READING

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READING
Unit 8, Unit 19, Unit 20, Unit 21, Unit 22, Unit
23

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Potential Energy

• You can think of potential energy as stored
  energy, energy ready to be converted into another
  form
• Gravitational potential energy is the energy
  stored as a result of an object being lifted
  upwards against the pull of gravity
• Potential energy is released when the object is
  put into motion, or allowed to fall.

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Conversion of Potential Energy

• Example
• A bowling ball is lifted from the floor onto a
  table
• Converts chemical energy in your muscles into
  potential energy of the ball
• The ball is allowed to roll off the table
• As the ball accelerates downward toward the
  floor, gravitational potential energy is
  converted to kinetic energy
• When the ball hits the floor, it makes a sound,
  and the floor trembles
• Kinetic energy of the ball is converted into
  sound energy in the air and floor, as well as
  some heat energy as the atoms in the floor and
  ball get knocked around by the impact

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Definition of Angular Momentum

• Angular momentum is the rotational equivalent of
  inertia
• Can be expressed mathematically as the product of
  the objects mass, rotational velocity, and radius
• If no external forces are acting on an object,
  then its angular momentum is conserved, or a
  constant

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Conservation of Angular Momentum

• Since angular momentum is conserved, if either
  the mass, size or speed of a spinning object
  changes, the other values must change to maintain
  the same value of momentum
• As a spinning figure skater pulls her arms
  inward, she changes her value of r in angular
  momentum.
• Mass cannot increase, so her rotational speed
  must increase to maintain a constant angular
  momentum
• Works for stars, planets orbiting the Sun, and
  satellites orbiting the Earth, too!

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The Origin of Tides

• The Moon exerts a gravitational force on the
  Earth, stretching it!
• Water responds to this pull by flowing towards
  the source of the force, creating tidal bulges
  both beneath the Moon and on the opposite side of
  the Earth

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Solar Eclipses

• At New Moon, the Moon is between the Earth and
  the Sun. Sometimes, the alignment is just right,
  allowing the Moon to block the light from the
  Sun, creating an eclipse

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Solar Eclipse the Shadow of the Moon

• In a solar eclipse, the Moon casts a shadow on
  the surface of the Earth. People within the
  shadow see the eclipse, and those outside the
  shadow do not.
• The Moons umbra is the darkest part of the
  shadow, directly behind the body of the Moon.
  Within the umbra, the Sun appears completely
  eclipsed (total eclipse).
• The penumbra of the Moon (not shown in figure) is
  the part of the shadow where the light from the
  Sun is only partially blocked (partial eclipse).

A solar eclipse seen from space
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Lunar Eclipses

• As the Moon passes behind the Earth, the Earth
  can cast a shadow on the surface of the Moon,
  creating a lunar eclipse
• The reddish glow of a fully eclipsed Moon is
  light that has been refracted through the Earths
  atmosphere and bounced back to Earth it is, in
  essence, the light of every sunrise and sunset on
  Earth reflected off the Moon!

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Lunar Eclipse the Shadow of the Earth

• In a lunar eclipse, the Earth casts a shadow on
  the surface of the Moon. In its orbit, the Moon
  passes through the penumbra and umbra of the
  Earth
• The penumbra of the Earth is the part of the
  shadow where the light from the Sun is only
  partially blocked. The Moon dims a little as it
  passes into the penumbra.
• The Earths umbra is the darkest part of the
  shadow, directly behind the body of the Earth.
  After the Moon moves into the umbra, its surface
  becomes very dark. This is a total lunar eclipse.

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Why dont eclipses happen all the time?

• In order for an eclipse to occur, the Moon must
  lie directly between the Earth and the Sun (solar
  eclipse), or the Earth must lie directly between
  the Moon and the Sun (lunar eclipse).
• The orbit of the Moon around the earth is
  inclined slightly to the plane of the ecliptic
  (the plane in which the Earths orbit lies).

• Most of the time, the Moons shadow misses the
  Earth, or the Earths shadow misses the Moon!

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Everything Must be Just Right

• For an eclipse to occur, the Moon must be
  crossing the ecliptic at the same time it passes
  either in front of (solar eclipse) or behind
  (lunar eclipse) the Earth (BD).
• Otherwise, no eclipses are possible (AC).

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The Nature of Light

• Light is radiant energy.
• Travels very fast 300,000 km/sec!
• Can be described either as a wave or as a
  particle traveling through space.

• As a particle
• Particles of light (photons) travel through
  space.
• These photons have very specific energies. that
  is, light is quantized.
• Photons strike your eye (or other sensors) like a
  very small bullet, and are detected.

• As a wave
• A small disturbance in an electric field creates
  a small magnetic field, which in turn creates a
  small electric field, and so on
• Light propagates itself by its bootstraps!
• Light waves can interfere with other light waves,
  canceling or amplifying them!
• The color of light is determined by its
  wavelength.

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The Effect of Distance on Light

• Light from distant objects seems very dim
• Why? Is it because the photons are losing
  energy?
• No the light is simply spreading out as it
  travels from its source to its destination
• The farther from the source you are, the dimmer
  the light seems
• We say that the objects brightness, or amount of
  light received from a source, is decreasing

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The Nature of Matter

• The atom has a nucleus at its center containing
  protons and neutrons
• Outside of the nucleus, electrons whiz around in
  clouds called orbitals
• Electrons can also be described using wave or
  particle models
• Electron orbitals are quantized that is, they
  exist only at very particular energies
• The lowest energy orbital is called the ground
  state, one electron wave long

• To move an electron from one orbital to the next
  higher one, a specific amount of energy must be
  added. Likewise, a specific amount of energy
  must be released for an electron to move to a
  lower orbital
• These are called electronic transitions

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The Chemical Elements

• The number of protons (atomic number) in a
  nucleus determines what element a substance is.
• Each element has a number of electrons equal to
  the number of protons
• The electron orbitals are different for each
  element, and the energy differences between the
  orbitals are unique as well.
• This means that if we can detect the energy
  emitted or absorbed by an atom during an
  electronic transition, we can tell what element
  the atom belongs to, even from millions of light
  years away!

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Periodic Table
D. Mendeleev
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Absorption

• If a photon of exactly the right energy
  (corresponding to the energy difference between
  orbitals) strikes an electron, that electron will
  absorb the photon and move into the next higher
  orbital
• The atom is now in an excited state
• If the photon is of higher or lower energies, it
  will not be absorbed it will pass through as if
  the atom were not there.

• This process is called absorption
• If the electron gains enough energy to leave the
  atom entirely, we say the atom is now ionized, or
  is an ion.

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Emission

• If an atom drops from one orbital to the next
  lower one, it must first emit a photon with the
  same amount of energy as the orbital energy
  difference.
• This is called emission.

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Seeing Spectra

• Seeing the Suns spectrum requires a few special
  tools, but it is not difficult
• A narrow slit only lets a little light into the
  experiment
• Either a grating or a prism splits the light into
  its component colors
• If we look closely at the spectrum, we can see
  lines, corresponding to wavelengths of light that
  were absorbed.

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Emission Spectra

• Imagine that we have a hot hydrogen gas.
• Collisions among the hydrogen atoms cause
  electrons to jump up to higher orbitals, or
  energy levels
• Collisions can also cause the electrons to jump
  back to lower levels, and emit a photon of energy
  hc/?
• If the electron falls from orbital 3 to orbital
  2, the emitted photon will have a wavelength of
  656 nm
• If the electron falls from orbital 3 to orbital
  2, the emitted photon will have a wavelength of
  486 nm

• We can monitor the gas, and count how many
  photons of each wavelength we see. If we graph
  this data, well see an emission spectrum!

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Wavelength

• The colors we see are determined by the
  wavelength of light.
• Wavelength is the distance between successive
  crests (or troughs) in an electromagnetic wave.
• This is very similar in concept to the distance
  between the crests in ocean waves!
• We denote the wavelength of light by the symbol ?.

• Wavelengths of visible light are very small!
• Red light has a wavelength of 7?10-7 meters, or
  700 nanometers (nm)
• Violet light has a wavelength of 4?10-7 meters,
  or 400 nm
• Colors in between red and violet (remember ROY G
  BIV?) have intermediate wavelengths

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Frequency

• Sometimes it is more convenient to talk about
  light in terms of frequency, or how fast
  successive crests pass by a given point
• You can think of frequency as a measure of how
  fast you bob up and down as the waves pass.
• Frequency has units of Hz (Hertz), and is denoted
  by the symbol ?
• Long wavelength light has a low frequency, and
  short wavelength light has a high frequency

• Frequency and wavelength are related by

c is the speed of light.
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White Light

• Light from the Sun arrives with all wavelengths,
  and we perceive this mixture of colors as white
• Newton demonstrated that white light could be
  split into its component colors with a prism, and
  then recombined into white light with a lens

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Measuring Temperature

• It is useful to think of temperature in a
  slightly different way than we are accustomed to
• Temperature is a measure of the motion of atoms
  in an object
• Objects with low temperatures have atoms that are
  not moving much
• Objects with high temperatures have atoms that
  are moving around very rapidly
• The Kelvin temperature scale was designed to
  reflect this
• 0 ? K is absolute zero the atoms in an object
  are not moving at all!

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Results of More Collisions

• Additional collisions mean that more photons are
  emitted, so the object gets brighter
• Additional hard collisions means that more
  photons of higher energy are emitted, so the
  object appears to shift in color from red, to
  orange, to yellow, and so on.
• Of course we have a Law to describe this

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Wiens Law and the Stefan-Boltzmann Law

• Wiens Law
• Hotter bodies emit more strongly at shorter
  wavelengths

• SB Law
• The luminosity of a hot body rises rapidly with
  temperature

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Taking the Temperature of Astronomical Objects

• Wiens Law lets us estimate the temperatures of
  stars easily and fairly accurately
• We just need to measure the wavelength (?max) at
  which the star emits the most photons
• Then,

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The Stefan-Boltzmann Law

• If we know an objects temperature (T), we can
  calculate how much energy the object is emitting
  using the SB law
• ? is the Stefan-Boltzmann constant, and is equal
  to 5.67?10-8 Watts/m2/K4
• The Sun puts out 64 million watts per square
  meter lots of energy!