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Lab6(1) - Experiment 6 The Study of Atomic Spectra 1...

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Experiment 6 – The Study of Atomic Spectra 1 Experiment 6 Study of Atomic Spectra 1 Introduction In this experiment, we will employ a plane diffraction grating to create a spectrometer, which we will use to measure a few atomic emission lines of hydrogen (H), sodium (Na) and mercury (Hg). We will use the Hg lines to calibrate the spectrometer. The goals of this experiment are (1) to use the H spectrum to estimate the Rydberg constant and (2) to determine the energy level diagram of the low lying levels of Na and the fine structure splitting of the 3 p configuration. 2 Background- see Pedrotti 3 , Section 6-1 and Chap. 12 2.1 Diffraction Grating In this experiment, we will use a plane diffraction grating, the large N limit of multiple slits. Diffraction gratings can be made by ruling a large number of equidistant lines on a glass substrate. Most gratings today, however, are replicas (molds of ruled gratings). The maxima produced by a diffraction grating are very sharp. For parallel light incident on a diffraction grating with angle θ i , the posi- tions of the maxima are given by = d (sin θ p + sin θ i ) , p = ± 1 , ± 2 , ± 3 , . . . (1) where p , d , θ p and θ i are defined in Fig. 1 with p designating the order of the spectrum. It is clear from Eq. (1) that for fixed p , the angle θ p will be a function of the wavelength of the light. Thus, if we illuminate the grating with light composed of several wavelengths, each wavelength will emerge with a different angle. Note, however, dispersion only occurs for | p | ≥ 1. At zero order, θ p = 0, we will see all the wavelengths superimposed in the beam.
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Experiment 6 – The Study of Atomic Spectra 2 Grating p=-2 p=-1 p=0 p=1 p=2 d ! i C o lli m a t e d li gh t i nc i d e n t on g r a t i ng t r a v e l s a l ong do tt e d p a t h ! p Figure 1: Schematic illustration of diffraction of light by a diffraction grating. Various orders of the spectrum are shown. The diffraction grating is a particularly simple instrument to use for studying the components of light produced by an excited atom. When the electrons in an atom are excited (have their energy increased), they return to lower states by emitting light of specific wavelengths known as spectral lines. The spectrum of an atom is one of its basic signatures. The existence of many elements in astronomical studies is often estab- lished by measurements of their spectra. Atomic spectroscopy has also played a fundamental role in the development of quantum mechanics. Hence, the great theoretical and experimental importance of atomic spectroscopy is well established. 2.2 Hydrogen Atom In 1889, Rydberg proposed the following formula to describe the fre- quency of the light emitted when a Hydrogen atom makes a transition between energy levels n and n 0 , ˜ ν n 0 n = E n 0 - E n hc = R 1 n 2 - 1 n 0 2 . (2) In Eq. (2), ˜ ν ( ν/c ) is called the wavenumber – the frequency of the light divided by the speed of light and expressed in units of cm - 1 E n is energy of level n , hc is Planck’s constant times the speed of light and the constant R is the Rydberg constant.
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