Download Feb20

Homework 4
Unit 21 Problem 17, 18, 19
Unit 23 Problem 9, 10, 13, 15, 17, 18, 19, 20
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 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.
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.
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 object’s
brightness, or amount of light
received from a source, is
decreasing
Brightness =
Total Light Output
4pd 2
This is an inverse-square law –
the brightness decreases as the
square of the distance (d) from
the source
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
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!
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!
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…
Wien’s Law and the Stefan-Boltzmann Law
• Wien’s Law:
– Hotter bodies emit more
strongly at shorter
wavelengths
• SB Law:
– The luminosity of a hot
body rises rapidly with
temperature
Taking the Temperature of Astronomical Objects
• Wien’s 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,
T=
2.9 ´10 6 K × nm
lmax
The Stefan-Boltzmann Law
• If we know an object’s
temperature (T), we can
calculate how much energy
the object is emitting using
the SB law
4
L = sT
•  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!
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.
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.
Seeing Spectra
• Seeing the Sun’s
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.
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, we’ll see an emission
spectrum!
Emission spectrum of hydrogen
• This spectrum is
unique to hydrogen
– Like a barcode!
• If we were looking
at a hot cloud of
interstellar gas in
space, and saw
these lines, we
would know the
cloud was made of
hydrogen!
Different atom, different spectrum!
•
Every element has its
own spectrum. Note the
differences between
hydrogen and helium
spectra below.
Absorption Spectra
• What if, instead of hot
hydrogen gas, we had a cloud
of cool hydrogen gas between
us and a star?
– Photons of an energy that
corresponds to the
electronics transitions in
hydrogen will be absorbed
by electrons in the gas
– The light from those photons
is effectively removed from
the spectrum
– The spectrum will have dark
lines where the missing light
would be
– This is an absorption
spectrum!
– Also like a barcode!
Types of Spectra
•
Kirchoff’s Laws:
– If the source emits light that is
continuous, and all colors are present,
we say that this is a continuous
spectrum.
– If the molecules in the gas are wellseparated and moving rapidly (have a
high temperature), the atoms will emit
characteristic frequencies of light. This
is an emission-line spectrum.
– If the molecules of gas are wellseparated, but cool, they will absorb
light of a characteristic frequency as it
passes through. This is an absorption
line spectrum.
Spectra of Astronomical Objects