Why does the rydberg equation only work for hydrogen

ATOMIC EMISSION SPECTRA

I. PURPOSE In this experiment, you will study different methods co identify substances by analyzing the light they emi t when you apply a great deal of energy to them. You will ob- serve and measure the emission spectra from transitions between quantum state of the electrons in hydrogen and helium gases; then, you will study the flame color of dif- ferent salts and determine which ion is responsible fo r the color of the flame.

II. BACKGROUND The first clear measuremcms of quantum mechanical be- havior were made Joseph von Fraunhofcr in 18 14, roughly I 00 years before they would be explained . Fraunhofer was a m aster optics maker, and in that year he inw nred the spectroscope, using a pinhole and !em to collect sunlight into a narrow beam and a p rism of extraord inarily h igh

precisio n to diffract rhe beam into the rainbow of colo rs observed by Newton. With this apparatus, Fraunhofer found that the spectrum of the sun was dark where certain

colors should have appeared.

The dark bands in the pectrum were determined to be

visible light emitted from the sun's interio r being absorbed

by atoms in the cooler o uter atmosphere. Q uantum me-

chanics requires that the energy of electrons in these at-

oms have only specific values. r n order fo r each atom to absorb light, the energy in one photon of the light must

be precisely equal to the energy needed to get to one of

rhe available higher energy levels. Therefo re, o nly certain

photon energies can be absorbed, and each of the e ener-

gies corresponds ro a speci fic wavelength of light:

E _k phoron - /\, ( 1)

Equation 1 describes the inverse relationship between the

Photon energy (Eh ) and its wavelength (/\,) ; where p oton

70 EXPERIMENT 8

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Planck's (h) constant, is equal to 6.626 X I 0- 34 J,s, the speed of light (c) , is equal to 3.000 X 108 mis.

In the case of atomic hydrogen, the wavelengths absorbed by the atoms satisfy Rydberg's equation:

(2)

Where n1 and n2 must be integers greater than zero, with n2 > n1, and where the Rydberg constant R = 1.096776 X 107 m - 1• This equation with that value of R works only for hydrogen; ocher atoms are more complex and cannot be modeled as easily. As such you should not use this equation for any other substance.

In Parts A & B of the experiment, you will observe the spectrum of two gases: hydro- gen and helium. Unlike Fraunhofer, you will observe the spectra in emission, rather than absorption. That means chat the gas will release energy as the atoms drop from higher energy states to lower energy states. In order to accomplish this, energy muse be put into the atoms, and we do chat by running an electric current through tubes fllled with either gas H2 or He ga . Under these conditions, the molecule H2 does not emit light in the visible range of the spectrum, but the electric current will break some H2 molecules up into H atoms, and they do emit in the visible spectrum. The emissions you will observe from the hydrogen sample will be from atomic hydrogen, not H2 molecules.

You will use two different spectrometers for chis experiment. One is a blue plastic spectrometer (from Project STAR), similar in principle to Fraunhofer's spectroscope, except that this uses a diffraction grating (which diffracts light as the light is reflected, unlike a prism which diffracts the light as it passc:s through the prism). This spectrom- eter will allow you ro directly see the colors of the radiation emitted by individual transition in rhe gas The second spectrometer, made by Ocean Optics, is a more sophisticated devi e, using a fiber optic to collect the radiation and diffract it off a small grating, after which the power at different wavelengths is measured by a charge- coupled device (CCD) detector, and the data sent to a handheld controller with an LCD display. The Ocean Optics spectrometer will allow you to measure the wave- lengths of the transitions more precisely than the Project STAR spectrometer, and will also report the relative intensines of the different transitions.

T he Chinese used the colors emitted from certain salts when strongly heated in fire- works starting as early as 1150 A.O. By the seventeenth century chemists, such as Robert Boyle, identified substances through the colors they emitted when they were inserted into a flame. With the introduction of the blowpipe, a device used to blow air on flames to make them burn hotter, by Cronstadt in the eighteenth century, more minerals yielded flame colors. This led the Swedish chemical group (of which Cronscadt, Scheele, and Bergman were members) to the discovery of several new ele- ments. In Part C, you will study the colors of flames emitted by a number of sales in order to determine which colors are associated with which salts and figure our which ion is responsible for the flame color.

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ATOMIC EMISSION SPECTRA 71

Ill. SAFE TY PRECAUTIONS AND PROPER HAN DLING OF THE EQUIPMENT •

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Safety glasses are always required as long as anyone in the lab is still performing lab- oratory work! For this lab it will be an exception when you are using the Project STAR pectrometer since it will be hard to appreciate the lines using the safery glasses.

An apron or lab coat and closed-toe/closed-heel shoes are required .

No food or drinks in the lab at any time .

Do not move the equipment from the location where they have been set up .

The sockets in the power supply that the tube rests in operate at high voltage (approximately 5 kV). Keep your hands away from the tube and the sockets at all time .

The gas tubes become extremely hot after a few seconds of use. They are also very fragile. Only your TA or stockroom personnel may handle the tubes.

The Ocean Optics spectrometer contains delicate and expensive optics, and the

fiber optic cable contains long glass fibers that will break if the cable is kinked. Please handle these items with care.

Remember ro put your hai r in a bun or ponytail (if short) when using the Bunsen

burner.

Hydrochloric acid is corro ive; handle with care. If exposed to it, rinse right away and notify your TA.

Dispose of all chemicals in the waste bottles in the hood. Do not pour waste down

thedmin.

IV. MATERI ALS AND REAGENTS

QT

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Equipment

Spray bottles

Bunsen burner

Ocean Optics spectrometer (set up on benches)

STAR Spectrometer (check out from your TA)

HAZARDOUS WASTE IS MINIMAL DUE TO CONTAMINATION OF THE

HCI AND DI WATER

Barium Nitrate

Barium Chloride

Calcium Chloride

Copper Chloride

Reagents

Strontium Nitrate

Strontium Chloride

Lithium Chloride

Sodium Chloride

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72 EXPERIMENT 8

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V. EXPERIMENTAL PROCEDURE You will work in pairs on chis experiment; you may start with either Part A or Pare B.

There will be a hydrogen or a helium discharge rube at the different stations around the lab. You will need to share all equipment in this lab with your classmates, so please be considerate and use your time with the equipment efficiently. Read these instruc- tions carefully before making your measurements.

You should make measurements for hydrogen and for helium using both the Ocean Optics spectrometer and the handheld Project STAR spectrometer.

A. PROJECT STAR SPECTROMETER Examine the spectrometer carefully before you begin so that you know where the input aperture is. The light does not come into the spectrometer from the direction your eyes will be pointing, so it can take some practice to line the spectrometer up correctly with the light source you want ro study.

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Figure 8-1 . Project STAR Spectrometer

I . Using the spectrometer, examine the spectrum of the overhead fluorescent lights in the lab. In your laboratory notebook, record the wavelengths that you observe. Next to each wavelength, write what you would call the color of the line ("red," "green," ere.) . If there is a noticeable difference in the intensities, indicate chis by writing "strong," "medium," or "weak" next to the corresponding wavelengths.

2. Now examine the spectra of the hydrogen and helium tubes, and record their wavelengths, colors, and intensities like in step I .

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ATOM IC EMISSION SPECTRA

B. OCEAN OPTICS SPECTROMETER l . Detailed instr11ctions far the set-11p and operation of tlm spectrometer are provided 111

Section VI of this expemnent. Read chose direccions before proceeding wich the experiment. T he specrromecer may already be sec up and running. If not, you will need ro point the fiber opcic carefully at the gas discharge rube located ac che Hation. Even a slight misalignment of the fiber optic may cause the spectrum ro not be recorded, or you may see stray light from other sources appearing in the spectrum.

2. If the room or hood lights are on, you may need ro point the fiber optic at the lights and record the spectrum, co make sure that this radiation is not interferi ng with your analysis of the gases. Label any peaks from these sources in your lab notebook.

3. Record the wavelengths and intensities of the hydrogen and helium gas spectra.

4. When you arc done recording your spectra for both hydrogen and helium, hit the Play key again. Let someone else use the: equipment while you analyze rhe data.

C. FLAME TEST I. You will have a set of solutions in spray bottles containing different ions. A couple

of the solutiom contain the ~ame canon. Create ,1 table with all the reagents' names and a column for observations.

2. Light up the Bunsen burner chat it is already set up.

3. Hold the spray bottle about 20 centimeters away from the flame and aim the solu- tion to be te~1cd at the wp of the flame lO avoid putting the flame out. Observe the color chat the flame emit . If rite flame goes out, be prepared ro relight quick- ly. In berween different solutions, let the fl ame burn off any remnants of previous salts ro avoid contamination. Failure ro do so will result in colors mixi ng during evaluation. You will be doing a total of 8 different salts. Record rhe color that is emitted by the flame and indicate rhe molecular formula (or name) of the alt, the cation, or rhe anion chat is responsible for the flame color.

4. When you are done, rurn off the Bunsen burner and be sure chat there is not an excess of solution around the bench. Check rhat each sec is complete.

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74 EXPERIMENT 8

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VI. DETAILED INSTRUCTIONS FOR OCEAN OPTICS SPECTROMETERS The Ocean Optics spectrometer is assembled as sketched in the diagram in Figure 8-2. Connect all of the cables before plugging in or powering on the GLX, or else it may not recognize chat it is connected co the spectrometer.

Ocean Optics Spectrometer

USB Cable

AC Power

Pasco GLX Readout

Gas Tube and Power Supply

AC Power

Figure 8-2. SchemlTtic of the setup for the Oce1Tn Optics Spectrometer

FoJlow the steps below if the GLX readout and discharge tube are not already running.

I . To power 011 the GU<, prt!ss and hold the power button for abour 2 seconds. It wi ll take .1 few more seconds for the GLX to load the spt! rromcter software. The specrromcrer doe!> not have a ,_eparJte power !>Witch. T here !>hould already be a ga mbe in rhe power supply, if so, the discharge rube can be turned 011 with the power :.witch on rhe side of rhe power supply.

ATOMIC EMISSION SPECTRA 75

2- To begin acquiring the spectrum , hit the Home key on the GLX, then Fl. If the bottom half of the screen shows a tab menu (" Integration rime", ere.) hit F4 ro

do. e the menu so the spectrum is displayed on the screen. If rhe display does not eem to change, then it may be on pau e. Press the Play key on the GLX to restart

the graph.

3 . The GLX will display a graph of radiation intensity versus the wavelength. The

x-axis (horizontal) is the radiation wavelength in nm. The radiation intensity is

displayed on rhe y-axis in units of "counts," which is proportional ro rhe number

of photons ar char wavelength reaching the dereccor. You should see a series of

spikes ("peaks") in the graph; each peak indicate that radiation at char wavelength is reaching the spectrometer.

4 . The quality of the spectrum depends on how well che rip of rhe blue fiber optic

lines up with the brightest part of rhe glowing tube. If rhe fiber optic is pointing co the side, the spectrometer will receive less light from rhe gas and more from

surrounding light sources like the room lights or windows. On rhe ocher hand, if the probe is tao clo~e ro rhe tube, rhe crongest peaks in che spectrum will be flat

ar the cop, or "clipped," because the detector of the spectrometer has reached its

maximum output. In that case it is hard to find rhe peak wavelength of the signal,

and you should move the fiber optic tip back away from the rube until rhe signals

arc on ~ca lc. A good spectrum from these gas tube will have several strong, sharp peaks. You should see at least 4 strong transi tions with rhe hydrogen, and ar lease

6 for rhe helium.

5. Once you feel char you have a good spectrum on the GLX display, hit the Play key co freeze it. If you are done with your collection of data you can turn off the

power for the ga rube.

6 . To get the precise wavelength of each transition in the spectrum you have frozen, hit F3 ("Tools") , select the "Smart Tool," and hit the Check key. This puts a cursor on the spectrum. Use the right/ left arrow key ro move the cursor along

the spectrum. Note that the up/down arrows will jump you to either end of the

graph. The movement of rhe cursor can be frustrating because it will overshoot

if you hold the key for roo long. Please be patient. The x-axis and y-axis values

will be written to the display as the cursor moves. For the most intense peaks in

each spectrum (at lease 4 and no more than 10 for each spectrum), record the

wavelength at the maximum of each peak into your laboratory notebook. (If any of the signals arc still clipped, try ro find the cenrer of the flat region and use chat

for your wavelength.)

7 . When you are done recording your spectra for both hydrogen and helium, hit the

Play key again. Let someone else use the equipment while you analyze the data.

8 . If the room or hood lights are on, you may need to point the fiber optic at rhe

lighn, and record the spectrum, ro make sure that chis radiation is not interfer-

ing with your analys is of the ga\. Label any peaks from these sources in your lab

notebook.

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76 EXPERIMENT 8

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VII. CALCULATION Use the Rydberg equation to assign the upper state quantum numbers for the transitions you observed in hydrogen. Do not try to solve the Rydberg equation fo r helium- it doesn't work. Make a table of the transition wavelengths, intensities, and quantum numbers for the hydrogen spectrum in your laboratory notebook.

VIII. DISCUSSION/QUESTIONS 1. Why does the Rydberg equation work for hydrogen but not for helium?

2. Do you observe any transitions in hydrogen that do not match the wavelengths predicted by the Rydberg equation? If so, what could be their origin?

3. Which spectrum (hydrogen or helium) is more complicated? Why do you think that is?

4. Can you use the values from the Ocean Optics spectrometer to assign precise wavelengths to the transitions that you observed with the STAR spectrometer?

5. Can scientists determine specific elements based off of a spectrum? Why or why not?

6. rind the spectra of the different ions you observed in Part C and explain why one ion was 5ecn and why the ocher ion wa not visible during the flame test. Is the flame color a characteristic properry from your observations?

REFERENCES Chemisrry anJ Biochemistry Department. "Manual for CHEM 200/202." Laboratory

Manual. San Diego tare University. San Diego. 201 3. Print.

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