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.