1

Lecture 6: Thermal radiation

Spectra of Astronomical Objects

2

Bright lines visible in a (non-continuous) spectrum

a) are related to the energy level inparticular elements.

b) are produced as electrons inatoms drop energy levels.

c) are characteristic of particularelements.

d) All of the abovee) None of the above

Measuring Temperature• It is useful to think of

temperature in a slightlydifferent way than we areaccustomed to

– Temperature is a measure of themotion of atoms in an object

– Objects with low temperatureshave atoms that are not movingmuch

– Objects with high temperatureshave atoms that are movingaround very rapidly

• The Kelvin temperature scalewas designed to reflect this

– 0 ° K is absolute zero –the atomsin an object are not moving at all!

0 kelvin = -459.67 degrees Fahrenheit= -273.15 degrees Celsius

3

Blackbodies

• A body that absorbs all energyincident on it and emits energyof all wavelengths is called ablackbody

• The Sun, a stovetop element,or a piece of charcoalapproximate a blackbody

YOU are a blackbody as well!

Blackbodies

4

The universe has a BB component

Blackbodies

5

The Blackbody Spectrum• As a blackbody is heated, the

atoms in it start to move fasterand faster.

– When they collide, they emit aphoton with an energyproportional to how hard they hit

• Some collide lightly, andproduce long-wavelengthradiation

• Some collide very hard, andproduce short-wavelengthradiation

• Most are somewhere inbetween

– As the body gets hotter, thenumber of collisions increase,and the number of hardcollisions increase

Gentle collisions

Hard collisions

Results of More Collisions• Additional collisions

mean that more photonsare emitted, so the objectgets brighter

• Additional hard collisionsmeans that more photonsof higher energy areemitted, so the objectappears to shift in colorfrom red, to orange, toyellow, and so on.

• Of course we have a Lawto describe this…

6

Wien’s Law and the Stefan-Boltzmann Law

• Wien’s Law:– Hotter bodies emit

more strongly atshorter wavelengths

– I.e hotter=bluer

• SB Law:– The luminosity of a

hot body rises rapidlywith temperature

– I.e. hotter = brighter

Taking the Temperature ofAstronomical Objects

• Wien’s Law lets us estimatethe temperatures of starseasily and fairly accurately

• We just need to measure thewavelength (λmax) at whichthe star emits the mostphotons

• Then,

max

6nmK 109.2

!

"#=T

7

!

T =2.9 "10

6 K # nm

$max

The Stefan-Boltzmann Law• If we know an object’s

temperature (T), we cancalculate how much energythe object is emitting usingthe SB law

• σ is the Stefan-Boltzmannconstant, and is equal to5.67×10-8 Watts/m2/K4

• The Sun puts out 64 millionwatts per square meter –lots of energy!

4TL !=

8

Given 5 stars with the colorsbelow, which has the lowestsurface temperature?

a) Blueb) Whitec) Redd) Orangee) yellow