Atomic Emission of H and Na—CH342L: Spectroscopy February 5, 2016

We’ll use a CCD spectrometer to measure the visible line spectra of and sodium. A strong electric field populates excited electronic states, and we’re detecting the visible light as atoms relax from these states to lower energy excited states or the .

The hydrogen will fit well with your experience with atomic emission spectra and hydrogen-like atoms in general chemistry. We will be able to calculate the from our H data. The additional in sodium make its analysis more complicated, but it’s a great opportunity to think about shielding effects in multielectron atoms. For both atoms, we’ll assign atomic transitions to as many peaks as we can and calculate defect correction factors which account for shielding.

All the energy levels for H and Na involved in this lab are well known and are tabulated in many places2−5, however following the methods in this manual, you’ll be able to assign many of the peaks yourself and see how a real spectroscopist might use a model-prediction method to assign peaks when encountering a spectrum for the first time. Pre-Lab Review shielding (also called screening) from your general chemistry textbook or class notes from the chapters on atoms, light and energy. Write a paragraph that defines shielding and states when it should be a large effect and when it should be a small effect. How should the sodium spectrum look with 100% shielding and how would it look with 0% shielding? Procedure We’ll collect the spectra via a fiber-optic cable carrying light from the gas-discharge lamps to a CCD spectrometer and visualize them using the SpecroVis software. Be sure to record the model number for the spectrometer. We will need to spend some time optimizing the signal—adjusting the position of the fiber optic cable, the integration time and the number of samples to average. Save your data to a place you’ll be able to access it from another computer and do your peak assignment at another work station. Hydrogen The 3 → 2 transition in the should be near its literature value of 656.46 nm. Youshould be able to assign the remaining lines in this series (n1 = 2) by inspection. The correlates the inverse of the transitions to the energy levels: [ ] 1 1 − 1 = R 2 2 (1) λ n1 n2 where light of wavelength λ is emitted when the drops from with principal quan- −1 tum number n2 to n1 and R is the Rydberg constant with units of cm . The spectrometer may not be perfectly calibrated, so you may not in general have precisely the correct for these line positions. Assume that there is a constant shift (λ0) in the measured wavelengths (λmeas) from the true

2014-2015 CH342L: Spectroscopy Atomic Emission Spectroscopy of H and Na—CH342L: Spectroscopy 2 value (λ):

λ = λmeas − λ0. (2)

While it may not be true that the shift is constant across the spectrum, making this correction is probably better than making no correction at all. For the Balmer series, equation 1 becomes [ ] 1 1 1 = R − . − 2 (3) λmeas λ0 4 n2

Identify each Balmer line on your spectra tabulating the wavelength (λmeas) and n2. You can fit this tabulated data to this formula using R and λ0 as free parameters in the fit. Sodium We’ll assign peaks in the sodium spectrum from the following series: S series (ns → 3p): first 4+ members P series (np → 3s): first 2 members (why not more? You’ll see later.) D series (nd → 3p): first 6+ members Be careful to discriminate between atomic Na peaks and possible impurity peaks. First, tabulate the positions of observed peaks in the spectra. In theory, each of the three series can be analyzed using a modified and more general form of the Rydberg formula: [ ] 1 1 − 1 − R = R 2 2 = T1 2 (4) λ (n1 − δ1) (n2 − δ2) (n2 − δ2) where T1 is the series limit as n2 → ∞ (T1 can also be thought of as the for an electron in the n1 state), and δ1 and δ2 are quantum defects which are corrections that are necessary to make the idealized one-electron Rydberg equation account for the interaction of the outermost electron with the inner core electrons. Note that each state has its own .

The strategy we’ll take is to first assign the D series, then assign the S series using the information form the D series with a few more hints. To get a feel for how a spectroscopist might assign peaks in a spectrum they’ve never seen before, follow these instructions to solve the peak-assignment puzzle:

• The D series should have a negligibly small quantum defect δ2 (2 refers to the initial for the transition). A large δ indicates a large interaction between the outer and inner electrons,

a small δ2 for the D series can be justified using concepts of orbital penetration and shielding—

what do you remember about the d-orbitals to support this? Assuming that δ2 → 0, equation 4 can be written 1 − R = T1 2 (5) λ n2 providing a simple linear relationship for fitting data and predicting peak positions. Use the literature value of the sodium D series member 4d → 3p at about 568.7 nm to locate this peak on

your spectrum. Be sure to use your measured wavelengths for analysis corrected with the λ0 from

2014-2015 CH342L: Spectroscopy Atomic Emission Spectroscopy of H and Na—CH342L: Spectroscopy 3

your hydrogen spectrum (not the literature values!). Use the position of this D line to estimate

T1 for this series using equation 5. You will find a better T1 later. This estimated value will help your peak assignments

• Next, use your approximate T1 values to predict the positions of the other members of the D series

(n2 = 3, 4, 5, ...). Compare these predicted values to your spectra and attempt a full assignment of the D series. Check with your instructor or TA before you proceed further with peak assignments if you are in doubt.

• For the P series, locate these two lines, and report your own values for their positions: 4p → 3s at about 330 nm and 3p → 3s at about 589 nm. Since there are only two members in this series, we won’t have enough information to check out the agreement with the modified Rydberg formula (equation 4), so it is not necessary to plot your data for the P series. What’s so strange about the 3p → 3s peak? Why does this peak stand out? The probability of a transition is related to the spatial overlap of the initial and final orbitals involved in the transition. Why do we only observe two members of this series?

• Assigning the S series is tricky because it has non-zero quantum defects. Twolines you’ll observe in the series are: 5s → 3p near 615 nm and 8s → 3p near 454 nm. Locate the intermediate members (6s,7s) in your spectra. Seek to identify as many other peaks as you can (look for 9s and 10s). Be able to explain your criteria for making your assignments. Be careful and check your assignments with your instructor or TA before analyzing the S series. Beware of impurity peaks, and ask for help if you’re stumped or unsure.

2 • Once you are comfortable with your peak assignments, make plots of 1/λ versus 1/n2 for the S and D series, and make sure they are linear. Once you have made these plots, you will want to revisit your spectra to recheck your peak assignments. How does the result of linearity (or nonlinearity) fit with the statements above about the D series quantum defect? Once you’ve finalized assignments,

fit the data to equation 5 to find ”new and improved” values for T1 and R. What do you notice

about the values of T1 for the S and D series?

What to include in your lab summary due next week Make figures of 1) the annotated spectra for both hydrogen and sodium labeling all peaks you were able to identify, 2) the energy level diagrams2,4,5 for hydrogen and sodium (S and D series) based on these peak assignments, and 3) plots with appropriate best fits for hydrogen and the S and D series of sodium.

In a table, summarize the following results: 1) R and λ0 from your hydrogen data, 2) R and T1 for the

D series of sodium, and 3) R, T1, and δ2 for the S series of sodium. Be sure to include errors in all reported values in this lab and use correct significant figures (only one significant figure in the error).

Briefly comment on 1) the value of λ0 and its effect on your fits, 2) the quality of your fits, and 3) your criteria for peak assignment in the S series for sodium. If there was ambiguity in picking a peak or

2014-2015 CH342L: Spectroscopy Atomic Emission Spectroscopy of H and Na—CH342L: Spectroscopy 4 leaving one out, explain why. Make sure you comment on values that should be similar (Would you expect R to be the same or different between H and Na? What about T1 between the S and D series?) and make sure to compare to literature values2−5. Formal write-up There will be a formal write-up for this lab which will be due the week before spring break. We’ll start to talk about this during our Wednesday afternoon meeting. References 1. Major parts of the analysis for this lab are drawn from: Hollingsworth, W.; Ferrett, T. Manual for Advanced Lab I: Spectroscopy; Carleton College: Northfield, MN, 2002; ch 3.

2. Matthews, G. P. Experimental Physical Chemistry; Oxford University Press: New York, 1985; pp. 193-206.

3. Stafford F.E.; Wortman J. H. J. Chem. Ed. 1962, 39, 630.

4. Handbook of Basic Atomic Spectroscopic Data http://www.nist.gov/pml/data/handbook/index.cfm (accessed Feb 15, 2015).

5. Douglas J.; von Nagy-Felsobuki E. I. J. Chem. Ed. 1987, 64, 552.

6. McQuarrie D. J. , 2nded; University Science Books: Mill City, CA, 1985; pp. 20-25, 353-357, and 475-479.

2014-2015 CH342L: Spectroscopy