How hot is the Sun? hydrogen atom energy levels: Answer now (on your own):

Transcription

1 hydrogen atom energy levels: Answer now (on your own): How hot is the Sun? 1) Which shows absorption of a photon to put the atom in the first excited state? 2) Which shows emission of the shortest wavelength photon? 3) Which shows deexcitation involving a photon in the visible wavelength range?

2 Goals for today 1) Review: Analyze how photon absorption and emission relates to atomic transitions. Use E=hν and c=λν to relate transitions to different color lines. Clarify ν. 2) Review: Interpret temperature as particle energy of motion. Explain how bright-line and blackbody spectra form, depending on gas temperature and opacity. 3) Revisit why the Sun (and other objects) shine. Classify blackbodies vs. reflectors vs. other types of spectra. 4) Contrast the temperatures in different layers of the Sun. 5) Correlate blackbody temperature with color and predict the relative (surface) temperatures of stars. 6) Clarify Stefan s Law.

3 Watch out! ν ( nu as in E=hν and c=λν) is a fancy Greek letter for frequency it s not a v! Even worse, ν is measured in units of Hertz this is just a fancy name for 1/seconds!! What is this ν showing? A) a photon of energy ν B) a photon of frequency ν C) a neutrino D) a positron

4 1 Temperature means motion 2 Collisions excite atoms 3 Hot diffuse(=not opaque) gas emits a bright line spectrum (a.k.a. emission line spectrum) atoms de-excite spontaneously

5 He The complexity of the atom determines what emission lines you see predict: what will a hot Hydrogen spectrum look like in the visible? Ne

6 What you should have seen (the Balmer series): How does the relative intensity of red and violet lines depend on gas temperature?

7 UV visible Hydrogen energy level transitions λ in Angstroms= λ in nm x 10 Singly ionized Helium (He+) energy level transitions, with the ground state cut off at the bottom Peer Leading Why should the energy levels of He + show similarities to those of H? How would you compute the energy of the transition between the first and second excited states of He +? (Set up the calculation, don t do it.) Explain why/which way the energy should differ from the analogous transition for H, based on the difference between the two nuclei.

8 Opaque gas traps photons As they bounce around, being scattered, absorbed, and re-emitted, photons experience memory loss and come to follow a blackbody (=thermal) spectrum: This is one type of continuum spectrum there are nonthermal types too Planck function (no, you don t have to memorize it!)

9 blackbodies are colored according to their temperatures WATCH OUT: most people think red means hot but red hot is pretty cool! Bluer photons are more energetic, from E=hν Fun with jargon: a blackbody at the Sun s temperature emits white light

10 Are blackbodies really black? perfect reflector vs. perfect blackbody a perfect reflector emits no light of its own a perfect blackbody emits only at its own temperature (absorbed light is trapped and converted to the same temp.)

11 We see almost everything, except for the Sun and stars, by reflected light. To see the inherent thermal radiation of people and planets, we would have to be able to see in the infrared. Why? infrared camera images

12 Think-Pair-Share Which of the following will show a blackbody spectrum, but not generated by the object itself? A) the Moon B) a person as seen by an infrared camera C) a brown dwarf star (a failed star that is heated by perpetual contraction but never ignites thermonuclear fusion) D) a puddle reflecting a neon sign

13 Peer Leading: Is the Sun a blackbody? corona chromosphere photosphere A BCDE F complete the review exercise at right make a list of pros & cons for thinking of the Sun as a blackbody layers not to scale (i) Order from highest to lowest in temperature. (C & F can be considered roughly equal.) Label the layers below D. (ii) Where are there transitions between opaque and diffuse? (iii) Which layer is closest to the 5800 K temperature derived from the shape of the Sun s spectrum?

14 so the blackbody temperatures of stars reveal their surface temperatures but we usually drop the word surface THINK-PAIR-SHARE Which are the two hottest stars? a) A, B b) A, C c) B, C d) No way to tell A C B Which star likely has temperature most similar to the Sun?

15 Stefan s Law madness we will come back to F=σT 4 later for now, key point is that for Stefan s Law, F F surf (F at surface!) defined as to get total energy, must sum over surface a big red star can be both cooler AND brighter than a small blue star but for a single object, hotter means brighter (= why sunspots look dark, just by comparison)

16 Which is true? Think-Pair-Share A) an object that emits a blue blackbody spectrum is brighter than another object that emits a red blackbody spectrum B) an object that emits a blue blackbody spectrum is cooler than another object that emits a red blackbody spectrum C) gas that emits a blue blackbody spectrum is hotter than gas that emits a bright line spectrum D) gas that emits a blue blackbody spectrum is denser than gas that emits a bright line spectrum