ven both energy levels and the wavelengths, it is possible to determine the actual levels associated with each wavelengt

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ven both energy levels and the wavelengths, it is possible to determine the actual levels associated with each wavelength. In this experiment your task will be to make determinations of this type for the observed wavelengths in the hydrogen atomic spectrum that are listed in Table 1. Table 1. Some Wavelengths (in nm) in the spectrum of the hydrogen atom 97.25 389.02 434.17 397.12 410.29 102.57 121.57 486.27 656.47 954.86 1005.2 1094.1 1282.2 1875.6 4052.3 Experimental Procedure There are several ways we might analyze an atomic spectrum given the energy levels of the atoms involved. A simple and effective method is to calculate the wavelengths of some of the lines arising from transitions between some of the lower energy levels and see if they match those that are observed. We shall use this method in our experiment. 1. Calculations of the Energy Levels of the Hydrogen Atom. Given the expression for E. in Equation 6, it is possible to calculate the energy for each of the allowed levels of the H atom starting with n=1. Calculate the energy in of each of the ten lowest levels of the H atom (n=1 to n-10). Note that all energies are mol negative, so that the lowest energy will have the largest allowed negative value. a. Enter these values in your report sheet in Table 2. b. On the energy level diagram provided (Figure 2), plot each of the six lowest energy levels by drawing a horizontal line at the allowed level and writing the value of the energy alongside the line, near the y- axis. 2. Calculation of the Wavelength of the Lines in the Hydrogen Spectrum. The lines in the hydrogen spectrum all arise from jumps made by the atom from one energy level to another. The wavelengths in nm of the lines can be calculated by Equation 4, where AE is the difference in energy (in) between any two allowed levels. For example, from the n-2 level to the n=1 level, calculate the difference, AE, between the energies of those two levels. Then substitute AE into Equation 4 to obtain this wavelength in nanometers. Using the procedure outlined above, calculate the wavelength (in nm) of all the lines we have indicated in Table 3. That is, calculate the wavelengths of all the lines that can arise from transitions between any two of the six lowest levels of the H atom. Enter these values in Table 3. 3. Assignment of Observed Lines in the Hydrogen Spectrum. Compare the wavelengths you have calculated in Table 3 with those in Table 1. If you have made your calculations properly, your wavelengths should match, within the error of your calculation, several of those that are observed. On the line opposite each wavelength in Table 4, write the quantum numbers of the upper and lower states for each line whose origin you can
recognize by comparison of your calculated values with the observed values. On the energy level diagram (Figure 2), draw a vertical arrow pointing downward (light is emitted, dE<0) between those pairs of levels that you associate with any of the observed wavelengths in Table 4, By each arrow, write the wavelength of the line originating from that transition. There are a few wavelengths in Table 4 that have not yet been calculated. Enter those wavelengths in Table 5. By assignments already made and by examination of the transitions you have marked on the diagram, deduce the quantum states that are likely to be associated with the as yet unassigned lines. This is perhaps most easily done by first calculating the value of JE, which is associated with a given wavelength. Then find two values of E, whose difference is equal to dE. The quantum numbers for the two E states whose energy difference is dE will be the ones that are to be assigned to the given wavelength. When you have found n and me for a wavelength, write them in Table 4 and Table 5; continue until all the lines in the table have been assigned. 4. The Balmer Series. This is the most famous series in the atomic spectrum of hydrogen. The lines in this series are the only ones in the spectrum that occur in the visible and near ultraviolet regions (-250-750 nm). Answer the questions in the report sheet relating to this series.
you Cilla ICH THOT Table 3. Calculation of Wavelengths in the spectrum of the H-atom. In the upper half of each box, write dE, the difference in energy in between En, and En In the lower half of each box, write & associated with that Male value of 4E. higher (Mai) Power (ne) 1 5 6 45.56 1 29.52 mul 2615.7nm 40524 nm 4235.4 1254561230x4 ml L. 26 984,3 l L 93.78AM 94.98m 97.25mm 102.57pm L 21.57mm 291.57 215.53 246.01 182.73 mal 410-28hm 434.17 nm 14186.17nm 56.46mm 09.34 93.3 mul 63.18 mel 1094.08nm 1182.18mm 1875-6mm 2.04 k) moll 12236 3nm mol 3 K) 2 AB Epper-E 2 (in nm)= 1.9627×105 16.04. 1.19627 x 10 2 (in nm) kl mole kj mole 119627 x 10- AF (in)
Figure 2. Energy Level Diagram 0 Energy in kJ/mole -100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 -1100 -1200 -1300 -1400 -1500 T