Download Energy Levels in Atoms

The Small
Angle
Approximation
The 2p shows
the fact that the
natural units for
angle here are
“radians”;
2p of them for a
full circle
(so 57.3 degrees
per radian).
Measuring distance with triangulation
Parallax – direct distances to the stars
d(parsec) = 1/p(arcsec) ; 1 parsec = 3.26 light years
The Luminosity Law
The intrinsic luminosity of a star depends on its temperature (because
blackbody radiation goes like T4 per unit area, and its size (to
account for its total area ~R2) :
LR T
2
l1
4
l2
L1
R2
R1
T1
L2
T2
Observation of stellar properties
You can tell something from the brightness and color of a star,
but there are complications.
•The color gives you an approximate temperature.
•It is hard to tell the distance from the brightness, because the size is also
quite variable:
•A small blue star can be as luminous as a larger red star. A blue star
can be the same brightness as a red star if they have the same size but
the red star is much closer.
•If you get the distance from parallax, then you can tell the size from the
color and apparent brightness.
•Since most stars are many light years away, their parallaxes are small
fractions of an arcsec.
•Observing from space helps with this.
•Their sizes are generally too small to be measured directly
(much smaller fractions of an arcsec).
•Interferometry will help with this.
The Inverse-Square Law
The apparent brightness of a source goes down like the square of the
distance to the source (and depends on the intrinsic luminosity of
the source : b  L 2
d
Energy Levels in Atoms
We can think of an atom as consisting of a positive nucleus (protons and
neutrons) surrounded by negative electrons. The electrons can be thought of as
“orbiting” the nucleus, but are only allowed in certain orbits (or energy levels).
A photon with exactly the right energy can excite the electron from one level to
another. The electron will drop back to the “ground state”, and emit photons
with specific energies as it does so.
Energy transitions and photons
The energy of photon that can interact with a level jump just depends on
the energy difference between the levels. Levels can be skipped.
Unique Atomic Signatures
Each atom has a specific set of energy levels, and thus a unique set of
photon wavelengths with which it can interact.
Astro Quiz
The spectra from two different atoms are observed. A spectral line in
the first atom has exactly one-half the wavelength of a spectral line
in the second atom. Which of the below is TRUE?
• The spacing between 2 levels in the first atom must be
twice the spacing between 2 levels in the second atom.
• The spacing between 2 levels in the first atom must be half
the spacing between 2 levels in the second atom.
• The energy of the upper of 2 levels in the first atom must
be half that of the energy of the upper of 2 levels in the
second atom.
Spectrometers
A spectrometer makes an
image (usually of its
entrance slit) at every
wavelength. A telescope
illuminates the slit with
starlight.
Diffraction gratings
Very fine facets or grooves will
act like many little slits and
produce an interference pattern
that spreads wavelengths.
far infrared grating
Transitions in
Hydrogen
Hydrogen is
particularly
important and
distinctive. The “Halpha” line is the one
from levels 2-3; the
Balmer series from
level 2 is in the
visible. The Lyman
series lines are all
ultraviolet.
The Solar
Spectrum
Stellar Spectral Types
Different stars show different spectral
lines, or different line strengths. They
were sorted by this appearance
(Annie Jump Cannon).
Decoding Stellar Spectra
The reasons why spectra change were a bit subtle, so the ordering of the
letters got scrambled when the temperature sequence was determined.
Properties of the Spectral Types
Most stars will be in their stable hydrogen-burning phase, called the
“main sequence”. For these, the spectral type has a simple relation
to the star’s properties. Note that luminosity has a large variation.
The
Brightest
and Nearest
Stars
Towards the “HR diagram”
Basketball player
Height
Adults
Skinny
Anorexic
Fat
Sumo
wrestler
Children
Weight
The Hertzsprung-Russell Diagram
Hertzsprung and Russell had the idea of plotting the luminosity of a
star against its spectral type. This works best for a cluster, where
you know the stars are all at the same distance. Then apparent
brightness vs spectral type is basically the same as luminosity vs
temperature. They found that stars only appear in certain parts of
the diagram.
Basics of
the HR
diagram
Size
Mass
Red dwarfs
Size/Luminosity
Hot stars are very bright but
very rare. They can affect
the light, but not the mass
of the Galaxy. Red
supergiants are more
common.