How hot is the Sun?

Answer now (on your own):

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?

hydrogen atom energy levels:

Goals for today1) 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.

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 νshowing?

A) a photon of energy ν

B) a photon of frequency ν

C) a neutrino

D) a positron

Temperature means motion1

2

3

Collisions excite atoms

Hot diffuse(=not opaque)gas emits a

bright line spectrum (a.k.a. emission line spectrum)

atoms de-excite spontaneously

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

He

Ne

What you should have seen (the Balmer series):

How does the relative intensity of red and violet lines depend on gas temperature?

visible

UV

Hydrogen energy level transitions

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.

λ in Angstroms= λ in nm x 10

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 non-thermal types too…

“Planck function”(no, you don’t

have to memorize it!)

WATCH OUT: most people

think red means hot – but

“red hot” is pretty cool!

Bluer photons are more

energetic, from E=hν

blackbodies are colored according to their

temperatures…

Fun with jargon: a “blackbody” at the Sun’s temperature emits “white light”

perfect reflector vs. perfect blackbodya 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.)

Are blackbodies really “black”?

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

Think-Pair-ShareWhich of the following will show a blackbody

spectrum, but not generated by the object itself?

A) the MoonB) a person as seen by an infrared cameraC) 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

Peer Leading: Is the Sun a blackbody?

• complete the review exercise at right

• make a list of pros & cons for thinking of the Sun as a blackbody

(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?

A DE F

chromospherephotosphere

corona

layers not to scale

BC

so the blackbody temperatures of stars reveal their surface temperatures – but we usually drop the word “surface” �

THINK-PAIR-SHAREWhich are the two

hottest stars?a) A, Bb) A, Cc) B, Cd) No way to tell

ABC

Which star likely has temperature most similar to the Sun?

Stefan’s Law madness

• we will come back to F=σT4 later• for now, key point is that for Stefan’s Law,

F≡Fsurf (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 starbut for a single object, hotter means brighter

(= why sunspots look dark, just by comparison)

Think-Pair-ShareWhich is true?

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