Chapter 5 Light and Matter - University of Floridafreyes/classes/ast2003/FR...Light and Matter Radio Light Visible Light X-ray Light Stars and galaxies are too far for us to send a

Chapter 5

Light and

Matter

Radio Light Visible Light X-ray Light

Stars and galaxies are too far for us to send a

spacecraft or to visit (in our lifetimes).

All we can receive from them is light

But there is much we can learn (composition,

temperature, speeds, etc.) by studying the LIGHT

they emit!

Radio “Light”

Centaurus A

Visible Light

An example are the following images of the galaxy NGC-5128 (Radio

source Centaurus A) obtained at different wavelengths

Visible Light

Infrared Light

Centaurus A

What is light?

Newton suggested that light is made of countless tiny

particles. Other scientist conducted experiments that

suggested that light behave like a wave.

This problem is still not solved: Is light a wave or a

particle?

This different behavior of light is called the wave-particle

duality of light.

For some experiments, it is better to treat light as a wave,

for others, it is better to treat light as a particle.

Light behave as an electromagnetic wave (electric and magnetic fields

oscillating)

Light can behave like a particle. These particles are called photons

Let’s take a look to the behavior of light

as a wave

•A simple example are waves

created by throwing a rock in

a pond

•The water doesn’t move in

the direction away from the

point were the rock created

the waves

•Information is carried from

place to place without

physical movement of

material

Wave characteristics:

How do we describe a

wave?

Parameters that describe

a wave:

Wavelength, amplitude,

frequency, wave speed

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

• Distance between successive wave peaks

Period (Units of time: s)

• Time between passing of wave crests

Frequency (Unit: Hertz, Hz = 1/s)

• Number of “vibrations” per unit time

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

• 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 = wavelength x frequency

C = λ x f

λ = wavelength (lambda)

f = frequency

Relationship between frequency and

wavelenghth for different frequencies

Low frequency means longer wavelength

Higher frequencies means shorter wavelength

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

(Vacuum).

• Visible light is an

electromagnetic wave

Effect on electrons by a passing electromagnetic wave

Magnetism

Moving electric charges also

produce Magnetic fields.

Example: electric motors

Another 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

Newton experimented with light. He sent white light

through a prism and was able to obtain all the colors of

the rainbow. This was something known already

Was it the prism that added something that produced the

colors?

If one of the colors is sent through the prism, it does not

produce all the colors. Colors are intrinsic to white light

One can split light onto colors using a prism or a

diffraction grating.

A diffraction grating is composed of many parallel lines (

example 1000 lines/mm)

A prism split light by refraction (dispersion)

A diffraction grating split light by diffraction (interference)

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?

The temperature scale Comparison of Kelvin, Celsius and Fahrenheit scales

The scale used in astronomy is Kelvin. The unit is Kelvin (K)

Blackbody Radiation

• The atoms and molecules that make up matter are in constant motion.

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

• The higher the temperature, the faster the particles move.

•When the charged particles change their state of motion, electromagnetic radiation is emitted.

Stellar Colors

• Reddish coolest stars (~3000 K)

• Orange-ish

• Yellowish

• White

• 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.

Blackbody

Spectrum:

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

characteristic spectrum of light:

Blackbodies with different temperatures look like this:

Hotter blackbodies are brighter and “bluer.”

(nm : nanometer 1 nm = 10⁻⁹ m)

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 radiation reaches a

maximum ( max )

max = 2,900,000

T (K)

If we know or we can find max from the radiation curve, using Wien’s law

equation we can measure a star’s temperature from its spectrum!

Or if we know the temperature T, we can find the max

Example: For the Sun, T= 5800 K, max =500 nm

nm

Stefan’s Law

• Hotter blackbodies are brighter

overall (at every wavelength).

where: F = total radiative flux

= constant

T = Temperature of black body in K

The total radiated flux or total energy radiated per second is

proportional to the fourth power of T. It is equivalent to the area

under the black body curve

F = T4

(Flu

x)

Comparison of

blackbody

curves from

four

astronomical

objects at

different

temperatures

1 nm = 10⁻⁹ m

Spectroscopy

(Analysis of Spectra)

Continuous Spectrum

Emission Line Spectrum

Emission Line Spectra

Each element produces its own unique pattern of lines

The set of emission or absorption lines is unique for a chemical

element. They are the fingerprint of an element

Absorption Line Spectrum

Absorption Line Spectra Spectrum of the Sun

The H letter (Hydrogen) followed by a Greek letter are used for the Balmer

series .

The Balmer series of H is the series of lines emitted in the visible part of the

spectrum

Three Types of Spectra

Continuous

Emission Lines

Absorption Lines

Kirchhoff’s First Law

• Hot, dense gases or solids produce a

continuous spectrum.

• Example: Light bulb filament

Continuous Spectrum

Published in 1859

Kirchhoff’s Second Law

• A hot, rarefied gases when exited (By an

electric current or UV emission)

produce an emission line spectrum.

• Examples: Neon signs, Sodium vapor street lamps,

emission nebulae

Emission Line Spectrum

Kirchhoff’s Third Law

• A cool gas in front of a hot continuous

source produces an absorption line

spectrum.

• Example: The Sun, stars

Absorption Spectrum

Summary of Kirchoff’s Laws:

1

2

3

How can we explain the discrete emission

or absorption in “lines?”

The Nature of Atoms

Three subatomic particles makeup an atom:

1. Proton - positive charge

2. Neutron - no charge

3. Electron - negative charge

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!!

If an atom loses or gains an electron, it is said to be ionized and it is therefore

an ion. It has a positive charge if it looses electrons or negative if it gain

electrons

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

molecules.

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?

Bohr 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

E = 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 (High voltage in a gas)will make

atoms collide.

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

What’s going on?

Albert Einstein

Light Energy 1/wavelength

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

The energy of a photon is related to the

wavelength or the frequency f:

Eph 1/ f

Eph = h f = h c/

(f = c/ )

h is the Planck’s constant

Larger orbital jumps have larger energy levels and radiates shorter wavelength (or higher frequency) photons

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 E.

Ep E Ep = E Photon

absorbed

photon emitted

Ep = E

• 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 .

An ionized atom has a different set of lines,

different from the neutral atom.

•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

Lyman (UV) Balmer (Visible) Paschen (IR)

Examples of spectra of different elements.

Every element (atom) emit a unique set of lines.

It is the fingerprint of that particular atom.

Bohr’s Hydrogen Atom

In modern quantum

mechanics:

Electrons are not just

particles, but also waves,

without exact locations.

In moving sources, like fire trucks and race cars, there is change

pitch of the sound of a siren as they go by.

The pitch is higher when they are approaching and lower 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 present the Doppler effect.

Light emitted by a moving object present Doppler effect

The equation of the Doppler effect related the radial speed of the

object with the change in wavelength

v/c = Δ / = ( shift - rest)/ rest

v is the radial velocity of an object

c is the speed of light

Δ is the change in wavelength (shifted - rest )

is the rest wavelength

The Doppler Shift

Stationary

source:

Moving

source:

The Doppler Shift

If the object is receding (moving away from observer), it will show

Doppler red shifted lines (lines shifted toward the red)

If the object is approaching the observer (moving toward the

observer) it will show Doppler blue shifted lines (lines shifted

toward the blue)

The example below show the Hydrogen Balmer series lines red

shifted, at rest, and blue shifted

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

If an 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

What can we learn from spectroscopy?

• The chemical composition by comparing spectral lines with laboratory

spectra of atoms.

• The temperature by matching overall spectral shape with blackbody curve

or by using the Wien’s law equation.

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

• The rotation rate by measuring 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