### Phys 4910 Spectroscopy Spring 2018 Assignment 5

#### Rydberg Levels of Potassium

Listed to the right are the energy levels of potassium, in cm-1. The last value in the table is the ionization potential of potassium, corresponding to n=∞. Ideally Rydberg levels should fit the equation

E - En = R/n²

where R is the Rydberg constant.

#### Assignment

• Copy the data into a spreadsheet(1), and make two graphs
• a plot of E - En vs 1/n².
• a plot of ln(E - En) vs ln(n).
• Ideally each graph should yield a straight line. Since the low lying levels are not true Rydberg levels the plots will show some curvature for these values of n. Decide from your graphs the minimum value of n for which the data from that point on is acceptably straight.
• For each graph find the slope and intercept (using linear regression, not the trend line).
• What should be the slope and intercept for the first graph, and how close do your values come to the "correct" values?
• What should be the slope and intercept for the second graph, and how close do your values come to the "correct" values?
• What might be done to improve your results?

(1) Here is the same data in a text file

n En
4 0
5 21026.551
6 27450.7104
7 30274.2487
8 31765.3767
9 32648.3511
10 33214.2267
11 33598.5597
12 33871.4788
13 34072.2393
14 34224.2113
15 34342.015
16 34435.1762
17 34510.119
18 34571.3017
19 34621.8976
20 34664.2161
21 34699.9692
22 34730.4476
23 34756.6407
24 34779.3147
25 34799.074
26 34816.3971
27 34831.669
28 34845.2004
29 34857.247
30 34868.018
31 34877.6871
32 34886.3999
33 34894.2785
34 34901.4264
35 34907.9301
36 34913.8657
37 34919.2976
38 34924.2808
39 34928.8634
40 34933.0874
41 34936.9892
42 34940.6009
43 34943.95
44 34947.062
45 34949.9585
46 34952.6589
IP = E 35009.814