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```Continuous and Discrete
How to Make Starlight (part 1)
Chapter 7
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• Up to Chapter 7.3, included
Origin of light
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Light (electromagnetic radiation) is just a
varying electric and magnetic fields that
propagate in space.
Now, two very important things happen in
nature:
• An electric field that varies in strength (e.g., due to
acceleration of an electron) generates
• An electromagnetic radiation, in turn, accelerates
electrons (or any electrically charged particle)
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We discuss two major mechanisms of light
production:
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Spectral Line Emission by atoms and molecules
contains bundles of waves of different
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 Difference Between Black and
White
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“White” light – contains all the frequencies of the
visible part of the spectrum.
White paint – diffusely scatters all frequencies of
the visible part of the spectrum equally.
Black paint – absorbs all frequencies of the
visible part of the spectrum equally.
“Blackbody Radiation” – emits and absorbs
radiation over a specific set of frequencies.
Reminder #2: Heat and
Temperature
•Temperature refers to the degree of
agitation, or the speed with which the
particles move (T~v2).
•All atoms and molecules are moving
and vibrating unless at absolute zero
temperature (T = 0 K = -459.7 F).
•Water freezes at 273 K and boils at
373 K.
•Heat refers to the amount of energy
stored in a body as agitation among its
particles and depends on density as
well as temperature.
Scales of Temperature
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°C = (°F-32) / 1.8
32
°C = °K - 273.16
273.16
°F = 1.8*°C +
°K = °C +
The physical scale of temperature is the
Kelvin one (°K degree)
The other scales are just convenient for
humans
At absolute zero of temperature (atoms
are still), and °K=0
The Generation of Light. I:
Continuum Emission
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Light and matter interact at the atomic level by
acceleration/deceleration of charged particles (mostly electrons
but also protons –-only protons are 2000x heavier than electrons)
Acceleration or deceleration of an electron (I.e. a charged particle)
result in the production of an electromagnetic wave
If the electron is decelerated:
• An e.m. wave is generated
• The mechanical energy losses of the electron are converted into e.m.
energy
• The harder the deceleration, the bigger the energy of the e.m.
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Conversely, an electron can be accelerated by e.m.
• The e.m. wave disappears
• The energy of the e.m. wave now goes into mechanical energy of the
electron
• The more energetic the e.m. wave, the harder the acceleration of the
electron
The Generation of Light. I: Continuum
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If matter is at thermal equilibrium, temperature does not
change, average velocities of atoms/molecules are constant
But electrons collide against atoms and each other all the time, i.e.
accelerate and decelerate all the time.
E.m. radiation continuously generated and absorbed, with energy
(wavelength) that only depends on mechanical energy of
electrons.
In this condition, there is equal exchange of energy between
matter and radiation: none of them gains or looses energy
The resulting distribution of energy (wavelength), I.e. spectrum of
e.m. radiation, is unique and it is called Black Body
The distribution of velocities of electrons decides the distribution of
Velocity depends on Temperature, hence distribution of energy of
One Temperature, one Spectrum
Black Body radiation is the e.m. emission of matter at
thermal equilibrium (constant T) with itself and with
Black body Spectrum
It is the spectrum of radiation at
thermal EQUILIBRIUM with
matter
It is continuum in wavelength, no
gaps from λ-0 to λ=∞
Its overall shape is universal, with
peak of intensity at some special λ
that depends on temperature T
Matter at equilibrium with e.m.
Radiation acts as a "perfect emitter"
or a "perfect absorber“.
A black object is the best way
to make the perfect B.B.
emitter and absorber.
Discussion Question
Why does NASA paint spacecraft white?
80%
Absorption
Absorption Spectrum
of Black Paint
40%
Visible
Infrared
Absorption Spectrum
of White Paint
0%
Frequency
Hotter objects have electrons moving with higher speed,
thus they emit photons with a higher average energy.
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Wien’s Law:
• The wavelength at the peak of the blackbody
emission spectrum is given by
l
 max
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= 3,000,000/T
(P.S. remember that E = hc/l)
Thus, the hotter the matter, the higher the energy
T decides λpeak which decides the color
The graph below shows the blackbody spectra of
three different stars. Which of the stars is at
the highest temperature? Which has the
highest energy (energy is the total area under
the curve)?
1) Star A
2) Star B
3) Star C
Energy
per
Second
A
B
C
Wavelength
Hotter objects emit more total radiation per unit area.
However, a big cold object can emit the same or more
energy (depending on how big it is) than a small, hotter
one
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 p R2 σ T4
You are gradually heating up a rock in
an oven to an extremely high
temperature. As it heats up, the rock
emits nearly perfect theoretical
blackbody radiation – meaning that it
1)
2)
3)
4)
is
is
is
is
brightest when hottest.
bluer when hotter.
both
neither
L=A T4
Campfires
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 to each
other harder ---> more light they emit and more wiggle per
second = frequency goes up = wavelength goes down. Thus
bluer.
Thus, as temperature goes up light gets stronger and gets
blue.
• Every object with a temperature
greater than absolute zero emits
• Hotter objects emit more total
• Hotter objects emit photons with a
higher average energy.
How to Make Light (Part 2):
Line Emission/Absorption
(light with discrete wavelengths)
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Structure of atoms
Energy levels and transitions
Emission and absorption lines
Light scattering
The Structure of Matter: Atoms
electrons, neutrons, and
protons.
A Planetary Model of the Atom
The bounding 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: 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.
Nuclear Density
If you could fill just a teaspoon
with material as dense as the
matter in an atomic nucleus, it
would weigh
~ 2 billion tons!!
Different Kinds of Atoms
• The kind of atom
depends on the
number of protons
in the nucleus.
• Most abundant:
Hydrogen (H),
with one proton
(+ 1 electron)
• Next: Helium (He),
with 2 protons (and
2 neutrons + 2 el.)
Helium 4
Different
numbers of
neutrons ↔
different
isotopes
Electron Orbits
• Electron orbits in the electron cloud are
restricted to very specific radii and energies.
r3, E3
r2, E2
r1, E1
• These characteristic electron energies are
different for each individual atom, i.e. element.
Energy Levels
In other words, the
electron in a given orbit
has the energy level that
competes to that orbit.
The higher the orbit, the
higher the energy.
Different atoms have
different energy levels, set
by quantum physics.
Quantum means discrete!
Atomic Transition: Excitation of Atoms
Inner orbitals are very tightly bound,
because electrical attraction with
nucleus is stronger
Each orbitals is characterized by a
given amount of energy
To change energy level, 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/l --- Larger energy
difference means higher frequency.
Different jumps in energy levels means
different frequencies of light absorbed,
i.e. different colors
Atomic Transitions: excitation of atoms
Remember that Energy = Wavelength = Colors
• An electron can
be kicked into a Eph = E3 – E1
higher orbit
Eph = E4 – E1
when it absorbs
a photon with
exactly the right
energy.
Wrong
energy
• The photon is
absorbed, and
the electron is in
(Remember that Eph = h*c/l)
an excited state.
• Photons with
other energy pass
by the atom
unabsorbed.
Spectral Line Emission
If a photon of exactly
the right energy is
absorbed by an
electron in an atom,
the electron will gain
the energy of the
outer, higher energy
orbit.
A photon of the same energy is emitted when the
electron falls back down to its original orbit.
Spectral Line Emission
Collisions (like in
a hot gas) can
also provide
electrons with
enough energy to
change energy
levels.
A photon of the same energy is emitted
when the electron falls back down to its
original orbit.
Energy Levels of a Hydrogen Atom
Different allowed
“orbits” or energy
levels in a hydrogen
atom.
Emission line spectrum
Absorption line spectrum
Spectral Lines of Some Elements
Argon
Helium
Mercury
Sodium
Neon
Spectral lines are like a cosmic barcode system for elements.
Atoms of different elements have unique
spectral lines because each element
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has atoms of a unique color
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has a unique set of neutrons
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has a unique set of electron orbits
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has unique photons
1.
A solid, liquid, or dense gas excited to
emit light will radiate at all wavelengths
and thus produce a continuous spectrum.
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
3. If light comprising a continuous
spectrum passes through a cool, lowdensity 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.
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.
Sources of spectral lines
Emission nebula
Reflection nebula
Absorption Spectrum Dominated
by Balmer Lines
Modern spectra are usually
recorded digitally and
represented as plots of intensity
vs. wavelength
An Object’s Spectrum
Encoded in an object’s spectrum