6: Optical Spectroscopy of Atoms (Experiment)
- Page ID
- 416885
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Hazard Overview
Chemical Hazards
Mechanical Hazards
Dispensary Provided Items
- Spectroscope
- 1 test tube rack
- Forceps
- 5 disposable test tubes
- Sharpie
- 6 nichrome wires
- Unknown (1/student)
Introduction
The most important evidence for quantization or discrete energy levels comes from the analysis of spectra, namely the light emitted or absorbed by atoms and molecules. In this experiment, you will observe and assign part of the emission spectrum of electronically excited hydrogen atoms. You will also observe the emission of light by several other excited gaseous species, and the absorption of light by a colored species in solution.
When the light emitted or absorbed by gaseous atoms is dispersed by a prism or grating, it is found to consist of discrete lines having characteristic colors or wavelengths, \( \lambda \). These \( \lambda \)'s correspond to the energy differences between the quantized energy states of the atom. The relationship between the energy, \( E \), of a light quantum or photon and its frequency or wavelength, \( \lambda \), is given by:
\[ E = h\nu = \frac{h c}{\lambda} \]
where \( h = 6.6206076 \times 10^{-34} \space J s \) is Planck's constant and \( c = 2.99792458 \times 10^8 \space m/s \) is the speed of light. Thus, the energy differences between the quantized states of an atom are readily determined experimentally by measurement of the wavelengths of its emitted light. We will consider two cases in more detail.
The simplest atom is hydrogen. As might be expected, it has the simplest energy level diagram and the simplest spectrum. The electronic energy levels, \( E_n \), of the hydrogen atom, from either primitive Bohr theory or the quantum theory, are given by
\[ E_n = \frac{-C}{n^2} \]
where \( n \) is the principal quantum number and \( C \) is a collection of constants. The quantum number, \( n \), can assume any positive integer value from one to infinity, with the value of infinity corresponding to the separated proton and electron and to an energy of zero. The energy difference between the two states of the hydrogen atom becomes:
\[ \delta E = E_i - E_f = C\left( \frac{1}{n_f^2} - \frac{1}{n_i^2}\right) \]
where \( n_i > n_f \). When the hydrogen atom undergoes a transition from a higher-lying initial state with \( n_i \) to a lower-lying final state with \( n_f \), the energy given by Equation \(\PageIndex{3}\) is liberated and appears as light. Using Equations \(\PageIndex{1}\) and \(\PageIndex{3}\), the wavelength of the emitted light is given by:
\[ \frac{1}{\lambda} = \frac{C}{hc} \left[\frac{1}{n_f^2} - \frac{1}{n_i^2}\right] = R_H \left[\frac{1}{n_f^2} - \frac{1}{n_i^2}\right] \]
where \( R_H \) is the Rydberg constant. Different spectral series result from Equation \(\PageIndex{4}\) if \( n_f \) remains fixed while \( n_i \) varies from \( n_f + 1 \) to infinity. These series are named after the scientists who discovered them: Lyman for \( n_f \) = 1, Balmer for \( n_f \) = 2, Paschen for \( n_f \) = 3, and Brackett for \( n_f \) = 4. Figure \(\PageIndex{1}\) shows a schematic energy level diagram for the hydrogen atom and the transitions associated with some of the spectral series. Each series occurs in a particular wavelength range.
The emission spectrum of the hydrogen atom can be generated by running a high-voltage discharge through a tube that contains gaseous hydrogen molecules. In the discharge, hydrogen molecules are knocked apart by bombardment with energetic electrons. The fragments contain electronically excited hydrogen atoms which can emit light as they relax to lower energy states and ultimately to the ground state. The discharge lamp is designed to maximize the emission of light by excited hydrogen atoms. This requires that the rate of recombination of excited atoms is not too fast. Two colliding atoms cannot recombine to form a stable molecule unless a third body is also present to carry away any excess energy. At the low pressure (about 1 Torr = 0.00131 atm = 0.132 kPa) in the discharge tube, such three-body collisions are sufficiently infrequent in the gas phase that most of the recombination occurs at the wall, which serves as the third body. Since water inhibits hydrogen-atom recombination on glass, a small amount of water has been added to the discharge tube to help maintain a high concentration of hydrogen atoms. Discharge lamps that emit atomic spectra are available commercially for a variety of atoms that can be generated from gaseous precursors.
The energy level diagrams and spectra of many-electron atoms are more complicated. The major reason for this is that the energies now depend on both the principal quantum number, \( n \), and the angular momentum quantum number, \( l \). Additional complications result if the electronic configuration involves a partially filled subshell with several electrons since different occupations and spins for the electrons within the subshell lead to states of different energies (Hund's rules). We will consider the lithium atom, which has the simple ground-state electron configuration of ls\(^2\)2s\(^1\). The lower-lying excited states of lithium result from the promotion of the 2s valence electron to the higher energy orbitals.
Not all possible transitions between the energy levels of an atom can occur through the absorption or emission of light. Rather, selection rules operate and limit the allowed transitions to those wherein \( \Delta l = \pm 1 \). For example, the 2s – 2p transition is allowed (\( \Delta l = \pm 1 \)), whereas the 2s – 3s transition is forbidden (\( \Delta l = \pm 0 \)). Since the energies in the hydrogen atom depend only on \( n \), with the possible values of \( l \) having the same energies for a given \( n \), the \( \Delta l = \pm 1 \) selection rule is not apparent in the spectrum of the hydrogen atom. The relative intensities of the spectral lines in the emission spectrum of lithium depend on the relative concentrations of lithium atoms whose valence electron has been excited to the various higher energy orbitals.
The atomic spectrum of most metallic elements cannot be obtained using a simple discharge tube, since most metals have too low a vapor pressure to support a discharge. Mercury is a notable exception. Conventional fluorescent lamps involve a discharge through mercury vapor. The light emitted by excited mercury atoms is absorbed by a phosphor that coats the inside wall of the fluorescent lamp. The absorbed light excites the phosphor, which then emits light. The solid phosphor acts to convert the discrete line spectrum emitted by the gaseous mercury atoms into a broad band of "white" light. Part of the mercury line spectrum does escape the fluorescent tube. This is readily seen by viewing a fluorescent light with a simple spectroscope. Non-discharge type lamps, and other means of excitation, can be used to observe the atomic spectra of other metals.
You will generate excited alkali and alkaline earth metal atoms using the heat of a Bunsen burner flame. When certain metal salts are heated in a flame, the salts vaporize and dissociate. Gaseous metal atoms in excited states are formed by the reduction in the flame of the metal cation to the metal. In the case of lithium, the only excited atoms present in sufficient concentration for visual detection of their emission in the flame are those whose valence electron is in a 2p orbital. Hence, only the line at 671 nm, which corresponds to the allowed 2s – 2p transition, is seen. Similarly, only select lines are seen for the other metal atoms that you will investigate using a flame source. This is due in part to the relatively low temperature of the Bunsen burner flame, and in part to the transmission properties of the grating in the spectroscope and the sensitivity of the eye. Other lines can be recorded using spectrophotometers together with alternate means of excitation.
Experimental Procedure
Mercury Spectrum
You will first measure the wavelengths of several of the emission lines from excited mercury atoms in the fluorescent lights in the lab. Aim a spectroscope at a fluorescent light. You should see three or four lines on top of the continuous "white" background emission from the phosphor. The colors of these lines are violet, blue, green, and yellow. You may not be able to observe the violet line above the continuous background, since it is weak and at the edge of the visible range. Record the wavelengths of each of the observed lines. After you are comfortable with the use of a spectroscope, and determining the wavelengths of any observed lines, the remaining three parts of this experiment can be done in any order.
Flame Spectra
The emission from other excited metal atoms will be observed using a Bunsen burner as a flame source. Aim the spectroscope so that the hottest part of the flame is just below the bottom of the slit. One of the team members dips a nichrome wire into a solution containing a dissolved salt of the metal and then places the wet wire in the hot part of the flame. A second member observes and records the wavelength(s) of the emitted line(s). The emission of light by the excited metal atoms lasts only for a few seconds until the solution is consumed. Repeated observations will be necessary to measure the exact wavelength(s) for each solution. Look carefully for weak lines in the violet region, since these are easily overlooked.
Label four test tubes (\( \ce{Li+} \), \( \ce{Na+} \), \( \ce{Ca^{2+}} \), \( \ce{Sr^{2+}} \)) and place about one mL of each standard solution in the appropriate test tube. Contamination is a problem, so do not return any solution to the standard bottles. Obtain a length of nichrome wire for each standard and for your unknown. Twist a small spiral loop at one end of each wire and heat the looped end in a Bunsen burner flame until the yellow sodium flame fades. Dip the looped end of the wire in dilute \( \ce{HCl} \) and repeat the heating until no sodium flame is observed. Assign a treated wire to each standard solution and your unknown solutions. Do not exchange these wires during the experiment, or contamination will result. Also, do not place the wire on the bench top; always put the wire back into the solution assigned. Another possible source of contamination in these measurements is the sodium present in the detergent. Do not wash any of the containers with detergent, since the last traces will be virtually impossible to rinse away.
For each solution and wire, the looped end of the wire is dipped into the solution and then placed into the hottest part of the flame. The flame is viewed simultaneously with the spectroscope to measure the wavelength(s) of the emission line(s). Record for each standard solution the color and wavelength of the line(s). Each student then measures
and records the wavelength(s) emitted by his/her unknown and, by comparison with the wavelengths determined for the standard solutions, identifies the metal ion(s) present in his/her unknown.
They are two compounds in your unknown. Do not dispose of any solutions until the unknowns are determined.
Absorption Spectrum of Aqueous \( \ce{Co2+} \)
A source of continuous intensity over a range of wavelengths is needed to observe absorption spectra. The light from this source is transmitted through a sample, and the reduction in intensity of the transmitted light at particular wavelengths recorded. A convenient source of continuous white light is an ordinary tungsten light bulb, which contains an electrically heated tungsten filament that radiates as a near blackbody.
View a tungsten lamp with a spectroscope. You should see the continuous spectrum of visible colors that are emitted by the lamp. Insert a square cuvette containing a stock aqueous solution of \( \ce{Co2+} \) between the tungsten lamp and the spectroscope. A range of wavelengths will be absorbed by the solution. Estimate and record this range by viewing the transmitted light with a spectroscope. Sharp lines are not seen in fluid solution, or for gases at high densities, due in part to the range of perturbations in the energy levels caused by the range of intermolecular interactions (different intermolecular distances and orientations).
Balmer Spectrum of Hydrogen
The emission spectrum of atomic hydrogen in the visible region is measured using a discharge lamp. View the lamp with a spectroscope and record the wavelengths of the emitted lines. You should be able to see three lines (blue-violet, blue-green, and red) with ease. The fourth, the violet line, may require patient adaptation of the eye, since it is close to the edge of the visible range and easily overlooked.
Lab Report
The observed atomic hydrogen lines belong to the same series. From a graphical analysis of the wavelength data, you can obtain the value of the Rydberg constant, \( R_H \), the quantum number of the final state, \( n_f \), involved in all four of the observed transitions, and the four values of the quantum number of the initial state, \( n_i \). Plotting \( \frac{1}{\lambda} \) against \( \frac{1}{n_i^2} \) allows the data to be fit to Equation \(\PageIndex{4}\) with a slope (m) of \( -R_H \) and an intercept (b) of \( \frac{R_H}{n_f^2} \). However, this result will be obtained only for the correct sequence of integer values for \( n_i \).
Be sure to calculate the following for your lab report:
- Report the transition assignments of your hydrogen series, the value of Rydberg constant. To find the correct sequence of \( n_i \)'s, use a spreadsheet to make plots of \( 1/\lambda \) in \( cm^{-1} \) for the four observed lines against \( \frac{1}{n_i^2} \) for the following three trial sets of values: \( n_i \) = 2, 3, 4, 5; \( n_i \) = 3, 4, 5, 6; and \( n_i \) = 4, 5, 6, 7. The wavelengths are associated with the \( n_i \)'s in inverse order for each set of values (red line with the smallest \( n_i \) and violet line with the largest \( n_i \)). The sequence of integers that gives the best straight line gives the correct assignment. Determine the slope of this line by least-squares analysis. Obtain the Rydberg constant in \( cm^{-1} \) from the slope, \( n_f \) (as a floating point number, not an integer) from the values of the slope and intercept, and the standard deviations in both parameters. Round \( n_f \) to an integer and assign integer values of the quantum numbers \( n_i \) and \( n_f \) to each of the observed lines in the hydrogen atom spectrum.
- Turn in printouts of your graph, showing all three plots of your data and the best-fit line for the most linear plot, and of your spreadsheet. Include in your spreadsheet the calculated value of \( n_f \) as a decimal number (not rounded to an integer) and its standard deviation.
Also, answer the following questions in the report.
- Calculate the wavelengths of the three lowest energy lines of the Paschen and Brackett series of the hydrogen atom. Do any of these occur in the visible region of the spectrum?
- Ionization of the \( \ce{H} \) atom from its ground state corresponds to the transition \( n_i = 1 \ce{->} n_f = \inf \). Light with this or greater energy will ionize the \( \ce{H} \) atom, with any excess energy going into the kinetic energy of the ejected electron. Calculate the kinetic energy in J and the speed in m/s, along with the respective uncertainties, of the ejected electron if the \( \ce{H} \) atom is ionized by light with a frequency of \( 5.00\pm0.03 \times 10^{15} \space s^{-1} \).
Data Tables
Mercury Spectrum
| Color | Wavelength (nm) |
|---|---|
Flame Spectra
| Ion | Color(s) | Wavelength (nm) |
|---|---|---|
| \( \ce{Li+} \) | ||
| \( \ce{Na+} \) | ||
| \( \ce{Ca^{2+}} \) | ||
| \( \ce{Sr^{2+}} \) |
| Unknown Number | Observed Wavelengths | Ions Present |
|---|---|---|
Absorption Spectra
| Wavelength Range (nm) |
|---|
Balmer Spectra
| Color | Wavelength (nm) | \( n_i \) | \( n_f \) |
|---|---|---|---|
Fitting Results
| Value | Percent error | |
|---|---|---|
| Rydberg Constant | ||
| Calculated \( n_f \) |