1. Continuous and Discrete Emission of Radiation, or How to Make Starlight (part 1) Chapter 7

2. Assigned Reading Today’s assigned reading is: Today’s assigned reading is: Up to Chapter 7.3, includedUp to Chapter 7.3, included

3. Origin of light Light (electromagnetic radiation) is just a varying electric and magnetic fields that propagate in space. Now, two very important things happen in nature: An electric field that varies in strength (e.g., due to acceleration of an electron) generates electromagnetic radiation. An electromagnetic radiation, in turn, accelerates electrons (or any electrically charged particle) We discuss two major mechanisms of light production: Blackbody Radiation.a.k.a. thermal radiation Spectral Line Emission by atoms and molecules

4. Reminder #1: E.m. Radiation generally contains bundles of waves of different wavelengths (colors) How much of each color is present in a given bundle of e.m. radiation, I.e. the distribution of intensity of each wavelength, is called the spectrum Here is an example of optical (visible) light:

5. The Difference Between Black and White “White” light – contains all the frequencies of the visible part of the spectrum. “White” light – contains all the frequencies of the visible part of the spectrum. White paint – diffusely scatters all frequencies of the visible part of the spectrum equally. White paint – diffusely scatters all frequencies of the visible part of the spectrum equally. Black paint – absorbs all frequencies of the visible part of the spectrum equally. Black paint – absorbs all frequencies of the visible part of the spectrum equally. “Blackbody Radiation” – emits and absorbs radiation over a specific set of frequencies. “Blackbody Radiation” – emits and absorbs radiation over a specific set of frequencies.

6. Reminder #2: Heat and Temperature Temperature refers to the degree of agitation, or the speed with which the particles move (T~v 2 ). All atoms and molecules are moving and vibrating unless at absolute zero temperature (T = 0 K = -459.7 F). Water freezes at 273 K and boils at 373 K. Heat refers to the amount of energy stored in a body as agitation among its particles and depends on density as well as temperature.

7. Scales of Temperature °C = (°F-32) / 1.8 °F = 1.8*°C + 32 °C = (°F-32) / 1.8 °F = 1.8*°C + 32 °C = °K - 273.16 °K = °C + 273.16 °C = °K - 273.16 °K = °C + 273.16 The physical scale of temperature is the Kelvin one (°K degree) The physical scale of temperature is the Kelvin one (°K degree) The other scales are just convenient for humans The other scales are just convenient for humans At absolute zero of temperature (atoms are still), and °K=0 At absolute zero of temperature (atoms are still), and °K=0 °C = -273.16 °F = -459.7°C = -273.16 °F = -459.7

8. The Generation of Light. I: Continuum Emission Light and matter interact at the atomic level by acceleration/deceleration of charged particles (mostly electrons but also protons –-only protons are 2000x heavier than electrons) Light and matter interact at the atomic level by acceleration/deceleration of charged particles (mostly electrons but also protons –-only protons are 2000x heavier than electrons) Acceleration or deceleration of an electron (I.e. a charged particle) result in the production of an electromagnetic wave Acceleration or deceleration of an electron (I.e. a charged particle) result in the production of an electromagnetic wave If the electron is decelerated: If the electron is decelerated: An e.m. wave is generatedAn e.m. wave is generated The mechanical energy losses of the electron are converted into e.m. energyThe mechanical energy losses of the electron are converted into e.m. energy The harder the deceleration, the bigger the energy of the e.m. radiationThe harder the deceleration, the bigger the energy of the e.m. radiation Conversely, an electron can be accelerated by e.m. radiation Conversely, an electron can be accelerated by e.m. radiation The e.m. wave disappearsThe e.m. wave disappears The energy of the e.m. wave now goes into mechanical energy of the electronThe energy of the e.m. wave now goes into mechanical energy of the electron The more energetic the e.m. wave, the harder the acceleration of the electronThe more energetic the e.m. wave, the harder the acceleration of the electron

9. The Generation of Light. I: Continuum Emission, or Black Body Radiation If matter is at thermal equilibrium, temperature does not change, average velocities of atoms/molecules are constant If matter is at thermal equilibrium, temperature does not change, average velocities of atoms/molecules are constant But electrons collide against atoms and each other all the time, i.e. accelerate and decelerate all the time. But electrons collide against atoms and each other all the time, i.e. accelerate and decelerate all the time. E.m. radiation continuously generated and absorbed, with energy (wavelength) that only depends on mechanical energy of electrons. E.m. radiation continuously generated and absorbed, with energy (wavelength) that only depends on mechanical energy of electrons. In this condition, there is equal exchange of energy between matter and radiation: none of them gains or looses energy In this condition, there is equal exchange of energy between matter and radiation: none of them gains or looses energy The resulting distribution of energy (wavelength), I.e. spectrum of e.m. radiation, is unique and it is called Black Body The resulting distribution of energy (wavelength), I.e. spectrum of e.m. radiation, is unique and it is called Black Body The distribution of velocities of electrons decides the distribution of energy (wavelengths) of e.m. radiation. The distribution of velocities of electrons decides the distribution of energy (wavelengths) of e.m. radiation. Velocity depends on Temperature, hence distribution of energy of e.m. radiation depends of Temperature. Velocity depends on Temperature, hence distribution of energy of e.m. radiation depends of Temperature. One Temperature, one Spectrum One Temperature, one Spectrum Black Body radiation is the e.m. emission of matter at thermal equilibrium (constant T) with itself and with radiation Black Body radiation is the e.m. emission of matter at thermal equilibrium (constant T) with itself and with radiation

10. Black body Spectrum It is the spectrum of radiation at thermal EQUILIBRIUM with matter It is continuum in wavelength, no gaps from λ-0 to λ=∞ Its overall shape is universal, with peak of intensity at some special λ that depends on temperature T Matter at equilibrium with e.m. Radiation acts as a "perfect emitter" or a "perfect absorber“. A black object is the best way to make the perfect B.B. emitter and absorber.

11. Discussion Question Why does NASA paint spacecraft white? Absorption Frequency Infrared Visible Absorption Spectrum of White Paint 40% 0% Absorption Spectrum of Black Paint 80%

12. Hotter objects have electrons moving with higher speed, thus they emit photons with a higher average energy. Wien’s Law: Wien’s Law: The wavelength at the peak of the blackbody emission spectrum is given byThe wavelength at the peak of the blackbody emission spectrum is given by max = 3,000,000/T max = 3,000,000/T (P.S. remember that E = hc/) (P.S. remember that E = hc/) Thus, the hotter the matter, the higher the energy of the e.m. radiation Thus, the hotter the matter, the higher the energy of the e.m. radiation

14. Black body Radiation T decides λ peak which decides the color

15. The graph below shows the blackbody spectra of three different stars. Which of the stars is at the highest temperature? Which has the highest energy (energy is the total area under the curve)? 1) Star A 2) Star B 3) Star C A B C Energy per Second Wavelength

16. Hotter objects emit more total radiation per unit area. However, a big cold object can emit the same or more energy (depending on how big it is) than a small, hotter one Cold Hot Stefan-Boltzmann Law: Emitted power per square meter = σ T 4 σ = 5.7 x 10 -8 W/(m 2 K 4 ) Total emitted power: E = 4  R 2 σ T 4

17. You are gradually heating up a rock in an oven to an extremely high temperature. As it heats up, the rock emits nearly perfect theoretical blackbody radiation – meaning that it 1) is brightest when hottest. 2) is bluer when hotter. 3) is both 4) is neither

18. L=A  T 4

19. Campfires Campfires are blue on the bottom, orange in the middle, and red on top. Which parts of the fire are the hottest? the coolest? As atoms get hotter, they wiggle faster and collide to each other harder ---> more light they emit and more wiggle per second = frequency goes up = wavelength goes down. Thus bluer. Thus, as temperature goes up light gets stronger and gets blue.

20. More on Blackbody Radiation (a.k.a. Thermal Radiation) Every object with a temperature greater than absolute zero emits blackbody radiation.Every object with a temperature greater than absolute zero emits blackbody radiation. Hotter objects emit more total radiation per unit surface area.Hotter objects emit more total radiation per unit surface area. Hotter objects emit photons with a higher average energy.Hotter objects emit photons with a higher average energy.

21. How to Make Light (Part 2): Line Emission/Absorption (light with discrete wavelengths) Structure of atoms Structure of atoms Energy levels and transitions Energy levels and transitions Emission and absorption lines Emission and absorption lines Light scattering Light scattering

22. The Structure of Matter: Atoms A Planetary Model of the Atom Atoms are made of electrons, neutrons, and protons. The bounding force: the attractive Coulomb (electrical) force between the positively charged protons in the nucleus and the negatively charged electrons around the nucleus.

23. The Structure of Matter: Atoms An atom consists of an atomic nucleus (protons and neutrons) and a cloud of electrons surrounding it. Almost all of the mass is contained in the nucleus, while almost all of the space is occupied by the electron cloud.

24. Nuclear Density If you could fill just a teaspoon with material as dense as the matter in an atomic nucleus, it would weigh ~ 2 billion tons!!

25. Different Kinds of Atoms The kind of atom depends on the number of protons in the nucleus. Helium 4 Different numbers of neutrons ↔ different isotopes Most abundant: Hydrogen (H), with one proton (+ 1 electron) Next: Helium (He), with 2 protons (and 2 neutrons + 2 el.)

26. Electron Orbits Electron orbits in the electron cloud are restricted to very specific radii and energies. r 1, E 1 r 2, E 2 r 3, E 3 These characteristic electron energies are different for each individual atom, i.e. element.

27. In other words, the electron in a given orbit has the energy level that competes to that orbit. The higher the orbit, the higher the energy. Different atoms have different energy levels, set by quantum physics. Quantum means discrete! Energy Levels

28.  Inner orbitals are very tightly bound, because electrical attraction with nucleus is stronger  Each orbitals is characterized by a given amount of energy  To change energy level, an electron must either absorb or emit a photon that has the same amount of energy as the difference between the energy levels  E = h = hc/ --- Larger energy difference means higher frequency.  Different jumps in energy levels means different frequencies of light absorbed, i.e. different colors Atomic Transition: Excitation of Atoms

29. Atomic Transitions: excitation of atoms An electron can be kicked into a higher orbit when it absorbs a photon with exactly the right energy. Photons with other energy pass by the atom unabsorbed. E ph = E 4 – E 1 E ph = E 3 – E 1 (Remember that E ph = h*c/ ) Wrong energy The photon is absorbed, and the electron is in an excited state. Remember that Energy = Wavelength = Colors

30. Spectral Line Emission If a photon of exactly the right energy is absorbed by an electron in an atom, the electron will gain the energy of the photon and jump to an outer, higher energy orbit. A photon of the same energy is emitted when the electron falls back down to its original orbit.

32. Spectral Line Emission Collisions (like in a hot gas) can also provide electrons with enough energy to change energy levels. A photon of the same energy is emitted when the electron falls back down to its original orbit.

33. Energy Levels of a Hydrogen Atom Different allowed “orbits” or energy levels in a hydrogen atom. Emission line spectrum Absorption line spectrum

35. Spectral Lines of Some Elements Argon Helium Mercury Sodium Neon Spectral lines are like a cosmic barcode system for elements.

36. Atoms of different elements have unique spectral lines because each element has atoms of a unique color has atoms of a unique color has a unique set of neutrons has a unique set of neutrons has a unique set of electron orbits has a unique set of electron orbits has unique photons has unique photons

37. 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.

38. 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

39. 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. Light excites electrons in atoms to higher energy states Frequencies corresponding to the transition energies are absorbed from the continuous spectrum.

40. The Spectrum of a star (the Sun) There are similar absorption lines in the other regions of the electromagnetic spectrum. Each line exactly corresponds to chemical elements in the stars.

41. Sources of spectral lines Reflection nebula Emission nebula

42. Absorption Spectrum Dominated by Balmer Lines Modern spectra are usually recorded digitally and represented as plots of intensity vs. wavelength

43. An Object’s Spectrum Encoded in an object’s spectrum is information about the emitter/absorber. This is how we learn what the Universe is made of!

44. Intensity, Imaging (spatial distribution of the light) Spectra (composition of the object and the object’s velocity) There are three basic aspects of the light from an object that we can study from the Earth. Variability (change with time)