Blackbody Radiation & Atomic Spectra

“Light” – From gamma-rays to radio waves

• The vast majority of information we have about astronomical objects comes from light they either emit or reflect

• Here, “light” stands for all sorts of electromagnetic radiation• A type of wave, electromagnetic in origin• Understanding the properties of light allows us to use it to

determine the– temperature – chemical composition – (radial) velocity

of distant objects

Waves• Light is a type of

wave• Other common

examples: ocean waves, sound

• A disturbance in a medium (water, air, etc.) that propagates

• Typically the medium itself does not move much

Wave Characteristics

• Wave frequency: how often a crest washes over you• Wave speed = wavelength () frequency (f)

Electromagnetic Waves

• Medium = electric and magnetic field• Speed = 3 105 km/sec

Electromagnetic Spectrum

Energy: low medium high

Electromagnetic Radiation: Quick Facts

• There are different types of EM radiation, visible light is just one of them

• EM waves can travel in vacuum, no medium needed• The speed of EM radiation “c” is the same for all

types and very high ( light travels to the moon in 1 sec.)

• The higher the frequency, the smaller the wavelength ( f = c)

• The higher the frequency, the higher the energy of EM radiation (E= h f, where h is a constant)

Visible Light• Color of light determined

by its wavelength

• White light is a mixture of all colors

• Can separate individual colors with a prism

Three Things Light Tells Us

• Temperature – from black body spectrum

• Chemical composition– from spectral lines

• Radial velocity– from Doppler shift

Temperature Scales

Fahrenheit Centigrade Kelvin

Absolute zero 459 ºF 273 ºC 0 K

Ice melts 32 ºF 0 ºC 273 K

Human body temperature

98.6 ºF 37 ºC 310 K

Water boils 212 ºF 100 ºC 373 K

Black Body Spectrum• Objects emit radiation of all frequencies,

but with different intensities

Higher Temp.

Lower Temp.Ipeak

Ipeak

Ipeak

fpeak<fpeak <fpeak

Cool, invisible galactic gas

(60 K, fpeak in low radio

frequencies)

Dim, young star

(600K, fpeak in infrared)

The Sun’s surface

(6000K, fpeak in visible)

Hot stars in Omega Centauri

(60,000K, fpeak in ultraviolet)

The higher the temperature of an object, the higher its Ipeak and fpeak

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Wien’s Law

• The peak of the intensity curve will move with temperature, this is Wien’s law:

Temperature * wavelength = constant

= 0.0029 K*m

So: the higher the temperature T, the smaller the wavelength, i.e. the higher the energy of the electromagnetic wave

Example: Wien’s Law• Sun T=6000K, Earth t=300K (or you!)

• The Sun is brightest in the visible wave lengths (500nm). At which wave lengths is the Earth (or you) brightest?

• Wien: peak wave length is proportional to temperature itself Scales linearly!

• Factor f=T/t=20, so f1 =201=20, so peak wavelength is 20x500nm=10,000 nm = 10 um

• Infrared radiation!

Energy & Power Units

• Energy has units Joule (J)

• Rate of energy expended per unit time is called power, and has units Watt (W)

• Example: a 100 W = 100 J/s light bulb emits 100 J of energy every second

• Nutritional Value: energy your body gets out of food, measured in Calories = 1000 cal = 4200 J

• Luminosity is the same as power radiated

Stefan’s Law

• A point on the Blackbody curve tells us how much energy is radiated per frequency interval

• Question: How much energy is radiated in total, i.e. how much energy does the body lose per unit time interval?

• Stefan(-Boltzmann)’s law: total energy radiated by a body at temperature T per second: P = A σ T4

• σ = 5.67 x 10-8W/(m2 K4)

Example: Stefan-Boltzmann Law

• Sun T=6000K, Earth t=300K (or you!)

• How much more energy does the Sun radiate per time per unit area?

• Stefan: Power radiated is proportional to the temperature (in Kelvin!) to the fourth power

• Scales like the fourth power!

• Factor f=T/t=20, so f4 =204=24x104=16x104

160,000 x

Measuring Temperatures

• Find maximal intensity

Temperature (Wien’s law)

Identify spectral lines of ionized elements Temperature

Color of a radiating blackbody as a function of temperature

• Think of heating an iron bar in the fire: red glowing to white to bluish glowing

Spectral Lines – Fingerprints of the Elements

• Can use this to identify elements on distant objects!

• Different elements yield different emission spectra

Kirchhoff’s Laws: Dark Lines

Cool gas absorbs light at specific frequencies

“the negative fingerprints of the elements”

Kirchhoff’s Laws: Bright lines

Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”

Kirchhoff’s Laws

1. A luminous solid or liquid (or a sufficiently dense gas) emits light of all wavelengths: the black body spectrum

2. Light of a low density hot gas consists of a series of discrete bright emission lines: the positive “fingerprints” of its chemical elements!

3. A cool, thin gas absorbs certain wavelengths from a continuous spectrum dark absorption ( “Fraunhofer”) lines in continuous spectrum: negative “fingerprints” of its chemical elements, precisely at the same wavelengths as emission lines.

Spectral Lines • Origin of discrete spectral lines: atomic structure of matter

• Atoms are made up of electrons and nuclei– Nuclei themselves are made up

of protons and neutrons

• Electrons orbit the nuclei, as planets orbit the sun

• Only certain orbits allowed Quantum jumps!

• The energy of the electron depends on orbit• When an electron jumps from one orbital to

another, it emits (emission line) or absorbs (absorption line) a photon of a certain energy

• The frequency of emitted or absorbed photon is related to its energy

E = h f

(h is called Planck’s constant, f is frequency)