Light Week 5 Properties of Light Lenses and Optical Tools Eye Structure and Function.
Chapter 2 Light and Matter - astro.ufl.edufreyes/classes/ast1002/Ch2.pdf · light but invisible to...
Transcript of Chapter 2 Light and Matter - astro.ufl.edufreyes/classes/ast1002/Ch2.pdf · light but invisible to...
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)
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
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)
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.
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).
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
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