Transcript Spectra
Spectra What determines the “color” of a beam of light? The answer is its frequency, or equivalently, its wavelength. We see different colors because our eyes react differently to electromagnetic waves of different frequencies. A prism splits a beam of light up into the familiar "rainbow" of colors because light rays of different wavelengths are bent, or affected by refraction and dispersion, as they pass through a prism—red light is bent the least, violet light is bent the most. (ROY G BIV) The Electromagnetic Spectrum Spectrograph Any hot radiating object, will produce a continuous spectrum of light. Spectrum Light Intensity as a function of Wavelength. Intensity Wavelength Spectrum Light Intensity as a function of Frequency. Intensity f = c/l Frequency Blackbody Radiation Stefan-Boltzman Law Energy Flux E = sT4 As the temperature increases, the energy output increases more dramatically Stefan-Boltzmann Constant s = 5.6705 x 10-5 erg cm2/K4 s Blackbody Spectrum Energy Intensity (Shape of Spectrum) E = 2 hc2/l5 [ehc/lkT - 1]-1 Planck’s Constant h = 6.625 x 10-27 erg-sec Boltzmann Constant k = 1.38 x 10-16 erg/K Speed of Light c = 3 x 108 m/s The Sun as a Blackbody Radiator (T=5800K) Hot Radiating Objects Imagine a piece of metal placed in a hot furnace. At first, the metal becomes warm, although its visual appearance doesn't change. As it heats up, it begins to glow dull red, then orange, brilliant yellow, and finally white hot. Objects that emit light energy are called blackbody radiators. How do we explain this energy increase and change in color? Wien’s Radiation Law Wien's law relates the temperature T of an object to the wavelength maximum at which it emits the most radiation. Mathematically, if we measure T in kelvins and the wavelength maximum (l) in nanometers, we find that* lmax = 3,000,000/T *3,000,000 is an approximation of the true value 2,900,000 (just like 300000000 m/s approximates the speed of light 299792458. Solar Spectrum Peak The Sun has a surface temperature of 5800 K. lmax = 3,000,000/T lmax = 3,000,000/5800 = 517.2 nm (green-YELLOW-orange) Wein’s Law and Color As the temperature of a radiating object goes up, 1) it emits more light, 2) the peak of its maximum emission moves to higher energies. (higher f, shorter l) Human lmax T = 98.60 F = 5/9(98.6-32) = 370 C = (37 + 273) = 310 Kelvin lmax = 3,000,000/T lmax = 3,000,000/310 = 9677 nm infrared (heat) Spectral Sensitivity of Electromagnetic Detectors Different Wavelength Views of Our Sun What you see depends upon what range of wavelengths you look at. The Sky at Many Wavelengths Visual, Ultraviolet, Radio and X-ray images of the Ring Nebula (M56). Atomic Spectra Absorption Spectrum Photons with the correct energy, are absorbed by the gas surrounding the continuous source. They are re-radiated in all directions yielded a decrease in light from wavelengths corresponding to the energies of atoms in the gas. Emission Spectrum Seen against the background of space, only the photons emitted by the excited atoms in the gas are seen. These wavelengths only come from allowed energies in the atoms of the gas. Emission and Absorption In order to absorb energy, radiation must contain photons of the energy that corresponds to energy differences found within the atom. Absorption of these photons excites the electrons to higher energy states. Electrons, like humans would rather be couch potatoes, so they soon give up their energy to seek the lowest energy state. To give up energy they emit photons that have energies corresponding to the energy differences needed to cascade down. They can do this in steps, emitting lots of low energy photons, or all at once, emitting one large energy photon. Energy Level Schematic • Solar System Analogy for an... – Massive Star – Planets in orbit – Kepler’s Laws – Atom Massive Nucleus Electrons in Orbit Conservation of Energy and Angular Momentum Atomic Energy States • The minimum energy state (lowest electron orbit) is the ground state. Atomic Energy Levels Emission and Absorption In order to absorb energy, radiation must contain photons of the energy that corresponds to energy differences found within the atom. Absorption of these photons excites the electrons to higher energy states. Electrons, like humans would rather be couch potatoes, so they soon give up their energy to seek the lowest energy state. To give up energy they emit photons that have energies corresponding to the energy differences needed to cascade down. They can do this in steps, emitting lots of low energy photons, or all at once, emitting one large energy photon. Energy Transitions E5 E4 E3 E2 eE1 This photon’s l was too short! E = hf = hc/l E5 E4 E3 E2 eE1 This photon’s l was just right! E = hf = hc/l E5 E4 E2-E1 = E E3 E2 eE1 Wow! E2-E1 = E E5 E4 eE3 E2 E1 Here It Comes Again! E3-E2 = E … NOT! E5 E4 eE3 E2 E1 Fickle electron? E3-E2 = E E5 E4 eE3 E2 E1 Yahoo! I feel energized! E5 E4 e- E3 E2 E1 I’m Getting Sleepy... E5 E4 e- E3 E2 E1 Ahhhhhh Photon Energy = E3-E1 E5 E4 E3 E2 eE1 Going Down EITHER THIS: E3-E1 Photon Energies E3-E1 = (E3-E2) + (E2-E1) OR THIS E3-E2 AND THIS E2-E1 E3 E2 eE1 Atomic Energy Transitions Hydrogen Atom Energy Level Model Atomic Energy Levels Are Unique A Spectrum can give you information about temperature, chemical composition, and density. Helium Carbon Molecular Energy States Molecules have unique energy states also. Atomic Signatures • Atomic Spectra are like… • All Unique, Get the picture? Atomic Spectra Mug Shots Atomic Energy Levels Energy of a Photon Atomic Energy Level Difference E = hf = hc/l DE = En - Em = h(fn-fm) Infrared A foggy day in visual light, and the same picture with a sensitive infrared camera. Fog is opaque to visible wavelengths and transparent in the infrared wavelengths Transparency of Earth’s Atmosphere The Orion Nebula Infrared, Visual and X-ray images in the direction of Orion. a-Orion the red star (Betelguese) and b-Orion the blue (Rigel) The Visible Solar Spectrum • Absorption Spectrum: Continuous spectrum with absorption lines Stellar Spectra Stellar Spectra Solar Composition Spectrum Parameters* Observations of Spectra Yield: 1. Distance (1/R2, assuming intrinsic brightness known) 2. Temperature (color, peak wavelength intensity) 2. Chemical Composition (spectral lines) 3. Densities (spectral line strengths) 4. Velocities (doppler shift) *Light contains a LOT of information!