Download 1Oct_2014

READING
Unit 22, Unit 23, Unit 24, Unit 25
Homework 4
Unit 19, problem 5, problem 7
Unit 20, problem 6, problem 9
Unit 21, problem 9
Unit 22, problem 7
Unit 23, problem 8
Unit 24, problem 6
Unit 25, problem 8
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!
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
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
‘c’ is the speed of light.
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
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!
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
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 106 K  nm
max
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
L  T
4
•  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!
Doppler Shift in Light
• If an object is emitting light and
is moving directly toward you,
the light you see will be shifted
to slightly shorter wavelengths –
toward the blue end of the
spectrum, or blue-shifted
• Likewise, if the object is moving
away from you, the light will be
red-shifted.
• If we detect a wavelength shift of
 away from the expected
wavelength , the radial (line-ofsight) velocity of the object is:
VR 


c
As a blackbody object becomes hotter, it also
becomes ____________ and _____________
•
•
•
•
a. more luminous, redder
b. more luminous, bluer
c. less luminous, redder
d. less luminous, bluer
•
•
•
•
Compare two blackbody objects, one at 200K and
one at 400K. How much larger is the flux from the
400K object, compared to the flux from the 200K
object?
a. Twice as much
b. Four times as much
c. Eight times as much
d. Sixteen times as much
Star A and star B appear equally bright in the sky.
Star A is twice as far away from Earth as star B. How
do the luminosities of stars A and B compare?
•
•
•
•
a. Star A is 4 times as luminous as star B
b. Star A is 2 times as luminous as star B
c. Star B is 2 times as luminous as star A
d. Star B is 4 times as luminous as star A
Which of the following factors does *not* directly
influence the temperature of a planet?
•
•
•
•
a. The luminosity of the Sun
b. The distance from the planet from the Sun
c. The color of the planet
d. The size of the planet