advertisement

Atomic Emission Spectroscopy You’ve done the experiment and you’ve collected the data. Now, how do you actually find the Rydberg constant (RH) using your data? 1. Construct a calibration curve from your data for Hg and He: Table 1: Dr J’s data for the Hg and He emission lines. Atom Color Wavelength, λ, (nm)♣ Distance, x, (cm)* Hg Violet 435.8 2.70 He Violet/Blue 447.3 2.90 He Green 501.7 3.50 Hg Green/Yellow 546.0 4.05 He Yellow 587.8 4.50 He Red 668.9 5.35 ♣This column corresponds to the λ’s listed in the lab manual. *This column corresponds to the distance data that you measured. Now construct a plot of λ vs x for your data. There are instructions on using MS Excel to construct a graph on the laboratory web page. (http://classes.colgate.edu/jchanatry/chem101/week5.htm). 800.0 Calibration Curve for Monochromator 750.0 700.0 y = 87.91x + 194.11 R 2 = 0.9986 650.0 600.0 550.0 500.0 450.0 400.0 350.0 300.0 0.00 1.00 2.00 3.00 Distance, x, (cm) 4.00 5.00 6.00 Figure 1: Dr. J’s calibration curve for CW’s monochromator. 2. Verification of the Rydberg Constant (RH). a. Solve for the λ’s for the Balmer series (i.e. hydrogen emission lines), using the equation of the best-fit line from the calibration curve: y = 87.91x + 194.11 where y = λ, x = distance that you measured for the Balmer series (remember, use the equation from your calibration curve for your data). Table 2: Dr J’s data for the Balmer series. Distance, x, (cm)* Wavelength, λ, (nm) 5.35 664.4 3.35 488.6 2.75 435.9 ∗ Use your distances and solve for λ. You can check the accuracy of your calculated wavelengths for the Balmer series by comparing your values with the literature values (see your textbook). Okay what’s next??? Let’s review what you’ve recently learned in class. Recall, the energy levels of the hydrogen atom are given by: −R E = 2H ,n = 1,2,3, n Using the equation above to calculate the difference between two levels, we get: −R H −R H − 2 n 2f ni where ni and nf are the initial and final values of n, respectively. −∆E = For the Balmer series, the final state is always n = 2, so the equation can be written: ∆E Balmer = −R H 1 +C n i2 where C is a constant. Yes! An equation for a straight line, we know how to deal with this – you just need to construct a linear plot that uses all three of your measured lines to estimate RH . b. The y-axis: ∆E Find ∆E using by the λ’s that you calculated for the Balmer series: ∆E = hc/λ where h is Planck’s constant (6.6261 x 10-34 J•s) and c is the speed of light (2.9979 x 108 m•s-1). *Remember, λ is in nm, so you have to convert to m (1 nm = 1 x 10-9 m). c. The x-axis: 1/n2 Note: n=3 corresponds to the lowest E transition (the most red λ) where as n=5 corresponds to the highest E transition (the most blue λ). d. Construct a plot of ∆E vs 1/n2 Table 3: Dr. J’s data for ∆E and 1/n2 Wavelength, λ, (nm) n 664.4 3 488.6 4 435.9 5 ∆E (J) 2.9897 x 10-19 4.0655 x 10-19 4.5575 x 10-19 1/n2 0.1111 0.0625 0.0400 The Rydberg Constant 5.0000E-19 y = -2.21E-18x + 5.44E-19 R 2 = 1.00E+00 4.5000E-19 4.0000E-19 3.5000E-19 3.0000E-19 2.5000E-19 2.0000E-19 0.0300 0.0500 0.0700 2 0.0900 1/n 0.1100 0.1300 Figure 2: Graph of ∆E vs 1/n2So your estimation of the Rydberg constant is the slope of the best-fit line. From my data, I found RH = 2.21 x 10-18 J. The literature value for RH is 2.178 x 10-18 J. Pretty good for an apparatus that cost only a few dollars and a little bit of time to construct.