space where an electron can be found. Bohr's most distinctive contribution was the discovery of the link between the quantized energies of electron "orbits" and the line emission spectrum. This was a critical breakthrough in understanding atomic structure. Bohr was able to derive a mathematical formula to predict the average distance of an orbit from the nucleus for each energy level, the energy of each orbit, and also the difference in energies between any two orbits. His results are highly accurate for an atom with a single electron, such as hydrogen and the lithium ion, Lit. However, it turns out that multi-electron atoms have spectra that are much more difficult to predict and interpret. Bohr used the assumption of a circular orbit and the idea that the electrostatic attraction to the nucleus was the only force holding the electron in the atom. His equations are based primarily on Coulomb's Law and geometry and involve the constants provided in Table 1. Table of Constants Used in the Bohr Model gaia Plank's constant h 6.626*10-34 Js speed of light C 2.998x108 m/s permittivity of free space Eo 8.8542*10-12 F/m mass of an electron me 9.10938x1031 kg charge of an electron e" -1.6022x10-19 C Rydberg constant RH 1.0973*10' mil Bohr Model Calculations Bohr determined that the radius of an allowed orbit can be found using the following equation, (1) In = ED Time2 X n2 h2 Since most of the numbers involved are constants, this simplifies to In = (5.29405 x 10 2 nm) x n2 In = bohr radius n = principle quantum number The energy of each orbital is given by the following: hCRH (2) En = - - n2 The Rydberg constant, RH, is actually a combination of a group of other constants: meet (3) RH = In order to simplify the energy equation, the constants hCRY are often combined in the form: S b = hCRH = 2.178 x 10-18]By extension, the difference between two energy levels comes from the subtraction of the energy of the individual orbitals which gives the following equations, (4) AE = Eng - En ( 5 ) AE = -hcRH (74 - ni) where no = the principle quantum number of the final energy level and ni = the initial energy level. Prelab Calculations On a separate sheet of paper, complete one example calculation for each question and turn them in with your Report Sheet. Be sure to number your calculations. Your results must be signed off by your lab instructor before you can collect spectrum data. 1. Calculate the radius associated with principal quantum numbers 1,2,3,4,5, 6, & 7 in the hydrogen atom. 2. Calculate the energy associated with principal quantum numbers 1,2,3,4,5, 6, & 7 in the hydrogen atom. 3. Using the results of #2 and equation (4), subtract the orbital energies in order to calculate the transition energy of each electron transition found in Table 1 of the Report Sheet. Record the results in the table. 4. Calculate and record the wavelength associated with a photon emitted for each transition in Table 1. Mhaifauno Procedure Lab safety Take care of your eyes - The light emitted by the hydrogen and mercury vapor my game lamps includes UV rays which can damage your eyes. It is best not to look directly at any of the lamps for longer than is necessary to line up the spectroscope. The light observed through the spectroscope is not intense enough to be harmful. Lab goggles may be worn to block out harmful UV. Never use a spectroscope to observe direct sunlight or a laser beam. These are both capable of causing severe eye damage. ans To varone erit Part A. Mercury Line Spectrum 1. Use a spectroscope to observe the line spectrum emitted by the mercury lamp. 2. Record the wavelength of each visible line. (See Table 1. Grey boxes indicate lines that may be too faint to see.) Part B. Hydrogen Line Spectrum 1. Use the same spectroscope to observe the line spectrum for hydrogen. 12 of hydrogen.) 2. Record the color and wavelength of each visible line. (You should see at least 3 lines for3. Use the calibration curve to find the corrected wavelengths. a. Find each measured value on the y-axis of the calibration curve and graphically determine the corresponding value on the x-axis. b. If graphed using a spreadsheet, use the equation of the best fit line to calculate the x-value (corrected wavelength) that corresponds to each y-value (measured wavelength) Part C. Observe an Additional Spectrum 1. (Time permitting) Choose an additional gas discharge lamp. 2. Record the type of gas in the lamp 3. Observe the spectrum and record the color and wavelength of each visible line. Part D. Prepare a Calibration Curve Using the Hg Lamp 1. Plot the accepted wavelength values for the mercury lines on the x-axis and the values measured by your spectroscope on the y-axis. a. If graphing by hand, use a clean sheet of graph paper and a ruler to prepare a calibration curve. Use a ruler to draw a best fit line through your data. b. If graphing through a program, print a copy of your graph with the equation of the best fit line shown on the graph. Technique Tip Calibration Curve - Even though it is called a curve, a calibration curve is usually a linear relationship between a set of measured values and their corresponding known values. Once that linear relationship is established, the calibration curve can be used to translate any measured value from the same instrument into an more accurate result. Part E. Calculations and Conclusions On a separate sheet of paper, complete one example calculation for each question and turn them in with your Report Sheet and graph. Be sure to number your calculations. 1. Calculate the energy associated with your corrected measured wavelengths for hydrogen and record them in Table 2. 2. Based on the values you recorded in Table 4, identify the transition associated with each corrected wavelength for hydrogen and fill in the last column of Table 2. 3. Draw a transition diagram for each hydrogen line. (See Figure 2 for an example of a transition diagram) Label each transition with its correct color, wavelength, and energy difference. Waste Products: This lab produces no waste products.Atomic Spectroscopy Materials Spectroscope Graph paper Hydrogen gas discharge lamp Calculator Mercury gas discharge lamp (3) Lamp holders Other gas discharge lamps ruler Purpose In this experiment, the visible line spectrum emitted by mercury, hydrogen, and at least one other atom will be observed using a spectroscope and gas discharge lamps. A calibration curve based on the known wavelengths of the mercury (Hg) spectrum will be used to determine the actual wavelengths of the hydrogen spectral lines. A series of calculations will be made using the Bohr model to relate the energy of transitions between energy levels to the wavelengths emitted. Based on this data, the energy level transitions that correspond with each observed wavelength will be determined. Background We experience situations in which matter emits light every day. For example, a hot stove glows red and most of our schools and offices are lit using fluorescent lights. Fluorescent lights, including neon lights, are based on the principles of a gas discharge tube. A gas discharge tube is a glass tube that is filled with a low pressure of a specific gas or group of gases. Metal electrodes at both ends of the tube can be connected into an electric circuit. When placed under a high voltage difference, electrons is the gas are continuously excited and emit light as they return to lower energy states. Different gases have different characteristic colors just as in a flame test. For example, many older street lights have a strong orange color due to the sodium discharge lamps that they are made from. However, the color emitted by a discharge lamp is actually the sum of a collection of wavelengths. When the emitted light is passed through a prism or diffraction grating, it can be separated into its different colors (wavelengths). A spectroscope uses a diffraction grating and a calibrated series of lines to show the wavelengths emitted by a light source. Using a spectroscope, it can be seen that a series of bright lines at specific wavelengths are emitted by the gas discharge lamp, with most wavelengths being absent. These line spectra are unique to each element and can act as a "fingerprint" for different atoms. As a result, astronomers can use emission spectra to help identify the components of stars and galaxies.Figure 1: A bright line emission spectrum as seen through a spectroscope. The Bohr Model Neils Bohr theorized that electrons within an atom are held in orbits that correspond to fixed energies such that when electrons move from a higher energy level to a lower energy level the loss of energy is always equal to the difference in orbit energies. He also thought that this energy is released from the atom as a photon of light. Since the energy of the photon is equal to the fixed difference in energies between the orbits, the photons released by a particular electron transition will always have the same wavelength. Electron transitions between different pairs of orbitals will release photons with different energies, and therefore different wavelengths. A set of transitions will therefore emit a series of specific wavelengths corresponding to each available electron transition. Some of these photons may have energies in the visible range which are seen as colored lines using a spectroscope. Some of the photons will have wavelengths that are outside of the visible range, but can be detected by other means. The following diagram represents the transitions between energy levels in the hydrogen W atom that are able to emit light in the visible portion of the electromagnetic spectrum, known as the Balmer series. It also shows the Lyman series which emit photons in the ultraviolet region. Figure 2: Electron transitions in the hydrogen atom. of of muley vard es Jalgil forin bris Excited W A states Balmer series 19 516 20 Lyman series Ground state Modified from image courtesy chemwiki. UCDavis.edu Bohr falsely imagined the electron orbits to be circular, similar to planets in a solar system. Even though this has proved false, the term "orbital" has remained to describe the region in TemData Table 3: Part B. Hydrogen Line Spectrum Measured Corrected wavelength wavelength Calculated Transition Line color ( nm) (nm) Energy (J) (see calculations) red 464 pm 140 nm 3.03 x 10- 19 3-2 blue- green 480 nm 430 nm 4.09 x 10-19 472 blue violet 434 nm 420 nm /4.58 x 10-19 b-2 violet 410 nm 410 nm /4. 5 x 10-19 Data Table 4: Part C. Additional Line Spectrum, Gas: Ne Measured Corrected wavelength wavelength Line color (nm) (nm) Red 490 Red - oran 60 15 orange- yellow 620 yellow- orange 585 400 yellow 580 590 green 495 495 BlueSpectroscope number Data Table 2: Part A. Mercury Vapor Lamp Accepted Measured Visible lines wavelengths (nm) Wavelengths (nm) Violet 404.7 410 Blue 435.8 440 Green 546.1 560 Yellow-orange 577.0 585 Yellow-orange 579.1 Orange-red 623.4 456 red 690.7Data Table 1: Calculated Electron Transitions in Hydrogen initial level(n;) - final level (n;) Electron Energy Photon Wavelength Transition (J ) (nm) 5-1 209x1018 94. 974 1 4-1 204 x 10 -18 97. 216 60 3- 1 1.94 x 10 102.57 2 - 1 1.14 X 10 18 121 .59 6- 2 4.84 x 10- 19 410 . 20 5 - 2 4.58 x 10 19 434.0 4- 2 4.09 x 10-19 486.1 3- 2 3.03 x 10-19 7- 3 1.98 * 10-19 100 5 6- 3 1.82 x 10 -19 1094Oke 5 - 3 1:55 x 10 -19 12824 4- 3 HOW X 10 -19 1875/10