Lecture Notes

Arny Chapter 3 - Light and Atoms

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We will not cover section 3.7

Note: This lecture includes some in-class demonstrations which cannot be duplicated here.
Sections of the following in RED talk about demonstrations done in class and will not make much sense if you were not in class.

Section 3.1 - Properties of Light

Light:
Electromagnetic waves.
Radiation.
Photons ("particles of light").

Wavelength = distance between waves.
Frequency = rate at which waves pass by or arrive.
All light waves move at the speed of light.
Short wavelength <---> High frequency.
Long wavelength <---> Low frequency.

Energy:
Light waves carry energy.
Higher frequency => more energy (and shorter wavelength).

Imagine standing at the beach, being hit by ocean waves.
When waves hit you, they transfer energy to you.
If waves hit you more often (higher frequency), there will be more energy transferred to you.
More energy when waves are close together.

Colors:
When a light wave enters our eyes, it reacts with the retina cells.
The amount of energy carried can cause different reactions.
Photons with wavelength 650 nm = 650 x 10^-9 m = 6.5 x 10^-7 m cause a reaction that our brain interprets as red light.
Photons with wavelength 651 nm will also appear to us as red, a slightly different shade.
Green light has wavelength 500 nm, blue 400 nm.
Visible light ranges from 350 nm to 700 nm.

Black is the lack of any light.
White light is all the colors mixed together.
When all the colors arrive at once, we see white.
White is not a separate color with its own wavelength.
How do we know?
Some processes can separate light into its colors.

Prisms:
Triangular slab of glass.
Light gets bent as it goes
from air to glass to air.
Different colors (energies)
get bent by different amounts.
A rainbow comes out.
[See figure 3.4 on page 99.]

Rainbows:
Light passing through raindrops (air to water to air) is affected similarly to glass.
White sunlight is split into a rainbow of colors.
If you're at the right place relative to the Sun and raindrops in the sky, you see a rainbow.

Diffraction Grating:
A grating can also separate
colors but works on a
different principle.
Show students a grating.
Looks like a clear slide,
but there's actually alternating
black lines (too thin to be seen)
and open areas.
Like a microscopic picket-fence.

Light gets spread and scattered in
interesting ways by this picket fence.


Laser (optional):
Turn on laser. Safety.
Shine laser through grating, point out various beams.
The laser puts out just a single color (wavelength 632 nm), so no rainbows are formed.
[Repeat using a CD?]

A CD has many parallel grooves which reflect light in a manner like the grating (the CD is an example of a 'reflection grating'), that's why you see so many rainbows in reflections off of CDs.

Spectrum Projector:
Box contains an ordinary light bulb.
Hole in box lets light escape through tube containing a lens.
White light - image of filament - comes straight through.
There is a diffraction grating at the end of the tube sticking out the hole.
Get rainbows off to the sides.

Section 3.2 - The Electromagnetic Spectrum: Beyond Visible Light

Colors of objects:
A white object reflects all colors.
Black absorbs all colors.
Red reflects red and absorbs all other colors.

Demonstrate with
colored felt.
colored balloons
colored filters
recombine with lens

Electromagnetic Spectrum:
Visible light is what our eyes can detect.
But there are other "colors" of light with wavelengths above and below that of visible light.

Radio	long wavelength	low frequency	less energy
Infrared
Visible
Ultraviolet
X-rays
Gamma rays	short wavelength	high frequency	more energy

[Note the three l's, long, low, and less for the Radio end of the spectrum.]

Learn the spectrum!
That is, learn the names and order of the electromagnetic spectrum.

Infrared - "heat rays", skin can detect as glow of heat
Ultraviolet - causes sunburns and skin cancer
X-rays & Gamma rays - can kill and mutate cells


Wien's Law ("Wien", a German name, is pronounced like "Veene")
Imagine heating a piece of metal (maybe with a blowtorch).
As it warms, you might feel a glow of heat from it (infrared radiation).
As you continue to heat it, it gets very hot.
It starts to glow with a deep red.
Then bright red as it gets hotter.
Then white hot, then blue.

The color of light emitted varies with the temperature.
Hotter => shorter wavelengths (more blue).
When the piece of metal is as hot as the Sun (5800K), it puts out mostly visible light (peaked in yellow), like the Sun.
This is why the Sun is the "color" that it is.
Cooler objects emit light that is more red (or infrared).
Our bodies emit radiation, infrared not visible.

This behavior of objects is called Wien's Law.
Hotter bodies radiate more strongly at shorter wavelength.
See figure 3.6 on page 99.
The hotter the object, the more light it emits at shorter wavelengths (blue or ultraviolet), affecting the overall color we perceive from the object.

Example: Chapter 3 Problem 5
An electric stove burner on "high" radiates most strongly at about 2000 nanometers. What is its temperature?

Solution:
lambda = 2000 nm
So by Wien's law, T = (3 x 10^6 K nm) / (2000 nm) = 1500 K

Section 3.3 - Atoms
Atoms are mostly empty space.
Atoms have a tiny central area called the nucleus.
The nucleus contains:

protons (positive charge)
neutrons (no charge, "neutral")

The number of protons determines the element:

1 proton = H (hydrogen)
2 = He (helium)
8 = O (oxygen)
92 = U (uranium)
[Different numbers of neutrons give different isotopes.]

Orbiting the nucleus:

electrons (negatively charged).

Opposite charges attract.
This electrical attraction holds the electron in orbit like gravity holds planets in orbit around the Sun.

The nucleus contains protons, which repel each other.
What holds the nucleus together?
There is an additional attractive force (the "nuclear" force) which holds protons and neutrons together.
[Too many protons make the nucleus unstable, radioactivity.]

Bohr Model:
In the early 1900's, experiments had revealed the structure of the atom that we just described.
But further experiments revealed some very surprising results.
It was Neils Bohr who first figured out how to modify this model to fit all the experimental evidence.


Electrons cannot be in just any orbit.
There are only a few special allowed
orbits for electrons.
What a strange requirement!
It's not like this with gravity and
the solar system.
[See figure 3.8 on page 102.]


Electrons were allowed to change orbits.
But they must instantaneously jump from one to another.
They can never be in an in-between orbit.
This "quantization" of orbits was the beginning of Quantum Mechanics.


Section 3.4 - The Origin of Light
[See figures 3.9, 3.10, and 3.12 in the textbook.]
Electrons in different orbits
have different energy.
Innermost orbit, ground state,
has the least energy.
When an electron changes orbits,
its energy will change.
But energy can't just appear out
of nowhere or magically disappear.
If something gains energy, something
else must lose energy.

An electron can jump from the ground
state to a higher orbit only if it is given some energy.
This energy could come from a passing photon.
The photon (light) disappears, its energy has been used by the electron.
Only if the photon has exactly the energy the electron needs can this happen.
Sometimes a photon gives an electron so much energy it escapes the atom entirely (ionization).

An electron in an outer orbit can drop down to a lower orbit.
In fact, this happens naturally, like rocks falling downhill.
The electron has too much energy, it sheds energy in the form of a photon (light, electromagnetic radiation).
The light will have energy corresponding to the difference between the orbits, the light will be some color.


Section 3.5 - Formation of a Spectrum
Atoms can emit and absorb light that corresponds to a difference in energy levels of the electron orbits.
Every hydrogen atom will have the same allowed orbits.
Hence, every hydrogen atom emits and absorbs exactly the same colors (energies, wavelengths) of light.
This is called the spectrum of the atom.

Every helium atom will have exactly the same spectrum.
Every element has its own distinct, unique spectrum.
Every isotope, ion, molecule has its own distinct spectrum.

Every element has its own spectrum.
A fingerprint or signature.
Scientists have measured the spectra of all the elements.
This is incredibly useful!
We can look at the light from any object and figure out what its made out of!

[The philosopher August Comte wrote in 1835: We can determine the shapes, distances, sizes, and motions of celestial bodies, but never, by any means, will we be able to study their chemical compositions.
Three years after his death, it was learned that a spectrum can be used to determine the chemical composition of distant objects.]

Spectroscopy:
We can figure out what a streetlight is made of.
Take its light, send it through a prism, look at the colors.
The spectrum we see can be compared with previously measured spectra.
We may find, say, that's a mercury lamp.

This is how astronomers figure out what things are made of.
The atmospheres of planets, stars, gas clouds out in space, etc.

Types of Spectra
[See figure 3.15 on page 110.]

A hot, dense object will create a continuous spectrum following Wien's Law.
Solid objects behave as blackbodies, they don't generate light by electron transitions, they use a different process (collision of atoms).
Incandescent lights (like in our spectrum projector) have a tungsten filament and emit a continuous spectrum.
Stars are hot, dense objects which emit a continuous spectrum of light from their surface.
See figure 3.11 on page 106

.
** Observer looking directly at the star:
Will see a continuous spectrum.

** An observer looking through a gas cloud towards star:
Some of the light passing through the cloud will have just the right energy to be absorbed by an electron changing orbits.
See right side of figure 3.15 on page 110.
Some colors will be absorbed.
If the light is sent through a prism, an absorption spectrum will be seen.
A complete rainbow except that a few colors are missing.
The missing colors are the spectrum of the atoms in the gas cloud.
The composition of the cloud can be determined.
Most stars have atmospheres so this can be the cloud.
We see absorption spectra from most stars.

** An observer looking at cloud but not star:
The absorbed photons boosted electrons to higher orbits.
When the electrons fall back to the lower orbits, light will be emitted.
This light will go off in all directions.
The person will see just a few colors (mixed together, need a prism or grating to see which colors are there).
This is called an emission-line spectrum.
The colors are the spectrum of the atoms in the cloud.
Again the composition of the cloud can be determined.

Old astronomy adage: If a picture is worth a thousand words, a spectrum is worth a thousand pictures.

The Sun:
Isaac Newton was the first to examine the spectrum of sunlight.
He saw a continuous spectrum.

Later, around 1800 with better equipment, Joseph Fraunhofer saw gaps in the solar spectrum.
Some colors were missing.
See figure 3.17 (bottom spectrum) on page 112.

The missing colors correspond to the spectrum of elements in the Sun's atmosphere (and partially the earth's atmosphere).
Many familiar elements were spotted on the Sun, sodium, hydrogen, calcium, etc.
There were a few colors that corresponded with no known element.
It was guessed that there was some new element in the sun that had never been found on Earth.

The new element was named after the Sun, it was called helium.
(Like heliocentric means Sun-centered.)
Years later new gas was identified on the Earth and its spectrum measured, it was helium.
Helium was discovered on the Sun before it was ever discovered on the Earth!

Section 3.6 - The Doppler Shift
The Doppler shift is a very useful astronomical tool.
[You can skip the mathematical details discussed in the text.]

Light moves as a wave.
Similar to waves created if you throw a rock into a pond.
Or the sound waves moving through the room as I talk.

Light waves always move the same speed, c = 3 x 10^8 m/s.
The different colors of light are due to different wavelengths (distance between successive waves).
For the moment, let's consider sound waves although the same arguments will apply to light waves.
Usually sound waves (and light waves) are created by some rhythmic disturbance.
The result is a series of moving waves (the curves represent successive crests of waves).
[See figure 3.19 on page 113.]

** Police car siren, car not moving

The distance from one wave to the next is the wavelength.

** Police car siren, car heading towards you

The car emits sound waves and it chases after its own waves.
The waves move at their usual speed.
But the car's movement causes the waves to be crowded together, a shorter wavelength.
This will sound like a higher pitch (higher frequency).

** Police car siren, car moving away from you

The car is moving away from the previously emitted sound waves.
The result is a longer wavelength (lower pitch or frequency).

You've all undoubtably experienced this effect.
A car or plane or train zipping past you makes sounds that shift from a higher pitch to lower as it passes by.
This shifting of sound is called the Doppler Shift.
It only occurs if the source of the sound is moving (at least partially) towards or away from you.

Light is affected in the same way.
Visible light (and radio, IR, UV, etc.) will have the wavelength (color) shifted to shorter or longer wavelengths depending on whether the source is moving towards or away from you.
Very high speeds are necessary to get a noticeable shift (because the speed of light is so large).
You never see these color shifts in everyday life, but most astronomical objects are moving fast enough for a measurable shift.

Doppler Shift Summary:
Source moving towards observer (or observer towards source):

shift to shorter wavelength (higher frequency)
yellow light shifted towards blue
"blue shift"

Source moving away from observer (or observer moving away):

shift to longer wavelength (lower frequency)
yellow towards red
"red shift"

Redshift when Receding.

Not only does the Doppler shift tell us whether the source is moving towards or away from us, but the amount of shift can be used to calculate the speed.
Again, we will skip that mathematical part of the text.

We will often talk about how fast things out in space are moving (like stars in binary systems, planets in their orbits, or galaxies moving through space), now you know how all those speeds were determined.

Section 3.7 - you can skip it

End Chapter 3.