What is light?What is light? Light is electromagnetic radiation.Light is electromagnetic radiation.

• Technically, light is the part of Technically, light is the part of electromagnetic (e.m.) radiation that electromagnetic (e.m.) radiation that humans (and other animals) see.humans (and other animals) see.

• Although incorrect, we usually call “light” Although incorrect, we usually call “light” all types of electromagnetic radiation, like all types of electromagnetic radiation, like X-ray light or UltraViolet lightX-ray light or UltraViolet light

Light is made of energy.Light is made of energy. Light always travels at the speed of light: Light always travels at the speed of light: cc.. Light is a wave.Light is a wave.

What is Electromagnetic What is Electromagnetic Radiation?Radiation?

Made of propagating waves of electric and Made of propagating waves of electric and magnetic fields.magnetic fields.

It carries energy with itIt carries energy with it• Sometimes called Sometimes called ““radiant energyradiant energy””• Think Think –– solar power, photosynthesis, solar power, photosynthesis,

photo-electric cells, the fireplace photo-electric cells, the fireplace ……

What is an electromagnetic wave?What is an electromagnetic wave?

It is electricity and magnetism moving through space.

So, when we say the speed of light is “c” what we really mean is that the speed of the electromagnetic

wave is “c”, regardless of its frequency.

Light as a waveLight as a wave

Waves you can see:Waves you can see: e.g., ocean waves e.g., ocean waves

Waves you cannot Waves you cannot see:see:• sound wavessound waves• electromagnetic electromagnetic

waves waves

Light is an electromagnetic wave

Properties of WavesProperties of Waves

WavelengthWavelength –– the the distance between distance between crests (or troughs) crests (or troughs) of a wave.of a wave.

FrequencyFrequency –– the the number of crests (or number of crests (or troughs) that pass troughs) that pass by each second.by each second.

SpeedSpeed –– the rate at the rate at which a crest (or which a crest (or trough) moves.trough) moves.

For light in general:speed = c = d/t = λ

λ = cλ = c/

wavelengthfrequency

speed of light = 3x108 m/s in vacuum

Light as a WaveLight as a Wave

• Wavelengths of light are measured in units of nanometers (nm) or Ångström

(Å):1 nm = 10-9 m

1 Å = 10-10 m = 0.1 nm

Visible light has wavelengths between 4000 Å and 7000 Å (= 400

– 700 nm).

Wavelengths and ColorsWavelengths and Colors

Different colors of visible light correspond to different

wavelengths.

Visible LightVisible Light ShorterWavelength

LongerWavelength

Remember: visible light isnRemember: visible light isn’’t the whole story. Itt the whole story. It’’s s just a small part of the entire electromagnetic just a small part of the entire electromagnetic

spectrumspectrum

Long Wavelength

(high frequency)(high energy)

Short Wavelength

(low frequency)(low energy)

Wavelengths and size of thingsWavelengths and size of things

Roy G. Biv

Reminder #1: E.m. Radiation generally Reminder #1: E.m. Radiation generally contains bundles of waves of different contains bundles of waves of different

wavelengths (colors)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:

The Multi-wavelength SunThe Multi-wavelength Sun

Radio infrared

X-rayoptical

Optical SkyOptical Sky

Near-infrared sky Near-infrared sky

Boldt et al.

Radio SkyRadio Sky

Soft X-ray SkySoft X-ray Sky

Different wavelengths carry different Different wavelengths carry different types of informationtypes of information

• Visible light: the glow of stars (dust

blocks the light)

• Infrared: the glow of dust

Visible light (top) and infrared (bottom) image of the

Sombrero Galaxy

Light as particlesLight as particles

•Light comes in quanta of energy Light comes in quanta of energy called called photons photons –– little bullets of little bullets of energy.energy.

•Photons are massless, but they Photons are massless, but they have momentum and energy. have momentum and energy.

Wave-particle dualityWave-particle duality

All types of electromagnetic radiation act as both waves and particles.

The two views are connected by the relation

E = h = h c /

h is the Planck's constant, c is the speed of light is the frequency, is the wavelength

The energy of a photon does not depend on the intensity of the

light!!!

IntensityIntensity

A photon's energy depends on the wavelength (or frequency) only, NOT the intensity.

But the energy you experience depends also on the intensity (total number of photons).

In Summary: properties of LightIn Summary: properties of Light

AllAll light travels through (vacuum) space light travels through (vacuum) space with a velocity = 3x10with a velocity = 3x1088 m/s m/s

The The frequencyfrequency (or wavelength) of a photon (or wavelength) of a photon determines how much determines how much energyenergy the photon the photon has (E=hhas (E=h).).

The The number number of photons (how many) of photons (how many) determines the determines the intensity.intensity.

Light can be described in terms of either Light can be described in terms of either energy, frequency, or wavelength.energy, frequency, or wavelength.

Compared to visible light, radio Compared to visible light, radio waves have:waves have:

higher energy and longer wavelengthhigher energy and longer wavelength

higher energy and shorter wavelengthhigher energy and shorter wavelength

lower energy and longer wavelengthlower energy and longer wavelength

lower energy and shorter wavelengthlower energy and shorter wavelength

all light has the same energyall light has the same energy

Origin of lightOrigin of light Light (electromagnetic radiation) is just varying

electric and magnetic fields that propagate through space.

Now, two very important things happen in nature: • An electric field that varies in strength (e.g., owing

to the acceleration of an electron) generates electromagnetic radiation.

• 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

Heat and TemperatureHeat and Temperature•Temperature refers to the degree of

agitation, or the average speed with

which the particles move (T~v2).

•All atoms and molecules are moving

and vibrating unless at absolute zero

Temp = -273 C = 0 K = -459.7 F

•Heat refers to the amount of energy

stored in a body as agitation among its

particles and depends on density as

well as temperature.

Scale of TemperatureScale of TemperatureFahrenheit Centigrade Kelvin

F C K

Water Boils

Water Freezes

Absolute Zero

212

32

-459.7

100

273

373

0

0

-273

Water Freezes

Water Boils

Absolute Zero

Scale of TemperatureScale of Temperature

C = (F-32) / 1.8 F = 1.8*C + 32C = (F-32) / 1.8 F = 1.8*C + 32 C = K - 273.16 K = C + 273.16C = K - 273.16 K = C + 273.16

Absolute zero of temperature (atoms Absolute zero of temperature (atoms are still)are still)

K = 0 C = -273.16 F = -459.7K = 0 C = -273.16 F = -459.7

Blackbody RadiationBlackbody Radiation Acceleration or deceleration of an electron results Acceleration or deceleration of an electron results

in the production of an electromagnetic wave.in the production of an electromagnetic wave. Heat makes electrons and atoms move: Heat makes electrons and atoms move: thermal thermal

motionmotion..• Electrons collide against atoms and each other Electrons collide against atoms and each other

all the time, i.e. accelerate and decelerate all the all the time, i.e. accelerate and decelerate all the time.time.

• Makes electromagnetic radiation so also called Makes electromagnetic radiation so also called thermal radiationthermal radiation..

Makes a continuous spectrum of radiation so also Makes a continuous spectrum of radiation so also called called continuum radiationcontinuum radiation..

Blackbody SpectrumBlackbody Spectrum

It is the spectrum of radiation from thermal motions of matter.

Temperature is how fast the electrons and atoms are moving on average.

Faster motions means more energetic collisions and higher energy photons.

Hotter objects have electrons moving with higher speed, Hotter objects have electrons moving with higher speed, thus they emit photons with a higher average energy.thus they emit photons with a higher average energy.

Wien’s Law:Wien’s Law:

• The wavelength at the peak of the blackbody The wavelength at the peak of the blackbody emission spectrum is given byemission spectrum is given by

maxmax (nm)= (nm)= 2,900,000/T2,900,000/T

(P.S. remember that E = hc/(P.S. remember that E = hc/)) Thus, the hotter the matter, the higher the energy Thus, the hotter the matter, the higher the energy

of the e.m. radiationof the e.m. radiation

Hotter objects emit more total radiation per unit area.Hotter objects emit more total radiation per unit area.However, a big cold object can emit the same or more However, a big cold object can emit the same or more energy (depending on how big it is) than a small, hotter energy (depending on how big it is) than a small, hotter

oneone

Cold Hot

Stefan-Boltzmann Law:

Emitted power per square meter = σ T4

σ = 5.7 x 10-8 W/(m2K4)

Total emitted power: E = 4 R2 σ T4

L=A T4

The graph below shows the blackbody spectra of The graph below shows the blackbody spectra of three different stars. Which of the stars is at three different stars. Which of the stars is at the highest temperature? Which has the the highest temperature? Which has the highest energy (energy is the total area under highest energy (energy is the total area under the curve)?the curve)?

1) Star A1) Star A

2) Star B2) Star B

3) Star C3) Star CA

B

C

EnergyperSecond

Wavelength

Reminder: Blackbody Radiation, i.e. a continuum of wavelengths with a characteristic distribution of strengths

You are gradually heating up a rock in You are gradually heating up a rock in an oven to an extremely high an oven to an extremely high temperature. As it heats up, the rock temperature. As it heats up, the rock emits nearly perfect theoretical emits nearly perfect theoretical blackbody radiation – meaning that itblackbody radiation – meaning that it

is brightest when hottest.is brightest when hottest. is bluer when hotter.is bluer when hotter.

is bothis both is neitheris neither

CampfiresCampfires

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 with each other harder ---> they emit more light and more wiggles per second = frequency goes up = wavelength goes down. Thus bluer.

Thus, as temperature goes up light gets stronger and gets blue.

More on Blackbody Radiation More on Blackbody Radiation (a.k.a. Thermal Radiation)(a.k.a. Thermal Radiation)

•Every object with a temperature Every object with a temperature greater than absolute zero emits greater than absolute zero emits blackbody radiation.blackbody radiation.

•Hotter objects emit more total Hotter objects emit more total radiation per unit surface area.radiation per unit surface area.

•Hotter objects emit photons with a Hotter objects emit photons with a higher average energy.higher average energy.

Color and TemperatureColor and Temperature

Stars appear in different colors,

via yellow (like our sun)

to red (like Betelgeuse).

from blue (like Rigel)

If the spectra of stars are black bodies, then

these colors tell us about the star’s

temperature.

Orion

Betelgeuse

Rigel

Stars come in different colors

How to Make Light (Part 2):How to Make Light (Part 2):Line Emission/AbsorptionLine Emission/Absorption

(light with discrete wavelengths)(light with discrete wavelengths)

Structure of atomsStructure of atoms Energy levels and transitionsEnergy levels and transitions Emission and absorption linesEmission and absorption lines Light scatteringLight scattering

The Structure of Matter: AtomsThe Structure of Matter: Atoms

A Planetary Model of the Atom

Atoms are made of electrons, neutrons, and protons.

The binding force: the attractive Coulomb(electrical) force between the positively charged protons in the nucleus and the negatively charged electrons around the nucleus.

The Structure of Matter: AtomsThe 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.

Electron OrbitsElectron Orbits• Electron orbits in the electron cloud are

restricted to very specific radii and energies.

r1, E1

r2, E2

r3, E3

• These characteristic electron energies are different for each individual atom, i.e. element.

In other words, the electron in a given orbit has the energy that corresponds 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 Energy Levels

Spectral Line EmissionSpectral Line Emission

Collisions (like in a hot gas) can provide electrons with enough energy to change energy levels.

A photon of the difference in energy between levels is emitted when the electron quickly falls down to a lower level.

Energy Levels of a Hydrogen Atom

Different allowed “orbits” or energy

levels in a hydrogenatom.

Emission line spectrum

Absorption line spectrum

Spectral Lines of Some Elements

Spectral lines are like a cosmic barcode system for elements.

Argon

Helium

Mercury

Sodium

Neon

Atoms of different elements have unique Atoms of different elements have unique spectral lines because each elementspectral lines because each element

has atoms of a unique colorhas atoms of a unique color has a unique set of neutronshas a unique set of neutrons has a unique set of electron orbitshas a unique set of electron orbits has unique photonshas unique photons

Spectral Line Emission again

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 level.

A photon of the same energy is emitted when the electron falls back down to its original energy level or of a different energy if it falls down to a different

energy level.

Atomic Transitions: excitation of atomsAtomic Transitions: excitation of atoms

• An electron can be kicked into a higher

orbit when it absorbs a photon with

exactly the right energy.

• All other photons pass by

the atom unabsorbed.

Eph = E4 – E1

Eph = E3 – E1

(Remember that Eph = h*c/)

Wrong energy• The photon is

absorbed, and the electron is in an

excited state.

Remember that Energy = Wavelength = Colors

To change energy levels, 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/ --- A larger

energy difference means a higher

frequency.

Different jumps in energy levels

means different frequencies of

light absorbed, i.e. different colors

Atomic Transition: Excitation of AtomsAtomic Transition: Excitation of Atoms

Kirchhoff’s Laws of Radiation Kirchhoff’s Laws of Radiation

1. A solid, liquid, or dense gas excited to emit light will radiate at all

wavelengths and thus produce a continuous spectrum.

Kirchhoff’s Laws of Radiation Kirchhoff’s Laws of Radiation 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

Kirchhoff’s Laws of RadiationKirchhoff’s Laws of Radiation

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.

Sources of spectral linesSources of spectral lines

Reflection nebulaReflection nebula

Emission nebulaEmission nebula

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.

The spectrum of a star: nearly a Black Body

The light from a star is usually concentrated in a

rather narrow range of wavelengths.

The spectrum of a star’s light is approximately a black body spectrum.

In fact, the spectrum of a star at the photosphere, before the light passes

through the atmosphere of the star, is a nearly

PERFECT black body one

Again, remember the two Laws of Black Body Radiation. I

1. The hotter an object is, the more energy it emits:

L = 4 R2T4

where

= Stefan-Boltzmann constant

L = Energy =

= Energy given off in the form of radiation, per unit time [J/s];

More area, more energy

Again, remember the two Laws of Black Body Radiation. II

2. The peak of the black body spectrum shifts towards shorter wavelengths when the

temperature increases.

Wien’s law:

max ≈ 2,900,000 nm / TK

(where TK is the temperature in Kelvin)

Stellar Spectra

The spectra of stars also contain

characteristic absorption lines.

With what we have learned about atomic structure, we

can now understand how those lines are formed.

The Spectra of StarsThe inner, dense layers of a star do produce a

continuous (blackbody) spectrum.

Cooler surface layers absorb light at specific frequencies.

The atmosphere also absorbs light at other specific frequencies=> Spectra of stars are B.B.absorption

spectra.

Analyzing Absorption Spectra• Each element produces a specific set of

absorption (and emission) lines.

By far the most abundan

t elements

in the Universe

• Comparing the relative strengths of these sets of lines, we can study the composition of

gases.

Lines of HydrogenMost prominent lines in many astronomical

objects: Balmer lines of

hydrogen

The Balmer Absorption Linesn = 1

n = 2

n = 4

n =

5n =

3

H H H

The only hydrogen lines in the visible wavelength range

Transitions from 2nd to

higher levels of hydrogen

2nd to 3rd level = H (Balmer alpha line)2nd to 4th level = H (Balmer beta line)

Observations of the H-Alpha LineEmission nebula,

dominated by the red H line

Absorption Spectrum Dominated by Balmer Lines

Modern spectra are usually recorded digitally and represented as plots of

intensity vs. wavelength

The Balmer ThermometerBalmer line strength is sensitive to

temperature:

Almost all hydrogen atoms in the ground state

(electrons in the n = 1 orbit) => few transitions

from n = 2 => weak Balmer lines

Most hydrogen atoms are ionized => weak Balmer

lines

Measuring the Temperatures of Stars

Comparing line strengths, we can measure a star’s surface

temperature!

Spectral Classification of Stars

Tem

pera

ture

Different types of stars show different characteristic sets of absorption lines.

Spectral Classification of Stars

Mnemonics to remember the spectral sequence:

Oh Oh Only

Be Boy, Bad

A An Astronomers

Fine F Forget

Girl/Guy Grade Generally

Kiss Kills Known

Me Me Mnemonics

0

Stellar Spectra

OB

A

F

GKM

Su

rface

tem

pera

ture

The Composition of StarsFrom the relative strength of absorption lines (carefully accounting for their temperature

dependence), one can infer the composition of stars.