Chemistry 151
THE VISIBLE ATOMIC SPECTRUM OF HYDROGEN
Many substances give off visible light when energetically excited in an electric discharge tube or when heated. The light is emitted only at certain wavelengths characteristic of the substance. When this light is passed through a prism or reflected off a diffraction grating, the various wavelengths are dispersed and each appears as a separate line in what is called the emission (line) spectrum. In this experiment you will observe and measure the line spectrum of hydrogen, and determine the energies of several of the lower electronic energy states of the hydrogen atom.
The Electromagnetic Spectrum
Electromagnetic radiation (light) consists of electric and magnetic fields oscillating at right angles to each other and traveling through space. The oscillating fields are waves, characterized by a wavelength, , and a frequency, . For any wave motion, the product of wavelength and frequency is the speed of the wave. For electromagnetic radiation this is,
= c [eqn. 1]
c = 2.998 x 108 m/s (speed of light in a vacuum)
= 2.998 x 1010 cm/s
For electromagnetic radiation, common wavelength units are meters (m), centimeters (cm) and nanometers (nm). The frequency unit is cycles per second (s-1), also called hertz (Hz).
The regions of the electromagnetic spectrum are shown in Figure 1. Our eyes are sensitive to a rather narrow band of wavelengths between roughly 400 nm (violet) and 700 nm (red). The part of the hydrogen spectrum involved in this experiment is in this visible region of the electromagnetic spectrum.
In addition to wave characteristics, electromagnetic radiation also can be considered as particles, called photons. The energy, E, of a photon is proportional to its frequency, .
Ephoton= h[eqn. 2]
h = 6.626 x 10-34 J·s. (Planck's constant)
The value of Planck's constant above has units of joule seconds (J·s). When this value of h is multiplied by frequency, , in Hz (s-1), the energy is in joules (J). Combining eqn. 1 and 2 gives,
Ephoton= hc/[eqn. 3]
Atomic emission (line) spectra
According to quantum mechanics, electrons can exist only in certain states called orbitals. Each orbital has a specified energy and "shape" which describes the probabilities of finding the electron in any region of space around the nucleus. When an electron in an atom changes its state it absorbs or emits energy equal to the difference between the energies of the initial (Ei) and final (Ef) states involved in the change. When atoms are energetically excited, energy is absorbed. The emission (line) spectrum results when excited atoms fall from higher (Ei) to lower (Ef)energy states emitting light. The energy of the emitted photon corresponds to the difference between the higher and lower state energies.
E = Ei Ef = Ephoton = h[eqn. 4]
The emitted light is dispersed by a prism as shown in Figure 2.
The spectroscope
A spectroscope is an instrument which separates light into its various wavelength components. The gas to be studied is in a gas discharge tube placed next to the slit on the spectroscope. When a sufficiently high potential difference (voltage) exists between the two electrodes in the tube, electrons flow, colliding with the gas atoms in the tube. These collisions excite atoms to higher energy levels. When they fall to lower energy levels, light is emitted.
You will use a Bunsen spectroscope (Figure 3). The emitted light enters the spectroscope through a slit, is collimated by a lens and refracted into the various wavelengths by the prism. Each wavelength gives a vertical line in the spectrum. One arm of the spectroscope contains a linear scale which is illuminated with a small external light, superimposing the linear scale on the spectrum as viewed through the eyepiece. When calibrated this scale is used to determine the wavelengths of the hydrogen atom spectrum.
Calibration of the spectroscope
The first task is to construct a calibration curve which will enable you to convert the arbitrary scale readings of the spectroscope to corresponding wavelengths. The known wavelengths of the mercury (Hg) vapor spectrum will be used for this purpose.
The instructor will show you how to place a mercury discharge tube in the power supply and turn it on. Set it as close as possible to the spectroscope slit. We only have one set of lamps (borrowed from the physics department) so be very careful. Before proceeding keep in mind the following hints on technique.
To avoid eyestrain, don't look in the eyepiece telescope for more than a minute. Look away occasionally.
The brightness of the spectrum is very dependent on the position of the discharge tube in front of the slit. Move the discharge tube slightly while viewing the spectrum to find the best position.
Rotate the eyepiece telescope so as to center the line being measured.
The focus may change with wavelength; if so refocus the eyepiece.
Open the slit to increase the intensity of a dim line; narrow the slit to sharpen bright lines.
The scale reading for a line is somewhat dependent on the position of the viewer's head (this is called parallax). Reduce the parallax error by centering each line in the middle of the telescope.
There are three adjustments on the spectroscope: (1) opening/closing the slit to adjust the intensity of the observed lines, (2) focusing the eyepiece, and (3) moving the telescope to center lines. Be sure you know what to turn to make these adjustments.
When viewed in the spectroscope the mercury line spectrum is superimposed on an arbitrary linear scale. Since you want to calibrate this scale, you need to correctly identify the colored lines seen in the spectroscope with the wavelength values given in blackand-white sketch in Figure 4. We will construct a calibration curve is constructed from the wavelengths (nm) given
in Figure 4 and the scale readings viewed in the spectroscope when all data have been collected.
The moderately strong red line seen when the discharge tube is first turned on (cold) is the 691 run line; read this line first as it becomes very weak as the tube heats up. The bright yellow pair of lines (seen as a pair only at narrow slit width), is the 577/579 nm doublet. The lines at 546 nm and 436 nm are also reasonably intense. You should be able to identify the rest of the lines in Figure 4. Ignore very faint lines and the rainbow backgrounds.
Record the scale reading, color, and wavelength for each of the eight mercury lines in a tabular format.
Measuring the Atomic Spectrum of Hydrogen
Place a hydrogen gas discharge tube in the power supply, set it next to the spectroscope slit and turn it on.
Adjust the slit opening until the lines are easily observed through the eyepiece. You should be able to see four lines although the line nearest the ultraviolet may be faint. Take scale readings for each observed line and record these scale readings in your notebook.
Calculations
1. Calibration of the Spectroscope
Open the Excel spreadsheet on your computer and name an empty worksheet “Calibration.” Make a table with your readings from the mercury lamp. Construct a calibration curve (like we did for the prelab) for the spectroscope scale. Check the quality of your calibration curve for systematic errors (bad data points). Use the slope and intercept spreadsheet functions and then transform to get x=mnew y + bnew.
2. Energy levels of hydrogen
Although a complete description of atomic electron orbitals requires several quantum numbers, the orbital energy for hydrogen (and only hydrogen) is especially simple and is defined by a single quantum number. This is the principal quantum number, n, which can take only integer values (n = 1, 2, 3). The hydrogen energy levels are given by the expression,
[eqn. 5]
where m and e are the mass and charge of the electron, respectively. When values for e and m in Sl units are inserted, this equation gives the energy in joules (J).
[eqn. 6]
For n = 1, the electron is in the lowest (ground state) energy. From the above equation, the ground state energy is 2.179 x 1018 J. The highest possible energy is zero (for n=).
Name an empty worksheet “Hydrogen” and make a table to calculate the hydrogen electron energy levels for n=1 thru 6 and 1000:
Row/Col / A / B / C
1
2 /
Hydrogen Energy Levels
34 / n / E (J)
5 / 1 / =-2.179E-18/B5^2
6 / 2 / “
7 / 3 / “
8 / 4 / “
9 / 5 / “
10 / 6 / “
11 / 1000
Be sure to label your columns.
3. Energy Level Diagram
To get a visual picture of the meaning of these energy levels, construct a diagram similar to Figure 7.22 (pg 270) in your Chang text as follows. To the right of your data, add three columns: the first should go from 1 to 6 and then “oo” (two lower-case zeros simulating the symbol) and the second of energies scaled by 1019 which converts the energies into near-whole numbers. A good column label would be “E(J * 1E19)” with a formula (=Cn*1e19 where n is a row number). Label the third column “n final” and enter the energy for n=2 in it. Select these three columns and make a new plot. This time, do not use XY scatter, instead use “Line Plot” choosing one of the options from the second row of pictures. Label the Y-axis “Energy (J) x1E19” and give the plot a title. Select the data for the first column, then select Format Selected Data Series from the format menu. In the Patterns tab, set Lines to none. Set the Marker to a horizontal line with a size of 20. In the Data Labels tab, select Show Label. Click Ok. Format the second column data (the flat one) with () Auto for the lines and ()None for markers. Format the Y-axis to range form –25 to +5. Clear the X-axis (select it and press Delete). Print this plot.
The levels on this diagram can be thought of as "rungs on an energy ladder." On a ladder you can only exist at heights corresponding to a rung, and when you change your position on the ladder, the change in height must equal to the difference between two rung heights. An electron can only exist on one of the allowed energy levels. When an electron changes levels, an amount of energy is emitted (or absorbed) equal to the difference between the two levels involved in the transition.
4. The Emission (Line) Spectrum of Hydrogen
Use the calibration curve to calculate the wavelengths of the four observed hydrogen lines. To do this, leave three blank columns on the left and make a table with your scale readings (be sure to label it) and then calculate wavelength using =mnewx+bnew. Be sure to label the new column. Format the calculated wavelength as a number with zero decimal places (round off to the ones column).
The four lines in the visible spectrum of hydrogen result from the excited state electrons with R. = 3, 4, 5, 6 and nf = 2. They are part of the Balmer series of lines named after J.J. Balmer who in 1885 first showed that the wavelengths of the visible spectrum of hydrogen could be explained with a relatively simple formula.
On the printout of the Energy Level Diagram for Hydrogen draw vertical arrows corresponding to the energy level transitions responsible for the four Balmer lines. If you want to keep the report electronic, open the View menu, Toolbars, drawing. There is an arrow tool that you can use to draw on the plot. Be sure not to move the graph after you draw arrows.
When an electron in an excited level falls to a lower level, the energy of the emitted photon is obtained by combining equations 4, 5, and 6 to give equation 7.
or
[eqn. 7]
Equation 7 can be expressed in terms of the wavelength () of the emitted light.
[eqn. 8]
EXAMPLE: When an electron in a hydrogen atom falls from the n=2'level to the n= 1 level, the energy of the emitted photon is,
The wavelength of the emitted light is,
This light is in the ultraviolet region of the electromagnetic spectrum and is not visible to our eyes.
Theoretical wavelength values for the four hydrogen lines can be calculated using the concepts and formulas above. In the table of calculated wavelengths, label the first two columns n final and n initial, respectively. Enter the nfinal =2 for all rows in your table. Enter 3, 4, 5, and 6 for ninitial. In the third column, calculate the four theoretical wavelengths. Compare the theoretical wavelengths with your measured wavelengths. Comment on how well they match. On the right-hand side of your table, calculate the energies and frequencies associated with each of these lines. Use this table to answer questions 1 through 3.
Questions:
1a. At what wavelength (nm) would you predict the n=5 to n=3 transition in hydrogen? Would the resulting line be in the visible, ultraviolet or infrared? Explain.
lb. Calculate the energy of the photon emitted for the n=5 to n=3 transition. What is the frequency of the wave associated with this photon?
2. Verify the energy and wavelength values in the Example (above).
3. The amount of energy required to completely remove an electron from an atom is called the ionization energy. This corresponds to raising an electron to the highest possible energy state (n=). What is the ionization energy of a hydrogen atom in its ground state (n= 1)?
4. The energy value obtained in Question 3 has the units J/atom H. Convert this value to kJ/mol H and compare with the value given in chapter 8 of your text.
Prelab Exercises
These exercises must be completed in Excel before you start data analysis for your experiment.
1. Calibration curves.
A calibration curve is essentially a plot of experimental data used to relate measured values to relatively error-free known values. In this example, we will create a calibration curve to relate true volume for a graduated cylinder. Typically, a linear regression is used to allow easy calculation of true values.
Enter the following values into a spreadsheet (label the worksheet “PreLab”).
<Table Missing due to word error>
Constructing a Calibration Graph.
You have done this several times before. The difference is that we will now call our graph a “calibration curve.” Use Excel to graph the data. It is important that the well-known values be on the X-axis, a requirement for the linear regression theory. In this case, the volumes based on mass calculations are very well-known and should go on the X axis. Clean up the graph using the settings we used in Experiment 1 and add a trend line with equation & r2 to the graph.
The trend line is a useful function but requires a human check for validity. For example, the data may not really be in a straight line. Another case is when a experimental data point has a large (probably systematic) error that that should be eliminated.
Slope and Intercept in the Spreadsheet.
Unfortunately, once you have a good trend line, you can’t automatically use the slope and intercept numbers in your spreadsheet calculations. Instead, you can calculate them using the “slope” and “intercept” spreadsheet functions which are used as follows:
=slope(y-data, x-data)e.g. =slope(A2:A6,C2:C6)
=intercept(y-data, x-data)e.g. =intercept(A2:A6,C2:C6)
If you want r2, the “correl” function works the same way. To use these functions in your spreadsheet, enter the appropriate functions below your data (or anywhere else that you prefer). Be sure to put a label next to them so someone else knows that they are slope and intercepts. To be sure you did the equations correctly, compare the numbers with trend line equation.
Making the Calibration Equation User-Friendly
After we make the calibration curve, we’d like to be able to use it. That is, if we measure more volumes using the graduated cylinder, we would like to be able to quickly calculate the correct volume. To do this, let’s examine our current equation
y = m x + b
Vgrad = m (Vmass) + b
where Vgrad is the volume we measured on the glassware and Vmass is the correct volume calculated from the mass of water and density. When we are using this calibration, we will have data for Vgrad and want Vmass. We will have to do algebra every time we want a corrected volume. Since the linear regression requires that we have well-know values on the X-axis, we will have to transform the equation algebraically into the following form:
Vcorr = mnew Vgrad + bnew
where Vcorr is our quickly calculated corrected volume, mnew is a new slope, and bnew is a new intercept. The algebra is as follows:
Enter and label these formulas into the Excel spreadsheet.
Using the Calibration Curve
While doing another experiment, I measured the following volumes:
Volume Reading
<table missing due to error>
Enter these values into the spreadsheet and calculated the correct values using the new calibration equation.
2. Hydrogen Line Spectra
2a. How many lines do we expect to see for the hydrogen spectrum?
2b. A reference manual identifies lines at the following wavelengths (nm):
<table missing due to error>
Which of these should we not be able to see? Why?
2c. Use Excel to calculate the energy and frequency of each of these wavelengths.
Armando HerbelinPage 1/101/12/2019
Exp8d.doc