Physics Laboratory Report onSpectroscopy

J. Shapiro and K. ShpundHebrew University of Jerusalem

Racah Institute for Physics

March 27th, 2007 – editio princepsMay 27th, 2007 – revised edition

Abstract

What follows is a brief review of the spectroscopy field with itsvery basic theory. We then move on to describing an experimentperformed as part of the third-year undergraduate physics laboratorycourse under the guidance of Prof. Jochannan Burde. The descriptionis followed by a presentation of the results and a discussion.

1

Contents

1 Introduction 31.1 Bohr’s Model for the Atom . . . . . . . . . . . . . . . . . . . . 31.2 Alkali Elements and the Spectrum of Sodium . . . . . . . . . . 41.3 Light Sources - Sodium and Mercury Lamps . . . . . . . . . . 41.4 The Spectroscope . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Grating Spectrometer . . . . . . . . . . . . . . . . . . . 51.4.2 Prism Spectroscope . . . . . . . . . . . . . . . . . . . . 5

1.5 Spectral Series . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Apparatus 6

3 Method 8

4 Results 84.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Measuring the spectrum of Mercury with two different filters . 84.3 Measuring of Tungsten Temeprature with a Pyrometer . . . . 104.4 Trying to measuring the spectrum of Tungsten . . . . . . . . . 104.5 Measuring transmission and reflection with filters . . . . . . . 154.6 Measuring the spectrum of Sodium in a glass lamps . . . . . . 154.7 Measuring the spectrum of Sodium in a lamp without glass . . 23

5 Discussion 235.1 Gauging Session . . . . . . . . . . . . . . . . . . . . . . . . . . 235.2 Mercury Filtered . . . . . . . . . . . . . . . . . . . . . . . . . 235.3 Tungsten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.4 Filtered Tungsten . . . . . . . . . . . . . . . . . . . . . . . . . 245.5 Sodium Encompassed With Glass . . . . . . . . . . . . . . . . 245.6 Sodium Without Glass Encompassing It . . . . . . . . . . . . 24

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1 Introduction

A quantum system such as an atom can only be found in discrete energylevels. The system may lose energy by emitting a photon as it descends fromone higher energy state, to a lower one. Thermal or electrical excitation ofatoms results in photon releasing. It is possible to measure a spectrum ofthese photons and thus find out about the energy states of the atoms, usingthe following formula:

En − En′ = hν (1)

Where En and En′ are the two energy states which the atom moves to andfrom, h = 6.626068 × 10−34m2kg/s is Planck’s constant, and ν is the fre-quency 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 theatom are:

• Electrons orbit the nucleus of the atom at discrete values of angular-momentum, L = n~, where n ∈ Z.

• The atom does not radiate unless one (or more) of its electrons tran-scends from one energy level to another.

• The interaction between the electrons and the nucleus is of Coulomb-like nature.

Based on these assumptions, Bohr calculated the energy levels of the Hy-drogen atom. The result matched the empirical data ”like a glove”. UsingKepler’s laws for orbital motion between two bodies, we can derive the fol-lowing formula for the energy differences between two states:

∆Ei,f = hcR

(1

n2f

− 1

n2i

)(2)

Where R = 10973731.6m−1 is Rydberg’s constant. For other atoms, thistheory does not hold.

3

1.2 Alkali Elements and the Spectrum of Sodium

The Sodium1 atom has a total of eleven electrons. They are configuredin two closed shells (one containing 2 electrons and acting effectively as aHelium atom, the other contains all together 10 electrons and acts effectivelyas a Neon atom) and one valence electron. Its energy at the lowest level ismarked by n = 3. The electron’s potential is in essence that of the positivenucleus, subtracting the screening of the other 10 negative electrons in theway. 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 aswell. It could be explained by the fact that larger angular momentum meansbigger radius for the electron around the nucleus and thus different screening.Effectively, the valence electron ”feels” a potential similar to that of theelectron in the Hydrogen-atom. For this reason, we would expect Bohr’stheory to predict the energy levels of the valence electrons, with the accuracyof small perturbations.

The energy of the valence electron in Sodium depends on two quantumnumbers - n and l - and is given by:

En,l = −RNa · h · c ·{

1

[n−∆ (n, l)]

}(3)

Here, RNa is Rydberg’s constant for Sodium, and ∆ (n, l) is the quantumdefect corresponding to the quantum numbers n and l. It increases as ldecreases 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 electriccurrent, energy is passed on to the atoms of the gas, which in turn emitphotons in a spectrum characteristic to the gas’ material. The radiation –the photons – passed through glass. Worth mentioning is the fact that thereis chemical interaction between the SiO2 glass and the Na vapor – destroyingthe SiO2 envelope – which by iself is transparent to the U.V. light. The glassused is saturated with Na (SiO2 + Na) and is not transparent to the U.V.radiation.

Contrary to that, in Mercury the glass does not absorb such frequencies.

1Also known as Natrium, the latin name, or Natran.

4

1.4 The Spectroscope

This is an instrument capable of determining which wavelengths exist in agiven input light. There are different kinds of spectrometers which all do thesame but using different methods.

1.4.1 Grating Spectrometer

The grating causes diffraction of light, which is given by the following for-mula:

|I (θ)|2 =

[sin(

πNlθλ

)sin(

πlθλ

) ]2

(4)

Where I is the light intensity, θ is the angle from the center of the lightsource, N is the number of lines, and the gap between them is l. In orderto get local maximal intensity, θ must obey [sin(i)± sin(θ)]× l = mλ wherem ∈ Z, i is the angle of incidence and θ is the angle of reflection. For everywavelength, θmaximum is different. Thus we may expect different locations fordifferent wavelengths.

1.4.2 Prism Spectroscope

The light passes through the prism and is dispersed due to difference inrefraction index – according to Snell’s law. Since the refractive index de-pends on the wavelength, we get different dispersion between the differentwavelengths.

1.5 Spectral Series

The most striking regularity in the spectra of many atoms is the classificationof the spectral lines into series. The complexity of the atomic spectrumincreases as the number of the electrons involved in it rises. However, thenumber of electorns involved needs not be the total number of electorns inthe atom. In the case of the Sodium, all of the ten electrons of the closedshell maintain a constant set of quantum numbers (and thus energy levels)regardless of changes in the quantum numbers of the outermost electron thatexceeds 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

vij = R

[1

(i + C1)2 −

1

(j + C2)2

](5)

. Here vij is the frequency of a line in the series, a so-called series number; Ris the Rydberg constant ; C1 and C2 are constants for the entire series; i andj 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 itpenetrates the inner shells and the energy changes.

The energy level for n = 3, 4, 5, ... and l = 0 is

W =−RNahc

(n− 1.35)2 (6)

When l = 1, the expression is

W =−RNahc

(n− 0.87)2 (7)

When l = 2, the expression is

W =−RNahc

(n− 0.01)2 (8)

When l = 3 or greater, the expression is

W =−RNahc

n2(9)

2 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

Figure 1: Oceanoptics HR4000 Composite-Grating Spectrometer with aCCD 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 asthe 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 softwarethat talks to the spectrometer – OceanOptics SpectraSuite – and settingthe various parameters (exposure time, integration time, et cetera). Thenwe would start the capturing process in the computer, and have the task ofsetting 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 werenot that far off from the literature. Table 1 summarises the offsets2.

4.2 Measuring the spectrum of Mercury with two dif-ferent filters

We used two kinds of filters for this section. However, first we made ameasurement with no filters at all and only a lens3. This result is shown

2Note that we have found more peaks (see Figure 2 - the peaks without arrows). Thesepeaks are either second order spectra or noble gases used to start the discharge in thelamp – Ar.

3The lens was a pure SiO2 (Quartz) lens.

8

Figure 2: Our results for the gauge-stage with a Mercury lamp. The wave-lengths pointed by the arrows are those identified by the data from Jenkins& White’s book[1].

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

4 3 5 . 8 9 n m 5 4 6 . 1 6 n m5 7 7 . 1 6 n m

5 7 9 . 2 1 n m

4 0 4 . 6 5 n m

4 0 7 . 9 6 n m

4 9 1 . 8 1 n m

3 6 6 . 5 5 n m3 6 5 . 1 4 n m

2 5 5 . 8 n m

2 9 6 . 9 6 n m

3 1 3 . 3 3 n m

9

Table 1: Offsets between our gauge session and the data from theliterature[1].

Our Experiment (nm) Jenkins & White, Ch. 21,Prof. B.†(nm)

255.8 233.65†296.96 N/A313.33 N/A365.14 365.01†366.55 366.3†404.65 404.656407.96 407.781435.89 435.835491.81 491.604546.16 546.074577.16 576.959579.21 579.065

in Figure 3. Then we introduced the two filters into the measurment. Wemeasured 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 Py-rometer

Our instructor showed us how to make the measurements with the pyrometer.We took the tungsten lamp and directed it at the pyrometer, which revealedthat 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 resultsare shown in Figure 6. It would seem the range of our measuring device isnot capable of sampling the full spectrum of Tungsten.

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Figure 3: Mercury spectrum with a lens and no filters.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

11

Figure 4: Mercury spectrum with a lens and a blue filter which cuts off UV.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

12

Figure 5: Mercury spectrum with a lens and a filter made of glass and iron.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

13

Figure 6: Distorted Tungsten lamp spectrum (not the real one, the rightside is limited by the sensetivity of the measuring system). The peak is at551.54nm.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

14

Figure 7: Tungsten lamp spectrum with blue and yellow filters. We put thefilters at different angles, for transmission, and at 45 degrees for reflection.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Cou

nts

W a v e l e n g t h ( n a n o m e t e r )

0 d e g r e e s 4 5 d e g r e e s 4 5 d e g r e e s ( b l u e r e f l e c t i o n ) 4 5 d e g r e e s ( y e l l o w r e f l e c t i o n ) 1 3 5 d e g r e e s 1 8 0 d e g r e e s

4.5 Measuring transmission and reflection with filters

We took blue and yellow interference filters that were given to us and checkedhow they affected the spectrum of the tungsten at different angles. Theresults 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 wasencompassed in glass, at different exposure times and distances from thespectroscope. The fact the Sodium was encompassed in glass meant that itcut off the UV wavelengths. The results of each measurement are shown inFigures 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.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

1 s e c e x p o s u r e t e s t

the lamp was beint built up, considering the fact that inside the lamp thereis also a gaseous matter which also contributes to the spectrum. Thus wemeasured different exposure times, and also at different intervals from whenwere lit up the lamp.

16

Figure 9: Spectrum of Sodium with glass lamp at exposure of 1 second anddistances of 3 and 6.3 centimeters. This measurement was done after waitinguntil the lamp arrived to a steady state in which its colors weren’t changing.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

1 s e c - 3 c m 1 s e c - 6 . 3 c m

17

Figure 10: Spectrum of Sodium with glass lamp at exposure of 5 secondsand distances of 3 and 6.3 centimeters. This measurement was done afterwaiting until the lamp arrived to a steady state in which its colors weren’tchanging.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

5 s e c - 3 c m 5 s e c - 6 . 3 c m

18

Figure 11: Spectrum of Sodium with glass lamp at exposure of 10 secondsand distance of 12.2 centimeters. This measurement was done after 0 and 10seconds from the time we turned on the lamp.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

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

19

Figure 12: Spectrum of Sodium with glass lamp at exposure of 20 and 130seconds and distance of 12.2 centimeters. This measurement was done after0 seconds from the time we turned on the lamp.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

2 0 s e c \ 0 s e c \ 1 2 . 2 c m1 3 0 s e c \ 0 s e c \ 1 2 . 2 c m

20

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 3/2or 1/2.

Experiment (aangstroem) Theory (aangstroem) Transition

5920 5895 3p → 3s3310 3303 4p → 3s2670 2680 6p → 3s5680 5688 4d → 3p4970 4978 5d → 3p4660 4668 6d → 3p4490 4497 7d → 3p6150 6160 ∗5s → 3p6280 6154 ∗5s → 3p5140 5148 6s → 3p4760 4748 ∗7s → 3p4790 4751 ∗7s → 3p

Table 3: The Series Spectrum of Sodium without Glass Experiment.Experiment (aangstroem) Theory (aangstroem) Transition of states

3300 3303 4p → 3s5930 5890 3p → 3s4350 4497 7d → 3p4980 4982 5d → 3p5680 5688 4d → 3p6170 6160 5s → 3p

21

Figure 13: Spectrum of Sodium with no glass. We used no filters. We waiteduntil the lamp’s color became yellow and then we made the capture of thespectrum. We could only have it open for a minute or so due to the fact itwould otherwise explode.

2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

Coun

ts

W a v e l e n g t h ( n a n o m e t e r )

22

4.7 Measuring the spectrum of Sodium in a lamp with-out glass

5 Discussion

5.1 Gauging Session

The gauging pretty much fits the literary values, with some minor offsetswhich are well within the resolution of the spectroscope. Adding the lensremoves 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 and425nm.

We can see that glass acts as a UV cut-off, however, the UV that is faraway from the seen-light.

5.3 Tungsten

It is possible to arrive to the peak in the tungsten radiation using Planck’sformula for black body radiation:

I =2hc2

λ5· 1

ehc

λkBT − 1(10)

If we derive (10) and equate it with zero we can find such λ that would bethe 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’sdisplacement law, which gives a relation between λmax and the temperature:

Tλmax = 2.898× 106nmK (11)

When we put in (11) the temperature measured by the pyrometer, we re-ceive that λmax should be 1274.96nm, not quite the figure we had hoped toreceive. 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 mea-surement 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 athousand degrees), we assume that the former option is the plausible one –or it may be that we did something wrong. Another possibility that has beenraised by Prof. B., which rules out the former option, is that the sensetivityof 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 and180 degrees is the same, until we arrive to the vicinity of 550nm. Then, wesee that the 180 degrees filter starts passing longer wavelengths. De facto,this is the same filter flipped from its zero degrees orientation. This meansthat the filter passes different wavelengths in each side. Also notice that thatthe 45 degrees passes more than the 135 degrees filter. This is because the45 degrees filter must have been oriented toward the other side of the filter.Finally, we have the reflection filters, which attenuate the intensity. The bluefilter, passes light with longer wavelengths of 400nm, as we would expect forblue, and the yellow filter’s peak is at approximately 550nm, which is indeedyellow.

5.5 Sodium Encompassed With Glass

It is apparent from Figure 9 that as the distance from the spectroscopeincreases, some of the lines disappear (see the red curve). However, whenwe enlarge the exposure time we see that some of these lines come back, asdepicted in Figure 10.

Then we wanted to see the dynamics of the lamp. So we too two mea-surements, one right after we turned it on, and one 10 seconds later. Figure11 shows those spectrums. As can be seen, these are two completely differentspectrums. For instance, right when you turn on the lamp, you have a lineat about 325nm which disappears after 10 seconds. We believe this might bea 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 introduc-tion to the Fundamentals of Experiment and Theory, 2E, Springer-VerlagBerlin Heidelberg New York London Paris Tokyo.

[3] Anne P. Thorne, Spectrophysics, 2E, Chapman and Hall.

List of Figures

1 Oceanoptics HR4000 Composite-Grating Spectrometer witha CCD detector. . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Our results for the gauge-stage with a Mercury lamp. Thewavelengths pointed by the arrows are those identified by thedata from Jenkins & White’s book[1]. . . . . . . . . . . . . . . 9

3 Mercury spectrum with a lens and no filters. . . . . . . . . . . 114 Mercury spectrum with a lens and a blue filter which cuts off

UV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Mercury spectrum with a lens and a filter made of glass and

iron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 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. . . . . . . . . . . . . . . . . . . . . 14

7 Tungsten lamp spectrum with blue and yellow filters. Weput the filters at different angles, for transmission, and at 45degrees for reflection. . . . . . . . . . . . . . . . . . . . . . . . 15

8 A test spectrum of Sodium with glass lamp. . . . . . . . . . . 169 Spectrum of Sodium with glass lamp at exposure of 1 second

and distances of 3 and 6.3 centimeters. This measurement wasdone after waiting until the lamp arrived to a steady state inwhich its colors weren’t changing. . . . . . . . . . . . . . . . . 17

10 Spectrum of Sodium with glass lamp at exposure of 5 secondsand distances of 3 and 6.3 centimeters. This measurement wasdone after waiting until the lamp arrived to a steady state inwhich its colors weren’t changing. . . . . . . . . . . . . . . . . 18

25

11 Spectrum of Sodium with glass lamp at exposure of 10 secondsand distance of 12.2 centimeters. This measurement was doneafter 0 and 10 seconds from the time we turned on the lamp. . 19

12 Spectrum of Sodium with glass lamp at exposure of 20 and 130seconds and distance of 12.2 centimeters. This measurementwas done after 0 seconds from the time we turned on the lamp. 20

13 Spectrum of Sodium with no glass. We used no filters. Wewaited until the lamp’s color became yellow and then we madethe capture of the spectrum. We could only have it open fora minute or so due to the fact it would otherwise explode. . . 22

List of Tables

1 Offsets between our gauge session and the data from the literature[1]. 102 The Series Spectrum of Sodium with Glass Experiment. The

∗5s → 3p and ∗7s → 3p transitions appear twice due to thespin being either 3/2 or 1/2. . . . . . . . . . . . . . . . . . . . 21

3 The Series Spectrum of Sodium without Glass Experiment. . . 21

26