MSE 110 Laboratory Manual Structure Characterization Properties Processing Performance Department of Materials Science and Engineering University of Arizona Tucson, AZ 85721 LAB 1: Atomic Spectra and Balmer's Experiment 1- Introduction: According to De Broglie's principle, particles with small masses and high velocity can exhibit quantum behavior. In effect, they behave like waves. Electrons orbiting around a nucleus indeed have wavelike characteristics. In particular, they interfere constructively to produce standing waves so that only the orbits which satisfy nλ= 2är are stable (where λ is the wavelength of the electron and r is the radius of the orbit). It derives that electrons can only exist on specific orbits with specific energies, as depicted for the simplistic Bohr hydrogen atom model in Fig. 1. E3 E2 hv Ef E1 hv-E-Ef Fig. 1: Left: Standing wave on a circular orbit. Right: Bohr hydrogen atom model. When an atom absorbs energy (for example in the form of an electric discharge), electrons can be promoted onto higher levels, but they eventually relax back down by re-emitting that energy in the form of a photon (Fig. 1). The photon energy if therefore a measure of the difference in energy between the atomic levels: hv Ef -Ei. The sum of all the photons emitted by an atom is called the "atomic spectrum” and contains information on all the electronic energy levels present in a given atom. = Balmer was the first to observe these atomic spectra back in 1885, although at the time he did not understand its relevance to quantization. Nevertheless, he was able to derive what is now known as the Rydberg constant which permits to quantify the difference in energy between electronic levels of the hydrogen atom. In this lab, you will use a modern spectrometer to duplicate Balmer's experiment and experimentally determine the value of the Rydberg constant. You will first assess the calibration and estimate the resolution of the spectrometer using a helium discharge lamp as a calibration standard. You will then use the spectrometer to measure the energy level of the hydrogen atom and derive an experimental value of the Rydberg constant. 2- Experimental Procedure: List of materials • An helium discharge lamp • A hydrogen discharge lamp A spectrometer Procedure Step 1: Calibration and resolution of the spectrometer 1- Log into the computer (click MSE110LAB) and open the SpectraSuite program. The software should display a flat spectrum (Fig. 2). 2- Bring the helium discharge lamp within an inch of the fiber connected to the spectrometer. 3- Turn on the lamp. A spectrum with multiple peaks should appear on the graph of the software. 4- Lower the Integration time (point A in Fig. 2) until the highest peak intensity is below the maxim of 4000 counts on the graph. Increase the Scans to Average (point B on Fig. 2) until the spectrum intensity stabilizes. 5- Save the spectrum (point C on Fig. 2). In the dialog box use the drop down menu to select the File Type as “Tab Delimited, No Header" (point D in Fig. 2). Browse to save the file on the Desktop. 6- Open Excel, browse for the file using "All Files" and open it. 7- Graph the spectrum on Excel. 8- From your data determine the wavelength resolution of the spectrometer. 9- Determine and record the wavelength of each peak at their maximum intensity. Step 2: Experimental derivation of the Rydberg constant. 1- Bring the hydrogen discharge lamp within an inch of the fiber connected to the spectrometer. 2- Turn on the lamp and lower the integration time as detailed in step 1. 3- Save and plot the spectrum with Excel as detailed in step 1. 4- Determine and record the position of the three peaks at their maximum intensity. A File View SpectrometProcessing Tools Window Help B Integration Time: Scans to 100 milliseconds 100 Boxcar A 1 Nonlinearity Data Sources RED Average: Width: Correction: Stray Light Correction: External Trigger: Normal II Strobe Lamp Enable: Electric Dark Correction: IK C Graph (A) x USB650 Q Q Q @ + 90 SATRI Acquisition Int time: 100ms, avg: 1, b No Pre-processor, Sco Result Properties Data Views Graph (A) Graph (A) Intensity (counts) 4000- 3000- 2000- SpectraSuite Save Spectrum ...Spectrometers Processing 0 USB2G40989 No Pre-processor, Scope Mode Filename: Browse... Spectrum View 120 100- 80- Desired Spectrum: Processed Spectrum File Type: OOI Binary Format Grams SPC CAMP-OX Tab Delimited 300 1000 Wavelength (nm) Tab Delimited, No Header D Save Close File name is required. 1000- Source: USB2G40989 400 500 Wavelength (nm): 1000.00 Oot Binary Format 600 700 Wavelength (nm) 800 900 1000 Fig. 2: View of the SpectraSuite software for collection of atomic spectra. ΜΕ 3- Calculations Knowing the wavelength resolution of the spectrometer, calculate the energy resolution (difference in energy between two adjacent measurement points), at 400 nm and 800nm. hc E = λ Express the energy resolution AE in Joules and in eV. Compare the values of the spectral line collected in step 1 to the National Institute of Standard and Technology values reported in Table 1. Intensity (relative) Wavelength (nm) 300 388.86 200 447.15 30 471.32 20 492.19 100 501.56 500 587.56 200 667.81 100 706.52 50 728.13 Table 1: Main lines of the atomic spectrum of helium from NIST. Estimate the Rydberg constant using the Balmer's relation: 1 λ = R H 1 22 - 1 n 2 Use Excel to plot versus λ (12/17) with n=3,4,5 and obtain the slope of the plot to derive the n Rydberg constant. Your report should include: 1- An Excel graph of atomic spectra for helium and hydrogen. 2- The energy resolution of the spectrometer at 400nm and 800nm in Joules and ev 3- A table comparing the values of helium spectral line collected experimentally to the standard values. 4- A discussion of whether the error on your measurement is within the wavelength resolution of the spectrometer. 5- A list of the spectral line for the hydrogen atom. 6- An Excel graph of versus 1 λ 1 1 and the derived Rydberg constant. 22 2 n 7- A discussion of how accurate your derivation is compared to the actual value and what could be the source of error./nHCP FCC lattice BCC measured 12.3mm a do 20mm 140m Measured do 45mm -70mm -> 17.3mm Calculated C21 mm-3 culculate ao 17.96mm CN 12 78.5% PPF B 44.66mm nighest density direction? Across me of the cube densest direction? atons Le (N 8712 CN PF PF atoms/u.c $74 PFF AFF Packmg Factor. 74.1% FCC BCC none/n

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