Physics Laboratory Report on
Spectroscopy
J. Shapiro and K. Shpund
Hebrew University of Jerusalem
Racah Institute for Physics
March 27th, 2007 – editio princeps
May 27th, 2007 – revised edition
Abstract
What follows is a brief review of the spectroscopy field with its
very basic theory. We then move on to describing an experiment
performed as part of the third-year undergraduate physics laboratory
course under the guidance of Prof. Jochannan Burde. The description
is followed by a presentation of the results and a discussion.
1
Contents
1 Introduction
1.1 Bohr’s Model for the Atom . . . . . . . . . . .
1.2 Alkali Elements and the Spectrum of Sodium .
1.3 Light Sources - Sodium and Mercury Lamps .
1.4 The Spectroscope . . . . . . . . . . . . . . . .
1.4.1 Grating Spectrometer . . . . . . . . . .
1.4.2 Prism Spectroscope . . . . . . . . . . .
1.5 Spectral Series . . . . . . . . . . . . . . . . . .
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3
4
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5
5
2 Apparatus
6
3 Method
8
4 Results
4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Measuring the spectrum of Mercury with two different filters
4.3 Measuring of Tungsten Temeprature with a Pyrometer . . .
4.4 Trying to measuring the spectrum of Tungsten . . . . . . . .
4.5 Measuring transmission and reflection with filters . . . . . .
4.6 Measuring the spectrum of Sodium in a glass lamps . . . . .
4.7 Measuring the spectrum of Sodium in a lamp without glass .
5 Discussion
5.1 Gauging Session . . . . . . . . . . . .
5.2 Mercury Filtered . . . . . . . . . . .
5.3 Tungsten . . . . . . . . . . . . . . . .
5.4 Filtered Tungsten . . . . . . . . . . .
5.5 Sodium Encompassed With Glass . .
5.6 Sodium Without Glass Encompassing
2
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1
Introduction
A quantum system such as an atom can only be found in discrete energy
levels. The system may lose energy by emitting a photon as it descends from
one higher energy state, to a lower one. Thermal or electrical excitation of
atoms results in photon releasing. It is possible to measure a spectrum of
these photons and thus find out about the energy states of the atoms, using
the following formula:
En − En0 = hν
(1)
Where En and En0 are the two energy states which the atom moves to and
from, h = 6.626068 × 10−34 m2 kg/s is Planck’s constant, and ν is the frequency of the electromagnetic wave (or photon) that is emitted.
1.1
Bohr’s Model for the Atom
The basic assumptions standing as the foundations for Bohr’s model of the
atom are:
• Electrons orbit the nucleus of the atom at discrete values of angularmomentum, L = n~, where n ∈ Z.
• The atom does not radiate unless one (or more) of its electrons transcends from one energy level to another.
• The interaction between the electrons and the nucleus is of Coulomblike nature.
Based on these assumptions, Bohr calculated the energy levels of the Hydrogen atom. The result matched the empirical data ”like a glove”. Using
Kepler’s laws for orbital motion between two bodies, we can derive the following formula for the energy differences between two states:
!
1
1
− 2
(2)
∆Ei,f = hcR
2
nf
ni
Where R = 10973731.6m−1 is Rydberg’s constant. For other atoms, this
theory does not hold.
3
1.2
Alkali Elements and the Spectrum of Sodium
The Sodium1 atom has a total of eleven electrons. They are configured
in two closed shells (one containing 2 electrons and acting effectively as a
Helium atom, the other contains all together 10 electrons and acts effectively
as a Neon atom) and one valence electron. Its energy at the lowest level is
marked by n = 3. The electron’s potential is in essence that of the positive
nucleus, subtracting the screening of the other 10 negative electrons in the
way. Due to this fact, the potential is no longer Coulomb-like in nature,
and thus the energy depends on the angular momentum of the electron as
well. It could be explained by the fact that larger angular momentum means
bigger radius for the electron around the nucleus and thus different screening.
Effectively, the valence electron ”feels” a potential similar to that of the
electron in the Hydrogen-atom. For this reason, we would expect Bohr’s
theory to predict the energy levels of the valence electrons, with the accuracy
of small perturbations.
The energy of the valence electron in Sodium depends on two quantum
numbers - n and l - and is given by:
1
(3)
En,l = −RN a · h · c ·
[n − ∆ (n, l)]
Here, RN a is Rydberg’s constant for Sodium, and ∆ (n, l) is the quantum
defect corresponding to the quantum numbers n and l. It increases as l
decreases and the screening rises. Allowed energy transitions are those where
∆l ± 1.
1.3
Light Sources - Sodium and Mercury Lamps
The Sodium and Mercury lamps contain gas in low pressure. Using electric
current, energy is passed on to the atoms of the gas, which in turn emit
photons in a spectrum characteristic to the gas’ material. The radiation –
the photons – passed through glass. Worth mentioning is the fact that there
is chemical interaction between the SiO2 glass and the N a vapor – destroying
the SiO2 envelope – which by iself is transparent to the U.V. light. The glass
used is saturated with N a (SiO2 + N a) and is not transparent to the U.V.
radiation.
Contrary to that, in Mercury the glass does not absorb such frequencies.
1
Also known as Natrium, the latin name, or Natran.
4
1.4
The Spectroscope
This is an instrument capable of determining which wavelengths exist in a
given input light. There are different kinds of spectrometers which all do the
same but using different methods.
1.4.1
Grating Spectrometer
The grating causes diffraction of light, which is given by the following formula:
"
#2
sin πNλ lθ
2
(4)
|I (θ)| =
sin πlθ
λ
Where I is the light intensity, θ is the angle from the center of the light
source, N is the number of lines, and the gap between them is l. In order
to get local maximal intensity, θ must obey [sin(i) ± sin(θ)] × l = mλ where
m ∈ Z, i is the angle of incidence and θ is the angle of reflection. For every
wavelength, θmaximum is different. Thus we may expect different locations for
different wavelengths.
1.4.2
Prism Spectroscope
The light passes through the prism and is dispersed due to difference in
refraction index – according to Snell’s law. Since the refractive index depends on the wavelength, we get different dispersion between the different
wavelengths.
1.5
Spectral Series
The most striking regularity in the spectra of many atoms is the classification
of the spectral lines into series. The complexity of the atomic spectrum
increases as the number of the electrons involved in it rises. However, the
number of electorns involved needs not be the total number of electorns in
the atom. In the case of the Sodium, all of the ten electrons of the closed
shell maintain a constant set of quantum numbers (and thus energy levels)
regardless of changes in the quantum numbers of the outermost electron that
exceeds the quota of the shell. The series found in the spectrum of Sodium
5
is similar to the Hydrogen series and followes the general equation of
1
1
−
vij = R
(i + C1 )2 (j + C2 )2
(5)
. Here vij is the frequency of a line in the series, a so-called series number; R
is the Rydberg constant; C1 and C2 are constants for the entire series; i and
j denote the two energy levels the outer electron moves from and to.
Using the orbital picture we can explain the change of the constants.
At big values of the l index the electron is in a non-circular orbit, thus it
penetrates the inner shells and the energy changes.
The energy level for n = 3, 4, 5, ... and l = 0 is
W =
−RN a hc
(n − 1.35)2
(6)
−RN a hc
(n − 0.87)2
(7)
−RN a hc
(n − 0.01)2
(8)
When l = 1, the expression is
W =
When l = 2, the expression is
W =
When l = 3 or greater, the expression is
W =
2
−RN a hc
n2
Apparatus
We used the following instrumentation in our experiment:
• Sodium lamp encompassed by glass.
• Sodium lamp not encompassed by glass – electric arc.
• Mercury lamp.
• Tungsten lamp.
6
(9)
Figure 1: Oceanoptics HR4000 Composite-Grating Spectrometer with a
CCD detector.
• A personal computer – PC.
• Pyrometer – measures temperature of radiating source.
• Optical filters.
• The instructor – Prof. J. Barda.
• Composite-Grating Spectrometer, which connects to the PC - HR4000CG.
See Figure
7
3
Method
The experiment consisted of the following stages:
1. Calibrating the whole measurement system using a Mercury lamp as
the radiation source.
2. Measuring the spectrum of Mercury with two different filters.
3. Measuring the temperature of Tungsten wire using a pyrometer.
4. Measuring the spectrum of Tungsten.
5. Measuring transmission and reflection with filters.
6. Measuring the spectrum of Sodium in a glass lamp.
7. Measuring the spectrum of Sodium on an arc lamp.
Each stage meant turning on the PC, loading the capturing software
that talks to the spectrometer – OceanOptics SpectraSuite – and setting
the various parameters (exposure time, integration time, et cetera). Then
we would start the capturing process in the computer, and have the task of
setting up the physical light source in front of the spectrometer left.
4
Results
4.1
Calibration
As Figure 2 depicts, the initial gauging session with the Mercury lamp were
not that far off from the literature. Table 1 summarises the offsets2 .
4.2
Measuring the spectrum of Mercury with two different filters
We used two kinds of filters for this section. However, first we made a
measurement with no filters at all and only a lens3 . This result is shown
2
Note that we have found more peaks (see Figure 2 - the peaks without arrows). These
peaks are either second order spectra or noble gases used to start the discharge in the
lamp – Ar.
3
The lens was a pure SiO2 (Quartz) lens.
8
Figure 2: Our results for the gauge-stage with a Mercury lamp. The wavelengths pointed by the arrows are those identified by the data from Jenkins
& White’s book[1].
3 6 5 .1 4 n m
3 6 6 .5 5 n m
4 0 4 .6 5 n m
5 7 7 .1 6 n m
4 3 5 .8 9 n m
1 8 0 0 0
5 4 6 .1 6 n m
2 5 5 .8 n m
1 6 0 0 0
5 7 9 .2 1 n m
1 4 0 0 0
C o u n ts
1 2 0 0 0
3 1 3 .3 3 n m
1 0 0 0 0
4 9 1 .8 1 n m
8 0 0 0
2 9 6 .9 6 n m
6 0 0 0
4 0 7 .9 6 n m
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
9
6 0 0
7 0 0
Table 1: Offsets between our gauge session and the data from the
literature[1].
Our Experiment (nm) Jenkins & White, Ch. 21,
Prof. B.†(nm)
255.8
233.65†
296.96
N/A
313.33
N/A
365.14
365.01†
366.55
366.3†
404.65
404.656
407.96
407.781
435.89
435.835
491.81
491.604
546.16
546.074
577.16
576.959
579.21
579.065
in Figure 3. Then we introduced the two filters into the measurment. We
measured the spectrum with no angles, that is, only at angle of zero degrees.
The results for the two filters are depcited in Figure 4 and Figure 5.
4.3
Measuring of Tungsten Temeprature with a Pyrometer
Our instructor showed us how to make the measurements with the pyrometer.
We took the tungsten lamp and directed it at the pyrometer, which revealed
that its temeprature is 2000◦ ± 10◦ Celsius.
4.4
Trying to measuring the spectrum of Tungsten
We measured what we thought was the spectrum of tungsten. Our results
are shown in Figure 6. It would seem the range of our measuring device is
not capable of sampling the full spectrum of Tungsten.
10
Figure 3: Mercury spectrum with a lens and no filters.
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
11
6 0 0
7 0 0
Figure 4: Mercury spectrum with a lens and a blue filter which cuts off UV.
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
12
6 0 0
7 0 0
Figure 5: Mercury spectrum with a lens and a filter made of glass and iron.
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
13
6 0 0
7 0 0
Figure 6: Distorted Tungsten lamp spectrum (not the real one, the right
side is limited by the sensetivity of the measuring system). The peak is at
551.54nm.
1 4 0 0 0
1 2 0 0 0
C o u n ts
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
14
6 0 0
7 0 0
Figure 7: Tungsten lamp spectrum with blue and yellow filters. We put the
filters at different angles, for transmission, and at 45 degrees for reflection.
0 d e
4 5 d
4 5 d
4 5 d
1 3 5
1 8 0
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
g re
e g r
e g r
e g r
d e g
d e g
e s
e e s
e e s
e e s
re e
re e
( b lu e r e fle c tio n )
( y e llo w r e fle c tio n )
s
s
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
6 0 0
7 0 0
W a v e le n g th ( n a n o m e te r )
4.5
Measuring transmission and reflection with filters
We took blue and yellow interference filters that were given to us and checked
how they affected the spectrum of the tungsten at different angles. The
results are depicted in Figure 7.
4.6
Measuring the spectrum of Sodium in a glass lamps
In this section, we measured the spectrum of the Sodium’s lamp which was
encompassed in glass, at different exposure times and distances from the
spectroscope. The fact the Sodium was encompassed in glass meant that it
cut off the UV wavelengths. The results of each measurement are shown in
Figures 8, 9, 10, 11, and 12. We were interested in how the spectrum of
15
Figure 8: A test spectrum of Sodium with glass lamp.
1 8 0 0 0
1 s e c e x p o s u re
te s t
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
6 0 0
7 0 0
W a v e le n g th ( n a n o m e te r )
the lamp was beint built up, considering the fact that inside the lamp there
is also a gaseous matter which also contributes to the spectrum. Thus we
measured different exposure times, and also at different intervals from when
were lit up the lamp.
16
Figure 9: Spectrum of Sodium with glass lamp at exposure of 1 second and
distances of 3 and 6.3 centimeters. This measurement was done after waiting
until the lamp arrived to a steady state in which its colors weren’t changing.
1 s e c - 3 c m
1 s e c - 6 .3 c m
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
17
6 0 0
7 0 0
Figure 10: Spectrum of Sodium with glass lamp at exposure of 5 seconds
and distances of 3 and 6.3 centimeters. This measurement was done after
waiting until the lamp arrived to a steady state in which its colors weren’t
changing.
5 s e c -3 c m
5 s e c -6 .3 c m
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
18
6 0 0
7 0 0
Figure 11: Spectrum of Sodium with glass lamp at exposure of 10 seconds
and distance of 12.2 centimeters. This measurement was done after 0 and 10
seconds from the time we turned on the lamp.
1 0 s e c -0 s e c -1 2 .2
1 0 s e c -1 0 s e c 1 2 .2
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
19
6 0 0
7 0 0
Figure 12: Spectrum of Sodium with glass lamp at exposure of 20 and 130
seconds and distance of 12.2 centimeters. This measurement was done after
0 seconds from the time we turned on the lamp.
1 8 0 0 0
1 6 0 0 0
2 0 s e c \0 s e c \1 2 .2 c m
1 3 0 s e c \0 s e c \1 2 .2 c m
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
20
6 0 0
7 0 0
Table 2: The Series Spectrum of Sodium with Glass Experiment. The ∗5s →
3p and ∗7s → 3p transitions appear twice due to the spin being either 3/2
or 1/2.
Experiment (aangstroem) Theory (aangstroem) Transition
5920
5895
3p → 3s
3310
3303
4p → 3s
2670
2680
6p → 3s
5680
5688
4d → 3p
4970
4978
5d → 3p
4660
4668
6d → 3p
4490
4497
7d → 3p
6150
6160 ∗5s → 3p
6280
6154 ∗5s → 3p
5140
5148
6s → 3p
4760
4748 ∗7s → 3p
4790
4751 ∗7s → 3p
Table 3: The Series Spectrum of Sodium without Glass Experiment.
Experiment (aangstroem) Theory (aangstroem) Transition of states
3300
3303
4p → 3s
5930
5890
3p → 3s
4350
4497
7d → 3p
4980
4982
5d → 3p
5680
5688
4d → 3p
6170
6160
5s → 3p
21
Figure 13: Spectrum of Sodium with no glass. We used no filters. We waited
until the lamp’s color became yellow and then we made the capture of the
spectrum. We could only have it open for a minute or so due to the fact it
would otherwise explode.
1 8 0 0 0
1 6 0 0 0
1 4 0 0 0
C o u n ts
1 2 0 0 0
1 0 0 0 0
8 0 0 0
6 0 0 0
4 0 0 0
2 0 0 0
0
2 0 0
3 0 0
4 0 0
5 0 0
W a v e le n g th ( n a n o m e te r )
22
6 0 0
7 0 0
4.7
5
5.1
Measuring the spectrum of Sodium in a lamp without glass
Discussion
Gauging Session
The gauging pretty much fits the literary values, with some minor offsets
which are well within the resolution of the spectroscope. Adding the lens
removes some of the noise.
5.2
Mercury Filtered
The blue filter cuts off anything below blue, which is UV radiation. However,
it also removes some of the higher-wavelength lines, the ones near 500nm and
425nm.
We can see that glass acts as a UV cut-off, however, the UV that is far
away from the seen-light.
5.3
Tungsten
It is possible to arrive to the peak in the tungsten radiation using Planck’s
formula for black body radiation:
1
2hc2
I = 5 · hc
λ
e λkB T − 1
(10)
If we derive (10) and equate it with zero we can find such λ that would be
the peak. This λ should be the one we found to be the peak in Figure 6.
Due to the fact that this calculation is rather complicated, we used Wien’s
displacement law, which gives a relation between λmax and the temperature:
T λmax = 2.898 × 106 nmK
(11)
When we put in (11) the temperature measured by the pyrometer, we receive that λmax should be 1274.96nm, not quite the figure we had hoped to
receive. We fail to explain this anomaly. This could mean either of two: a)
The tungsten lamp does not act like a black body. b) the pyrometer’s measurement was inaccurate. Due to the fact that we relied on the pyrometer’s
23
measurement (at least enough as not to think it would be wrong by about a
thousand degrees), we assume that the former option is the plausible one –
or it may be that we did something wrong. Another possibility that has been
raised by Prof. B., which rules out the former option, is that the sensetivity
of the spectrometer falls off at the longer wavelengths.
5.4
Filtered Tungsten
The first thing to notice about Figure 7 is that the curve for zero degrees and
180 degrees is the same, until we arrive to the vicinity of 550nm. Then, we
see that the 180 degrees filter starts passing longer wavelengths. De facto,
this is the same filter flipped from its zero degrees orientation. This means
that the filter passes different wavelengths in each side. Also notice that that
the 45 degrees passes more than the 135 degrees filter. This is because the
45 degrees filter must have been oriented toward the other side of the filter.
Finally, we have the reflection filters, which attenuate the intensity. The blue
filter, passes light with longer wavelengths of 400nm, as we would expect for
blue, and the yellow filter’s peak is at approximately 550nm, which is indeed
yellow.
5.5
Sodium Encompassed With Glass
It is apparent from Figure 9 that as the distance from the spectroscope
increases, some of the lines disappear (see the red curve). However, when
we enlarge the exposure time we see that some of these lines come back, as
depicted in Figure 10.
Then we wanted to see the dynamics of the lamp. So we too two measurements, one right after we turned it on, and one 10 seconds later. Figure
11 shows those spectrums. As can be seen, these are two completely different
spectrums. For instance, right when you turn on the lamp, you have a line
at about 325nm which disappears after 10 seconds. We believe this might be
a Mercury line. Also notice how the peak around 600nm becomes thinner.
5.6
Sodium Without Glass Encompassing It
As can be seen in Figure 13, there is no UV cut-off, as we expected.
24
References
[1] Jenkins, F A and White, H E , Fundamentals of Optics, 4E, McGraw-Hill,
1976.
[2] H. Haken and H. C. Wolf, Atomic and Quantum Physics - An introduction to the Fundamentals of Experiment and Theory, 2E, Springer-Verlag
Berlin Heidelberg New York London Paris Tokyo.
[3] Anne P. Thorne, Spectrophysics, 2E, Chapman and Hall.
List of Figures
1
2
3
4
5
6
7
8
9
10
Oceanoptics HR4000 Composite-Grating Spectrometer with
a CCD detector. . . . . . . . . . . . . . . . . . . . . . . . . .
Our results for the gauge-stage with a Mercury lamp. The
wavelengths pointed by the arrows are those identified by the
data from Jenkins & White’s book[1]. . . . . . . . . . . . . .
Mercury spectrum with a lens and no filters. . . . . . . . . .
Mercury spectrum with a lens and a blue filter which cuts off
UV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mercury spectrum with a lens and a filter made of glass and
iron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Distorted Tungsten lamp spectrum (not the real one, the right
side is limited by the sensetivity of the measuring system).
The peak is at 551.54nm. . . . . . . . . . . . . . . . . . . .
Tungsten lamp spectrum with blue and yellow filters. We
put the filters at different angles, for transmission, and at 45
degrees for reflection. . . . . . . . . . . . . . . . . . . . . . .
A test spectrum of Sodium with glass lamp. . . . . . . . . .
Spectrum of Sodium with glass lamp at exposure of 1 second
and distances of 3 and 6.3 centimeters. This measurement was
done after waiting until the lamp arrived to a steady state in
which its colors weren’t changing. . . . . . . . . . . . . . . .
Spectrum of Sodium with glass lamp at exposure of 5 seconds
and distances of 3 and 6.3 centimeters. This measurement was
done after waiting until the lamp arrived to a steady state in
which its colors weren’t changing. . . . . . . . . . . . . . . .
25
.
7
. 9
. 11
. 12
. 13
. 14
. 15
. 16
. 17
. 18
11
12
13
Spectrum of Sodium with glass lamp at exposure of 10 seconds
and distance of 12.2 centimeters. This measurement was done
after 0 and 10 seconds from the time we turned on the lamp. . 19
Spectrum of Sodium with glass lamp at exposure of 20 and 130
seconds and distance of 12.2 centimeters. This measurement
was done after 0 seconds from the time we turned on the lamp. 20
Spectrum of Sodium with no glass. We used no filters. We
waited until the lamp’s color became yellow and then we made
the capture of the spectrum. We could only have it open for
a minute or so due to the fact it would otherwise explode. . . 22
List of Tables
1
2
3
Offsets between our gauge session and the data from the literature[1]. 10
The Series Spectrum of Sodium with Glass Experiment. The
∗5s → 3p and ∗7s → 3p transitions appear twice due to the
spin being either 3/2 or 1/2. . . . . . . . . . . . . . . . . . . . 21
The Series Spectrum of Sodium without Glass Experiment. . . 21
26