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SPECTROSCOPY AND THE STARS K H h g G d F b E D C B 400 nm 500 nm 600 nm 700 nm by DR. STEPHEN THOMPSON MR. JOE STALEY The contents of this module were developed under grant award # P116B-001338 from the Fund for the Improve- ment of Postsecondary Education (FIPSE), United States Department of Education. However, those contents do not necessarily represent the policy of FIPSE and the Department of Education, and you should not assume endorsement by the Federal government. SPECTROSCOPY AND THE STARS CONTENTS 2 Electromagnetic Ruler: The ER Ruler 3 The Rydberg Equation 4 Absorption Spectrum 5 Fraunhofer Lines In The Solar Spectrum 6 Dwarf Star Spectra 7 Stellar Spectra 8 Wien’s Displacement Law 8 Cosmic Background Radiation 9 Doppler Effect 10 Spectral Line profi les 11 Red Shifts 12 Red Shift 13 Hertzsprung-Russell Diagram 14 Parallax 15 Ladder of Distances 1 SPECTROSCOPY AND THE STARS ELECTROMAGNETIC RADIATION RULER: THE ER RULER Energy Level Transition Energy Wavelength RF = Radio frequency radiation µW = Microwave radiation nm Joules IR = Infrared radiation 10-27 VIS = Visible light radiation 2 8 UV = Ultraviolet radiation 4 6 6 RF 4 X = X-ray radiation Nuclear and electron spin 26 10- 2 γ = gamma ray radiation 1010 25 10- 109 10-24 108 µW 10-23 Molecular rotations 107 10-22 106 10-21 105 Molecular vibrations IR 10-20 104 SPACE INFRARED TELESCOPE FACILITY 10-19 103 VIS HUBBLE SPACE Valence electrons 10-18 TELESCOPE 102 Middle-shell electrons 10-17 UV 10 10-16 CHANDRA X-RAY 1 OBSERVATORY Inner-shell electrons 10-15 X 10-1 10-14 10-2 10-13 10-3 Nuclear 10-12 γ 10-4 COMPTON GAMMA RAY OBSERVATORY 10-11 10-5 6 4 10-10 2 2 -6 4 10 6 8 2 SPECTROSCOPY AND THE STARS THE RYDBERG EQUATION The wavelengths of one electron atomic emission spectra can be calculated from the Use the Rydberg equation to fi nd the wavelength ot Rydberg equation: the transition from n = 4 to n = 3 for singly ionized helium. 1 2 1 1 In what region of the spectrum is this wavelength? = RZ ( 2 - 2 ) λ n1 n2 where λ = wavelength (in m.) and Z is the atomic number. Z = 1 for hydrogen. R is called the Rydberg constant and R = 1.096776 x 107 m-1 and we also require that n2 > n1 Why is it Z2, instead of, say, Z? What if n2 < n1? What is wrong with n2 = n1? Give both a math- ematical answer and an energy level answer. We will calculate the red Balmer line. For the red Balmer line n1 = 2 and n2 = 3. Note very carefully the difference between the sub- scripts and the energy level. Also note that n1 refers to the energy state after emission. Is n1 = 2 for all the lines in the Balmer series? For hydrogen, is n1 = 2 for any line not a Balmer line? For hydrogen, what do we call the lines where n1 = 1? So for the red Balmer line: 1 1 1 1 2 - n 2 = 2 - 2 = 0.1389 n1 2 2 3 1 2 6 -1 λ = RZ x 0.1389 = 1.523 x 10 m λ = 6.564 x 10-7 m = 656.4 nm 3 SPECTROSCOPY AND THE STARS ABSORPTION SPECTRUM Several factors are required to produce an absorption line. First, there must be a continuous emission back- ground. Then, between the continuous emission and the observer there must be some cooler atoms which Sun absorb and re-emit a particular wavelength of light. Then the absorption line results from the geometry. The cooler atom absorbs light in the line of sight but re-emits it in all directions. Thus most of the light (of Sodium atoms that particular wavelength) which would have reached the observer is instead spread out in all directions. The observer sees this as a black line (missing light) against a continuous spectrum. �� �� � � � � � � � � � � � � Sodium Absorption Line Solar Spectrum FRAUNHOFER ABSORPTION LINES IN THE SOLAR SPECTRUM K H h g G d F b E D C B 400 nm 500 nm 600 nm 700 nm Use the scale to measure and list the wavelength of each of the Fraunhofer absorption lines shown in picture 2. Check to see if any of them are familiar to you from the hydrogen spectrum. 4 SPECTROSCOPY AND THE STARS BLACK BODY RADIATION AND STELLAR SPECTRA O has temperature = 30000 K O B has temperature = 10000 K A has temperature = 7500 K F has temperature = 6000 K G has temperature = 5000 K K has temperature = 4000 K M has temperature = 3000 K B Intensity of Radiation A F G K M 1 0 nm 100 400 700 2500 nm Wavelength In picture 1, fi nd the wavelength at which each spec- Suppose we had evolved in a solar system with an M tral class has maximum radiation. type ‘sun’; predict in what wavelength range we might Our sun is a G type star. In what color range does have evolved vision and give your reasons. our sun radiate most intensely. O B A F G K M 350 nm 400 450 500 550 600 650 700 750 nm 2 Wavelength For each spectrum shown in picture 2, fi nd a star on In picture 2, for the stellar classes OBAFGK, which the main sequence of the Hertzsprung-Russell dia- line is not part of the Balmer series? gram which might have produced that kind of spec- trum and mark the star with the spectral class: O, B, A, F, G, K or M. 5 SPECTROSCOPY AND THE STARS DWARF STAR SPECTRA Measure the wavelengths of the priminant dips in the fl uxes shown on this page and compare them with- with the spectral lines on the previous page. 6 SPECTROSCOPY AND THE STARS STELLAR SPECTRA Here is a set of real stellar spectra, from very hot O THE ORIGIN OF BALMER LINES type stars down to relatively cool M type stars. Many of the stronger lines are lebeled. The lines with Greek letters label the Balmer lines of hydrogen. The Balmer line labeled β is the 486 nm line. What are the wavelengths of the Balmer γ and δ lines? Approximately where is the edge of the visible spec- n = 2 n = 2 trum; draw a vertical line marking the edge. What kind of electromagnetic radiation is involved in the lines to the left of the visible spectrum? Would the ionized calcium lines be visible? 1 Approximately what color, in an emission spectrum, 2 would the TiO (titanium oxide) bands be? Emission Absorption Picture 1 shows electrons moving into the n = 2 orbital of hydrogen, either from higher energy (n > 2) orbitals or from the ionized state. Picture 2 shows electrons being energized out of the n = 2 orbital. 7 SPECTROSCOPY AND THE STARS WIEN’S DISPLACEMENT LAW Wien’s Displacement Law -3 λ = 2.898 x 10 mK max T Suppose T = 5000 K. Then we can substitute that value into Wien’s Displacement Law: -3 λ = 2.898 x 10 mK max 5 x 103 K λ -7 max = 5.796 x 10 m = 579.6 nm λ Is max in the visible wavelength region and, if so, what color is it? THE COSMIC BACKGROUND RADIATION > > 1.0 mm 2.0 mm λ Find max for the Planck curve above (by measure- ment) and use the result in Wien’s Displacement Law to calculate the temperature of the universe. 8 SPECTROSCOPY AND THE STARS DOPPLER EFFECT C S V 2 A B D Suppose picture 2 shows a rotating star (like our sun). The left edge of the star is rotating toward us, while the 1 right is is moving away. Therefor the light from the left edge will be bluer than the light from the center and the light from the right edge will be reddder than the light from the center. In picture 1 a light emitting source S is moving to the right at velocity V. The same spectral line is observed at the four positions A, B, C, and D. Use the picture to tell whther the line is red shifted or blue shifted or unchanged at each of the four observing Approaching Receding positions. Using the Doppler equation: λ – λ V obs lab = λ c lab we can fi nd the velocity V of the source of electromag- 3 λ netic radiation by measuring a spectral line obs coming from the moving source and comparing it to the same Wavelength λ spectral line lab from a non moving source. (c is the speed of light.) Suppose we measure the light blue Balmer line from an λ astronomical spectrum at obs = 500 nm. We know that λ for this line lab = 486.4 nm. Then: λ – λ 500 nm – 486.4 nm obs lab = = 2.79 x 10-2 4 5 λ lab 486.4 nm If the spectral line shown in picture 4 is broadened due V = c x 2.79 x 10-2 = 8,388 kms-1 to the Doppler effect, what do you suppose might cause a spectral line to be split like the one in picture 5? In the example above, is the source moving toward us or away from us? How do we know? 9 SPECTROSCOPY AND THE STARS SPECTRAL LINE PROFILES Actual spectra are rarely the simple set of lines you can see in a discharge tube spectrum. There are pro- Thermal or Doppler Broadening cesses which split lines and processes which broaden Atoms and molecules are in motion.
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