By: Howard Andres

In Experiment 10, the purpose of the lab was to analyze the atomic spectrum of hydrogen, given its energy levels.  In this experiment, the spectrum of hydrogen was analyzed by calculating the wavelengths of some of the lines arising from the transitions between some of the lower energy levels, and see if they matched those that had been observed.  The experimental procedure of the lab followed several parts.

In the first part of the lab, it was necessary to calculate the energy of each of the allowed energy levels of the hydrogen atom starting with n=1 up to n=10.  Using the equation E_n=-1312.04/n², the energy for each energy level was found, with the level having the lowest energy being the one with the largest negative value, which was n=1 with an energy of -1312.04 kJ/mol.  When the six lowest energy levels were plotted on the given graph, it can be observed that as n increased, the difference between the energies decreased.

In the second part of the experiment, the wavelengths in nm of jumps between different energy levels were determined by first calculating  E, the difference between two energy levels (E_hi-E_lo).   Then, by putting this value into Planck’s Equation,  (nm)=1.19627×10⁵/ E, the wavelengths were found.  By carrying the answer out to a good amount of significant figures, it was found that the calculated wavelengths were quite close to the observed wavelengths in Table 10.1.  The differences probably resulted in the reason that observed data obtained in a lab is usually somewhat different from calculated data. The wavelengths on Table 10.1 that were not found on Table 10.3 were 389.02 nm, 397.12 nm, 954.86 nm, and 1005.2 nm.  This was because the transition levels for these wavelengths were n=8 to n=2, n=7 to n=2, n=8 to n=3, and n=7 to n=3, respectively, and were not determined in Table 10.3.  This was determined by using Planck’s Equation by substituting the wavelengths into it and determining the  E value.  By finding the difference between the two energy levels that matched this, the n_hi and n_lo were determined.  It was found that the calculated wavelengths matched exactly with the observed wavelengths, except for the n=8 to n=3 transition, which was .02 off from each other (954.86 nm observed and 954.88 nm calculated). This is probably the result of the same reasoning that observed data is somewhat different from calculated data.

The final parts of the lab related to the Balmer, or visual spectrum, series in which the range of its wavelengths was determined to be between, from n=7 to n=2, 397.12 nm to about 700 nm.  Anything less was in the Lyman, or UV, series, and anything greater was in the Paschen, or IR, series.  Additionally, it was determined that the energy required to ionize a hydrogen atom was 1312.04 kJ/mol, since its energy level contained -1312.04 kJ/mol in order to remove the electron from that level.  Finally, different ways to express the ionization energy was found, in joules per atom and electron volts per atom (92.17869×10^-18 J/atom, and 13.5998 ev/atom.)  Overall, the lab provided a good review over what was learned in Chapter 7 in working with the atomic spectrum of light.

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