70
70
80
80
70
70
90
80
130
130
130
80
20
50
25
4400
800
8800
P
P
P
P
4219.74
4233.85
4250.65
4369.86
4379.40
4379.55
4385.06
4391.99
4397.99
4409.30
4413.22
4421.39
4428.52
4428.63
4430.90
4430.94
4457.05
4522.72
4569.06
4704.395
4715.347
5330.778
5341.094
5400.562
5764.419
5820.156
5852.488
5872.828
5881.895
5902.462
5906.429
5944.834
5965.471
5974.627
5975.534
5987.907
6029.997
6074.338
6096.163
6128.450
6143.063
6163.594
6182.146
6217.281
6266.495
6304.789
6334.428
6382.992
6402.246
6506.528
6532.882
6598.953
6652.093
6678.276
6717.043
6929.467
7024.050
7032.413
7051.292
7059.107
7173.938
7213.20
7235.19
7245.167
7343.94
7472.439
7488.871
7492.10
7522.82
7535.774
7544.044
7724.628
7740.74
7839.055
7926.20
7927.118
7936.996
7943.181
8082.458
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4113.70
4123.08
4233.26
4240.90
4276.79
4292.48
4292.86
4308.81
4309.04
4320.91
4321.40
4324.62
4337.29
4344.11
4368.60
4375.22
4387.49
4390.03
4392.81
4393.34
4405.12
4446.70
4447.41
4454.74
4455.23
4457.21
4474.63
4478.80
4481.67
4490.15
4490.87
4494.18
4497.66
4499.62
4506.97
4519.21
4524.98
4533.32
4551.53
4590.92
4664.81
4668.56
4722.23
4731.10
4741.67
4751.82
4768.79
4788.79
4978.54
4982.81
5148.83
5153.40
5191.65
5208.55
5400.46
5414.55
5682.63
5688.19
5688.20
5889.95
5895.92
6154.22
6160.74
6175.25
6199.26
6234.68
6260.01
6274.74
6361.15
6366.41
6514.21
6524.68
6530.70
6544.04
6545.75
6552.43
7373.23
7809.78
7810.24
8183.25
8194.79
8194.82
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34
PHYSICS COURSE NAME
LAB x
Appendix 3: Another Treatment Relating to EQ L3.12
By David DeForge, North Island College - Web-based Associate of Science Project
I. Bohr’s Model of Hydrogen
In 1913 Niels Bohr proposed a model of the hydrogen atom that correctly predicted the observed lines
in the spectrum of light emitted by hydrogen. The theory involves a simple application of classical
mechanics to a point electron and nucleus where the interaction is assumed to be the Coulomb force.
He also made the following assumptions that have no classical justification:
1. The hydrogen atom exists in stationary states in which it does not radiate. (Remember that
classical electromagnetism predicts that electrons radiate energy when accelerated in orbits
around a positive nucleus. This cannot be the case for electrons in an atom.)
2. The orbital angular momentum of the electron is quantized: l  nh where n is an integer and
h
h
34
, h  6.626  10 J  s
2
3. Radiation occurs only when an atom makes a transition from a higher energy state Ei to a
lower energy state E f such that hf  Ei  E f where f is the frequency of the light emitted.
These assumptions led Bohr to predict the following allowed energy states of the simple hydrogen atom:
me4 1
13.6 eV
En   2 2 2  
8 0 h n
n2
(2)
where m is the mass of electron (9.11 × 10-31 kg), e is the charge of the electron (1.60 × 10-19 C), o is the
permittivity constant (8.85 × 10-12 C/V-m), h = Planck’s constant (6.63 × 10-34 joule sec) and n is the
“principle quantum number”, the natural number indicating the energy state. An electron volt, eV, is a
unit of energy, 1 eV  1.60  10
19
J.
The difference in energy between initial state ni and final state n f is therefore
 1
1 
E  13.6 eV  2  2 
 ni n f 


Creative Commons Attribution 3.0 Unported License
(3)
35
PHYSICS COURSE NAME
LAB x
II. Categories of Transitions between Energy States
The transitions that occur in hydrogen are categorized into series according to the energy state after
transition.

Lyman series: transitions from ni  2, 3, 4, … states to n f  1 state.

Balmer series: transitions from ni  3, 4,5,... states to n f  2 state.

Paschen series: transitions with n f  3 .

Brackett series: transitions with n f  4 .

Pfund series: transitions with n f  5 .
Transitions in the Balmer series cause the emission of radiation in the visible spectrum. Therefore, we
can measure the wavelengths of these emissions with the spectroscope. The Lyman series emissions
are ultraviolet, and the other emissions are infrared. Note that these other transitions are occurring,
but our eyes do not respond to the frequencies of the associated radiation. Other equipment is
necessary to measure their wavelengths.
As mentioned earlier, the energy of an emitted photon is equal to the difference in the energies of the
states before and after the transition, so
E  hf  hc / 
(4)
It is convenient to express these energies in electron-volts rather than in joules, so do the following
exercises.
Exercise: Calculate hc in eV-nm rather than in J-m so that you can work directly in electron-volts and
nanometers. The resulting formula for E in terms of  should appear in your report.
Exercise: Also, complete the following table of values of E (in eV) using equation (3). Do this before
you begin the experiment, and check with your instructor that the table has been filled correctly.
Initial State
1
2
Final State
3
1
2
0
10.2
3
4
5
6
0
0
4
5
6
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0
0
0
36
PHYSICS COURSE NAME
LAB x
Each row corresponds to a series of spectral lines. In your report, write the appropriate name of the
series to the right of each row in the table.
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37