Chapter 2

Light and

Matter

Reading assignment: Chapter 2

Radio Light Visible Light X-ray Light

Stars and galaxies are too far for us to send a

spacecraft to study them (in our lifetimes).

All we can receive from stars and galaxies is light

But there is much we can learn by studying the LIGHT they

emit! Such as chemical composition, temperature, speeds,

etc.

(Antennae galaxies NGC 4038/4039, Corvus constellation)

Radio “Light”

Centaurus A

Visible Light

Active Galaxy NGC 5128

(Radio source Centaurus A. Located in the constellation of Centaurus. A

means the first radio source discovered in that constellation)

Visible Light

Infrared Light

Centaurus A

Light and radiation

Questions:

How astronomers learn about the chemical elements that made up stars

and galaxies?

How do they know about the temperature of planets, stars and galaxies?

How do they know about the speed at which they are moving?

The answer:

Through the interpretation of light or the electromagnetic radiation

received from these objects.

Electromagnetic radiation refers to waves in which the energy is carried in the form of

oscillating electric and magnetic field.

Visible light is a particular type of electromagnetic radiation visible to the human eye.

Radio, infrared, ultraviolet, X-rays and Gamma rays are electromagnetic radiation or

light but invisible to the human eye

The difference between all these types of electromagnetic radiation is the wavelength

(or the frequency)

Light behave like a wave or a particle

• The pebble cause the water to

move up and down but there is no

displacement of water away from

the point where the pebble hit the

water.

•But the information (and energy)

is carried from place to place

without physical movement of

material in radial direction.

•The twig moves up and down.

Energy is transferred from the

wave to the twig.

(This is called the duality of the behavior of light )

Let us take a look to the behavior of light as a wave

Wave characteristics

Parameters that describe

a wave:

•Wavelength

•Period

•Amplitude

•Frequency

•Wave speed

Wavelength (λ) (Unit of length: m, cm, nm, …)

• Distance between successive wave peaks

Period (Units of time: s)

• Time between the passing of wave crests

Frequency (f) (Unit: Hertz, Hz = 1/s). Multiples: kHz, MHz

• Number of “vibrations” per unit time

Frequency = 1/ Period or Period x Frequency = 1

Wave Speed (Units of velocity: km/s, m/sec)

• Wave Speed = Wavelength x Frequency

Important: Light at all wavelengths travels in vacuum at the same

speed: c = 300,000 km/s

In the case of light, c is the speed:

c = wavelength x frequency

c = λ x f

λ = wavelength (lambda)

f = frequency

Electrically charged particles and

electromagnetic waves

Electrons have - charge

Protons have + charge

Both have electric fields

+ - attract,

++ and - - repel

• The changing position of a charged

particle creates “waves” called

electromagnetic waves

• The electromagnetic waves

travels through empty space

eventually interacting with a distant

charged particle.

• Visible light is an

electromagnetic wave

Magnetism

Effect on electric charges

Moving electric charges also

produce Magnetic fields.

Example: electric current

passing through a coil.

Another example: electric

motors and alternators

Another interesting

example:

The Earth’s magnetic field

is produced by the

spinning of charges in the

liquid metal core of the

Earth.

Conversely,

magnetic fields force

charged particles to

move….

= E&M Waves = LIGHT!

Accelerated charges (electrons, protons) produce:

Ripples in the ElectroMagnetic (E&M) field

An

electromagnetic

wave is

composed of two

oscillating fields,

an electric field

and a magnetic

field

perpendicular to

each other

Visible light ranges in wavelength from

~400 to ~700 nanometers.

400nm 500nm 600nm 700nm

Wavelength means COLOR

Electromagnetic Spectrum

communication

heat

detected by

our eyes

sunburn most

energetic

penetrate

tissue

Microwaves,

cooking

Visible light

is a small

part of the

EM

spectrum.

Did you ever wonder why astronomers put

telescopes on mountaintops or in space?

The temperature scale Comparison of Kelvin, Celsius and Fahrenheit scales

The scale most used in sciences, physics and astronomy is Kelvin.

The unit is kelvin (K)

Blackbody Radiation

• The atoms and molecules that make up matter are in constant motion. Atoms and molecules are normally neutral (No electric charge).

• The temperature of an object measures the amount of microscopic motion of the particles.

•The kinetic energy is E = ½ m v²

• The higher the temperature, the faster the particles move (larger v) and the larger the kinetic energy.

•When the charged particles change their state of motion (change in speed, direction, acceleration), electromagnetic radiation is emitted.

Blackbody Spectrum:

Thermal Radiation

Blackbodies, like stars, incandescent light bulbs and irons, emit this

characteristic spectrum of light. A body at a temperature higher than 0 K

will emit as a blackbody. (No emission if the temperature of a body is 0 K)

The intensity peaks at a given frequency and fall off to lesser values

above and below that frequency.

This plot is in logarithmic scale. The intensity and frequency scales appears compressed

Peak

of intensity

Blackbodies with different temperatures look like this:

Hotter blackbodies are brighter and “bluer.”

(nm : nanometer; 1 nm = 10^-9 m)

An example: The spectrum of the Sun

Wien’s Law • Hotter bodies radiate more strongly at shorter wavelengths

(i.e. they’re bluer).

• Cooler bodies radiates more at longer wavelengths (i.e.

they are redder)

• There is a wavelength at which the intensity of the

radiation reaches a maximum (max )

max = 0.29 cm

T (K)

Using this equation we can measure a star’s temperature

from its spectrum!

Stefan’s Law

• “Hotter blackbodies are brighter overall (at

every wavelength).”

where: F = total radiative flux (total energy radiated per second)

= constant

The total radiated flux or total energy radiated per second is

proportional to the area under the black body curve

Also note that the total energy radiated per second is proportional to the

fourth power of an object’s temperature

Example: If the temperature T of a body is increased to 2T, the total

energy radiated per second is increased to (2T)4 = 16 T4

F = T4

Important properties of blackbodies a different

temperatures

max

max shift to shorter wavelengths if the temperature T increases

The total energy emitted increases as T to the fourth power

The energy emitted at a single wavelength in larger as the T increases

Application of Stefan’s and Wien’s Laws The plot is in linear scale

Stefan’s Law

Increasing the temperature from

6,000 K to 12,000 K of a black body

will increase the total radiated flux

(Total energy radiated per second)

by a factor of 16

The total radiated flux is

proportional to the area under the

curve. The area under the 12,000 K

curve is 16 times larger than the

area under the 6,000 K curve

Wien’s Law

max = 2,900,000(nm)/T (K)

The max shift from the visual,

around 483 nm (green-yellow, for a

6,000 K) to around 242 nm

(ultraviolet for a 12,000 K).

max =242 nm

max =483 nm

(Flu

x)

The

temperature

of the stars

and the Sun

Radiation

from the Sun

Radiation of three stars at

three different temperatures

Stellar Colors

• Reddish coolest stars (~3000 K)

• Orange-ish

• Yellowish

• Bluish hottest stars (~50,000 K)

Sun (~6000 K)

• A Blackbody is a perfect emitter and absorber, whose

temperature defines how much light it emits at each

wavelength.

• Stars, light bulbs, irons, etc., are ~Blackbodies with

different colors, depending on their temperature.

Comparison of blackbody curves from four

astronomical objects

Binary Star Albireo, β (Beta)

Cygni

For the Gator fans: The Gator

star !

Temperature of the orange-yellowish star =

4,080 K

Temperature of the blue star = 13,200 K

Cloud of

interstellar dust

T= 60 K

Nebula

T = 600K

Sun

T = 6,000 K

Globular cluster

(including white

dwarfs)

T= 60,000 K

Spectroscopy

(Analysis of Spectra) Light can be separated into different wavelengths

(separated in colors) to produce a spectrum.

The instrument used to produce and analyze a spectrum

is known as a spectroscope

It consist of a opaque barrier with a slit to produce a

narrow beam of light, a prism or a diffraction grating and

a detector (it can be the eye) or a screen to project the

spectrum.

Continuous Spectrum

Emission Line Spectrum

Emission Line Spectra

Each element produces its own unique pattern of lines

Absorption Line Spectrum

Absorption Line Spectra Spectrum of the Sun

The H (Hydrogen) letter followed by a Greek letter

are used for the Balmer series (Visible H lines).

Three Types of Spectra

Continuous

Emission Lines

Absorption Lines

Kirchhoff’s Laws of Radiation

Kirchhoff’s First Law • Hot, dense gases or solids produce a

continuous spectrum.

• Emits light at all wavelengths

• Example: Light bulb filament

Continuous Spectrum

(Published in 1859)

Kirchhoff’s Second Law • A hot, low-density gas when exited ( by an

electric current or UV emission) produce an

emission line spectrum.

• These lines are characteristic of the chemical

composition of a gas

• The lines are the “fingerprints” of the chemical

element. They are unique to the element.

• Examples: Neon signs, Sodium vapor street lamps,

emission nebulae

Emission Line Spectrum

Kirchhoff’s Third Law

• A Low-density cool gas in front of a hot

continuous source produces an absorption line

spectrum.

• These lines are characteristic of the chemical

composition of the gas

• For the same gas, the absorption lines occur at the

same wavelengths of the emission lines

• Example: The Sun, stars

Absorption Spectrum

Summary of Kirchhoff’s Laws:

1

2

3

How can we explain the “lines” that appear in discrete

emission or absorption spectrum?

Using Kirchhoff ‘s laws we can describe the phenomenon

but do we have a theory to explain it?

The Nature of Atoms

Three subatomic particles makeup an atom:

1. Proton - positive charge

2. Neutron – (proton+electron) no charge

3. Electron - negative charge

• The nucleus is composed of protons and

neutrons.

Like charges repel so a large amount of force

is required to keep the protons in the nucleus

together.

mass of proton mass of neutron

1836 x mass of electron

Atoms are mostly empty space! And, since all matter is made up of atoms, matter is

mostly empty space!!

Atoms are neutral, they have no electric charge (equal number of electrons and protons)

If an atom loses or gains an electron, it acquires an electric charge. It is said to be

ionized and it is therefore an ion.

Atoms can bond with other atoms of the same kind or different kind to form molecules.

Example: Molecular Oxygen, O₂ ; Water, H₂O

Each atom of a given element contains a specific number of

protons and electrons thus making that element unique.

p+

e-

Electron orbits the proton (i.e. nucleus) kept in place by the Coulomb Force (Fc).

Bohr’s Hydrogen Model

Niels Bohr

RF c 2

1

How does this structure lead to unique emission and absorption lines?

In 1913, Bohr developed a model of the atom that provided the

first explanation of the hydrogen’s spectral lines

Bohr’s Model

• Electrons can only be

in particular orbits

(energy states).

• Energy is

“quantized” (Quantum

Mechanics).

Ground state (lowest energy)

p

Excited state (higher energy)

• Excitation requires

energy to be

added to the atom

• De-excitation -

energy is released

from the atom

e

electrons

nucleus

R1

R2

R3

Electron needs to gain energy to move from R1 to R3 (excited).

Electron needs to lose energy to move from R3 to R1(de-excited).

R1

R2

R3

E1

E2

E3

gain energy

lose energy

DE = E3-E1

How does the electron get the energy it needs to become excited?

1. Collisions between atoms can excite electrons to higher energy

levels. Passing an electric current (applying a high voltage to a low

density gas)will make atoms collide.

2. The absorption of energy from light can excite electrons.

What’s going on?

Albert Einstein

Photon energy 1/wavelength

Photon energy frequency

Light Intensity = # photons

arriving/second

Light can behave as a particle.

Light energy must be carried in packets called photons.

Einstein was awarded the Nobel Prize in 1921 for his

theory of the photoelectric effect. The effect can be

explained if light is considered as a particle (photons)

• Low energy photons cannot cause e- ejections.

• High energy photons cause ejection of e- (can ionize an element)

The energy of a photon is related to the wavelength:

Eph 1/ f

Eph = h f = h c/

(f = c/ )

h is the Planck’s constant

Larger orbital jumps shorter wavelength photons.

(Larger orbital jumps have larger energy levels)

Important: A radio photon has long wavelength (low frequency) and low energy

A gamma ray photon has short wavelength (high frequency) and high energy

Atoms can only absorb or emit

photons with energies exactly equal

to the energy difference between

electron orbits.

Quantum Mechanics:

The energy of the photon must be precisely equal to DE.

Ep DE Ep = DE Photon

absorbed

photon emitted

Ep = DE

• Atoms of different elements have

unique energy level structures. The

figure on the left, shows some of the

energy levels of Hydrogen

• Every e- “transition” corresponds to

a unique wavelength.

• Ionization = ejection of e-.

• The figure at the bottom shows the

Balmer series of Hydrogen. Part of the

lines of this series are in the visible

part of the spectrum.

Hydrogen

Balmer series

The Hydrogen atom

Balmer

Hγ Hβ Hα

Examples of spectra of different elements. Every element (atom) emit or

absorb a particular set of lines. It has a unique signature or fingerprint of

that element

Bohr’s Hydrogen Atom

In modern quantum

mechanics:

Electrons are not just particles,

but also waves, without exact

locations.

Moving sources, like fire trucks and race cars, change the pitch of

the sound (siren) as they go by.

The pitch is higher (higher frequency) when they are approaching

and lower (lower frequency) when they are moving away.

This is an example of Doppler effect in sound waves

The Doppler Effect

Doppler effect

Motion along the line of sight (radial motion)

produces a Doppler effect

No Doppler effect if the motion is perpendicular

to the line of sight

Doppler effect in electromagnetic

waves

Electromagnetic waves also show a Doppler effect.

Light emitted by a moving object also present the

Doppler effect

v/c = Δ / = (shift - rest)/ rest

v is the radial velocity of an object

c is the speed of light

Δ = (shift - rest) is the change in wavelength

shift is the shifted or observed wavelength

rest is the wavelength at rest

The Doppler Shift

Stationary

source:

Moving

source:

An example of a body emitting the Balmer series of hydrogen

Red shift and blue shift of hydrogen Balmer series lines

Important!

If the body emitting the Balmer series is receding (moving away from

observer), the lines are shifted to the red part of the spectrum. The

spectrum is said to be red shifted. The body do not necessarily looks red

If the body is approaching the observer, the lines are shifted to the blue part

of the spectrum. The spectrum is said to be blue shifted. The body do not

necessarily looks blue

Obtaining the rotation of an object from the width of the Doppler lines

We will assume that the object is not approaching or receding from the

observer. It is only rotating.

If the object (a planet, a star or a galaxy) is rotating, the side approaching the

observer will be blue shifted. The side moving away form the observer will be

red shifted.

The line emitted from the center will have no shift.

As a consequence, the line will be wider that it would if the object had no

rotation.

The rotation rate of the object can be determined by measuring the width of

the spectral lines

The Zeeman Effect

A single emission lines can split into two or more under the

presence of magnetic field

The presence of magnetic field split the energy levels of an

atom

Splitting of an emission line

in a sunspot due the

presence of magnetic field in

the sunspot

What can we learn from spectroscopy?

• The chemical composition by matching the spectral lines with laboratory

spectra of atoms.

• The temperature by matching overall spectral shape with blackbody curve

(Wien’s law).

• The line-of-sight velocity by determining the Doppler shift.

• The rotation rate by measuring the broadening of spectral line due to

Doppler shift.

• The pressure of the gas in the emitting region due to broadening of spectral

lines. The greater the pressure, the broader the line

• The magnetic field (Zeeman effect) which splits a single line into two or

more lines