3/26/2018. Atoms Light and Spectra. Topics For Today s Class. Reminder. Topics For Today s Class. The Atom. Phys1403 Stars and Galaxies

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1 Foundations of Astronomy 13e Seeds Foundations of Astronomy 13e Seeds Phys1403 Stars and Galaxies Instructor: Dr. Goderya Chapter 7 Atoms Light and Spectra Reminder Homework for Chapter 5, 6 and 7 is posted online. All homework's are due April 30 th for Extra -Credit Topics For Today s Class Atoms Structure and Electric (Coulomb) Force Isotopes, Ion and Binding Energy, Radioactivity Summary of Bohr Model of the Atom Spectroscopy A tool for Astronomers Interaction of Light and Matter Heat and Temperature Kelvin Scale Measuring Temperature A Black Body Radiator Radiation from Heated Objects Two Radiation Laws The Balmer Thermometer Topics For Today s Class Stellar Spectra Spectral Classification of Stars and Temperature Chemical Composition of Stars Absorption Lines Kirchhoff's Laws of Radiation Doppler Effect Red shift and Blue shift Calculating Doppler velocity Electron (-) Protons (+) Nucleus The Atom Quarks Smallest part of matter Nucleus, Protons, Neutrons and Electrons The elementary particle Quark Symbol - Z X A Z = Atomic Number Number of protons A = Mass Number Neutrons 1

2 Most Abundant Atoms in the Universe What Holds the Atom Together? 1H 1 2He 4 thinglink.com Charles-Augustin de Coulomb ( ) Electrons in an atom are bound to the nucleus via an electric force called coulomb force. Electrons are negative and Nucleus is positive so attraction force. k is a constant / Even though k is large, the charges are extremely small and that makes the electric force very small and short range. Apulsephysics.com What is an Isotopes? What is an Ion? An atom has lost one or more electrons wikipedia.com Chemistry-batz-wikispaces.com What is Ionization and Binding Energy? What is Radioactivity? Spontaneous emission of radiation in the form of particles or high energy photons resulting from a nuclear reaction α β How much energy is needed to keep the electron bind to the atom staff.orecity.k12.or.us α, β, γ γ chemistrytutorvista.com 2

3 Example of α Decay (Radiation) What is an Excited Atom is a radioactive particle Daughter Alpha decay can be represented by emission of 2 protons and 2 neutron from a nucleus Or emission of a Helium atom Parent Tackk.com Incoming photon can be absorbed if it has the correct energy It causes the electron to jump to a higher energy level scienceonline.com Summary of Bohr Model of the Atom Electron and an atom can only occupy discrete (quantized) energy levels. Photons are emitted / absorbed when an electron makes a transition from one energy level to another Wavelength depends upon the energy difference between the two levels ( ). Each spectral line represents an electron transition between two energy levels Each element has a unique set of spectral lines that can be used to identify its presence Texasgateway.org A Spectroscope Can Show a Spectrum What A Single Spectral Line Look Like? (a) Magnified view of one spectral line (Intensity Profile) (b) Measurement of Intensity Profile: Full Width Half Maximum (FWHM) astronomy.nju.edu.cn 3

4 A spectrum shows the structure of an atom The emission of light from an atom can be mapped in a diagram called the spectrum Hydrogen A Chemical has its Own Unique Spectrum Every atom and molecule has its own distinct spectrum Spectra differ in number of lines and the spacing between the lines The configuration of energy levels of each chemical element is Unique 300nm 500nm 700nm Helium Wonderwhizkid.com The Chemical Elements Each chemical element has a specific atomic configuration and therefore a unique spectrum. The periodic table will show this for any known chemical element. Why is Spectroscopy of Stars Important? Spectra of Stars and Spectroscopy can allow us to determine the temperature of stars. allow us to determine the chemical composition of stars. allow us to determine the radial velocity of stars. allow us to determine density of gas in a star. So let s learn how Heat and Temperature a common misconception Misconception: Temperature and heat can be used interchangeably Truth: Temperature is a measure of the average motion of the particles, whereas heat is the thermal energy moving from a hot object to a cool object 4

5 Temperature Scales Fahrenheit and Celsius scales are based on boiling and freezing point of water Kelvin Scale is a thermodynamic temperature scale based on the fact that at absolute zero all atomic motion ceases. More reliable and accurate. Astronomers use this scale because it is based on the motion of particle in an object Temperature Conversions F 32 C 32 K 273 Some Everyday Examples of Kelvin Temperature Wavelength and Kelvin Temperatures What is a Black Body? Hot Objects are Black Body Radiators Black Body Radiator. A hypothetical object that emits Electromagnetic radiation and whose spectrum is continuous with a peak in the wavelength that corresponds to the temperature of the object. Cavity Black Body Curves Blackbody Radiator Spectrum of a Hot Source: Continuous Spectrum 5

6 Celestial Objects Produce Blackbody Radiation Two Laws of Blackbody Radiation The Stefan-Boltzmann law: The hotter an object is, the more energy (Luminosity L) it emits L=E = *T 4 Where, E = Energy Flux = Energy given off in the form of radiation, per unit time and per unit surface area [J/s/m 2 ] = 5.7 x 10-8 J/sm 2 /K 4 Stefan-Boltzmann constant Two Laws of Blackbody Radiation (cont'd.) Wien s Law: The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases max 3,000,000 / T ( o K) where T is the temperature in Kelvin or T ( o K) 3,000,000 / max (nm) So if we know max we can find the surface temperature of stars. The sun =500 nm T = 3 x 10 6 /500 = 6000 K 10,000 o F Wein s Law gives the surface temperature of Sun Sun s Temperature Sun s Luminosity The sun: T= 6000 K, R=7 x 10 8 meters. What is its Luminosity (Energy)? L=E = 4x 3.14 x (7 x 10 8 ) 2 x 6 x 10-8 (6000) 4 = 5 x Watts (J/s) Compare with 40 watts light bulb 1.25 x W bulbs 100 million nuclear bombs every second Black Body Radiation (1) The light from a star is usually concentrated in a rather narrow range of wavelengths. The spectrum of a star s light is approximately a thermal spectrum called a black body spectrum. A perfect black body emitter would not reflect any radiation. Thus the name black body. 6

7 Two Laws of Black Body Radiation 1. The hotter an object is, the more luminous it is: L = A* *T 4 where A = surface area; = Stefan-Boltzmann constant 2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases. Wien s displacement law: max 3,000,000 nm / T K (where T K is the temperature in Kelvin). Surface Temperature of Stars from Color Stars can be considered to behave as black bodies. Stars appear to have color These colors tell us about the star s temperature Each color peak at a specific wavelength in the black body curve We can use Wein s law to find the temperature of stars. However, there are other better methods. The Color Index (1) The Color Index (2) The color of a star is measured by comparing its brightness in two different wavelength bands: The blue (B) band and the visual (V) band. B band V band We define the Color Index B V (i.e., B magnitude V magnitude). We define B-band and V-band magnitudes just as we did before for total magnitudes (remember: a larger number indicates a fainter star). The bluer a star appears, the smaller the color index B V. The hotter a star is, the smaller its color index B V. Chemical Composition of Stars Spectra of stars are more complicated than pure blackbody spectra. They contain Remember Absorption Lines characteristic lines, called absorption lines. To understand those lines, we need to understand atomic structure and the interactions between light and atoms. a) Spectrum of the Sun b) NGC 2392 Emission Nebula 7

8 The Hydrogen Atom: The Balmer Lines n = 1 Transitions from 2 nd to higher levels of hydrogen H H H The only hydrogen lines in the visible wavelength range. Hydrogen Absorption Spectrum Dominated by Balmer Lines Modern spectra are usually recorded digitally and represented as plots of intensity vs. wavelength 2 nd to 3 rd level = H (Balmer alpha line) 2 nd to 4 th level = H (Balmer beta line) Observations of the H-Alpha Line Excited clouds of gas in space emit light at all of the Balmer wavelengths, but you see only the red, blue, and violet photons blending to create the purplepink color typical of ionized hydrogen. Emission nebula, dominated by the red Hα line The Balmer Thermometer Balmer line strength is sensitive to temperature: Most hydrogen atoms are ionized => weak Balmer lines Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n = 2 => weak Balmer lines What if we find to two equal line strength instead of a one at peak? How do we know which one to use? Measuring the Temperatures of Stars Comparing line strengths, we can measure a star s surface temperature! 8

9 Kirchhoff s Laws of Radiation (1) 1. A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum. Kirchhoff s Laws of Radiation (2) 2. A low-density gas excited to emit light will do so at specific wavelengths and thus produce an emission spectrum. Light excites electrons in atoms to higher energy states Transition back to lower states emits light at specific frequencies Kirchhoff s Laws of Radiation (3) 3. If light comprising a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum. The Spectra of Stars Inner, dense layers of a star produce a continuous (blackbody) spectrum. Light excites electrons in atoms to higher energy states Frequencies corresponding to the transition energies are absorbed from the continuous spectrum. Cooler surface layers absorb light at specific frequencies. => Spectra of stars are absorption spectra. Spectral Classification of Stars (1) Spectral Classification of Stars (2) Different types of stars show different characteristic sets of absorption lines. Temperature O B A F G K M Surface temperature Kirchhoff's Laws of Radiation allow us to do just that 9

10 Spectral Classification of Stars (3) Chemical Composition of Stars Mnemonics to remember the spectral sequence: Only Oh Only Brilliant Boy, Bad Artistic An Assistants Females F Forget Generate Grade Generally Killer Kills Known Mnemonics Me Mnemonics Cecilia Payne-Gaposchkin A spectrum can tell you the chemical composition of the star. C: Hydrogen; D: Sodium; E: Iron; F: Hydrogen; G: Iron; H& K: Calcium ExtremeTech Analyzing Absorption Spectra Each element produces a specific set of absorption (and emission) lines. Comparing the relative strengths of these sets of lines, we can study the composition of gases. By far the most abundant elements in the Universe Spectra can also tell us about velocity The Doppler effect allows us to measure the component of the source s velocity along our line of sight The Doppler Effect Blue Shift (to higher frequencies) v r Red Shift (to lower frequencies) The light of a moving source is blue/red shifted by / 0 = v r /c 0 = actual wavelength emitted by the source Wavelength change due to Doppler effect v r = radial velocity The Doppler Effect (3) Take of the H (Balmer alpha) line: 0 = 656 nm Assume, we observe a star s spectrum with the H line at = 658 nm. Then, = 2 nm. We find = = 3*10-3 Thus, or v r /c = 0.003, v r = 0.003*300,000 km/s = 900 km/s. The line is red shifted, so the star is receding from us with a radial velocity of 900 km/s. 10

11 The Doppler Effect (cont d.) The Doppler Effect (cont d.) Source: Web Doppler Broadening Blue shifted abs. v r Atoms in random thermal motion v r Red shifted abs. In principle, line absorption should only affect a very unique wavelength. In reality, also slightly different wavelengths are absorbed. Lines have a finite width; we say: they are broadened. One reason for broadening: The Doppler effect! Observer Line Broadening Higher Temperatures Higher thermal velocities broader lines Doppler Broadening is usually the most important broadening mechanism. Atomic Density If you could fill a teaspoon just with material as dense as the matter in an atomic nucleus, it would weigh ~ 2 billion tons!! 11

12 Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. 12