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Transcript
Astronomy 2
Overview of the Universe
Winter 2006
5. Lectures on Spectroscopy and Atomic Physics.
Joe Miller
Spectroscopy: the study of the spectra of light.
The spectrum of a light source is a presentation of
the intensities of the various wavelengths of light
that make up that light. The intensity of light is
shown as a function of wavelength. A common
spectrum is a rainbow.
Carefully studied, a spectrum can give us direct
information on how the light was produced.
Spectroscopy is an absolutely fundamental and
extremely powerful tool for our understanding of the
universe.
Kirchoff”s Laws of Spectroscopy: empirical laws
discovered in the 19th century with no understanding of the
underlying physical principles (in some ways analogous to
Kepler’s Laws).
First Law:
A glowing solid or glowing liquid or glowing very high
density gas emits a continuous spectrum.
Continuous spectrum: all wavelengths are emitted.
Example: tungsten light bulb, hot toaster wire.
Second Law:
A glowing gas emits radiation only at specific, discrete
wavelengths.
This is often called an “emission line spectrum,”
because spectrographs used to record spectra typically have
recorded these emissions as narrow lines.
Where we are headed: the pattern of emission lines emitted
by a glowing gas is determined by the chemical elements in
the gas and their physical condition.
Third Law:
A cool gas in front of a source of a continuous
spectrum produces an absorption spectrum.
The light of certain, specific wavelengths is removed
from the continuous spectrum. These dark spectral
regions are often referred to as “absorption lines.”
Here is hydrogen gas in absorption:
Spectra can be very complicated!
Example: the spectrum of the sun
Summary of Kirchoff’s Three laws:
To understand the physics of astronomical
objects, how they work, we must understand the
physical processes that result in these three
different kinds of spectra: the production and
absorption of light itself.
Light is generally produced and absorbed by
processes that take place in the realm of the atom or
molecule and involve energy transfers with
electrons. To understand these processes requires an
understanding of how atoms work.
The structure of the atom:
A simple atom has two parts: the nucleus and a cloud
of electrons in orbit around it.
The simplest atom is hydrogen:
It has a single particle called a proton at its center
and single particle called an electron in orbit around
the proton. The proton has a positive charge (+), and
the electron has a negative (-) charge.
The hydrogen atom
Like charges repel, opposite charges attract
according to a formula that looks a lot like the Law
of Gravity:
q1 q2
F  C 2
d
where F is the electrostatic force, C is a constant, q1
and q2 are the charges on the two particles, and d is
their separation. The minus sign acknowledges that
the force can be attractive (+) or repulsive. This is
called Coulomb’s Law and is another example of an
inverse square law.
Helium, the next most complex atom:
Helium has a nucleus of two protons plus two more particles
called neutrons. Neutrons have no charge, but help bind the
nucleus together. Helium in its normal state has two electrons
orbiting the nucleus.
The atomic number of helium = the number of protons =2
The atomic weight = no. of protons plus neutrons = 4.
It is the number of protons and electrons that determines the
chemical nature and behavior of an atom, and thus the atomic
number determines what the element is. For example, iron
has 26 protons, but normally 30 neutrons, so its atomic
weight is 56.
The helium atom:
The carbon atom:
Isotopes
Isotopes are different versions of the same element
with different atomic weights. That is, though the
various isotopes of a give element must all have the
same number of protons, and thus the same atomic
number, they have different numbers of neutrons.
Two examples:
1. Deuterium is a form of hydrogen that has a
nucleus of one proton (that’s why it’s still hydrogen)
plus one neutron.
2. Tritium is another form of hydrogen with one
proton and two neutrons in the nucleus.
Isotopes (cont.)
If a nucleus has too many or two few neutrons, it may be
unstable and fall apart by radioactive decay.
Many isotopes are naturally occurring, but many are also
made only in nuclear reactors.
Ions:
When an atom has an equal number of electrons and protons,
it is neutral; there is no net charge. However, if an electron is
removed, the atom left behind is now said to be an ion and
has a net positive charge. The process of removing an
electron is called ionization. Atoms with many electrons can
be singly ionized, doubly ionized, etc., gaining ever more
charge as more electrons are removed.
How light is created inside the atom
Bohr’s Theory (the beginnings of quantum mechanics.)
In Bohr’s picture, electrons can reside in only in certain orbits
and nowhere else. These orbits are said to be “quantized.”
The closer an orbit is to the nucleus, the more tightly bound is
the electron there to the nucleus.
To move an electron from a low orbit to a higher
one requires energy. Conversely, an electron
moving from a higher orbit to a lower one gives up
energy. Often the energy involved is a photon,
either being absorbed or emitted.
Consider the hydrogen atom:
There are many possible transitions (electron
jumps) between level just in the lower levels.
An alternative way of looking at things: the energy
level diagram: hydrogen (left) and sodium (right).
The immense variety of spectra
Each atom has its own particular set of energy levels.
Thus it has its own set of possible electron decay
paths which lead to the creation of photons and
therefore its own set of wavelengths for the pattern
of spectral lines it can form. Furthermore, the same
can be said of each stage of ionization of each atom.
Neutral oxygen is capable of producing a different
set of spectral lines than singly ionized oxygen,
doubly ionized oxygen yet another unique set, and so
on. Fortunately for the spectroscopist, not all
elements and ions of all elements are equally
abundant, or interpreting spectra would be an almost
impossible job.
Even so, spectra can be very complicated!
A portion of the spectrum of the sun:
Summary of electron transitions:
• Excitation: electron goes from a lower orbit to a higher
one: two ways to do this– Radiative (photo-) excitation: a photon of exactly the
right energy to go up from one level to another is
absorbed. Part of a photon’s energy can’t be used. It’s
all or nothing. The photon is destroyed.
– Collisional excitation- an atom collides with another
atom or electron. Some of the kinetic energy is lost,
exciting the electron to a higher level.
• Ionization: if the absorbed photon or the collision gives
the electron enough energy, it can be removed entirely
from the atom. This is called either photo-ionization or
collisional ionization.
Electron transitions (cont.)
• De-excitation: an electron goes from a higher orbit to a
lower one.
– Radiative de-excitation- the electron drops to a lower
energy level and gives up a photon of energy equal to
the difference in energies between the two levels.
– Collisional de-excitation- the atom collides with
another atom or electron, and the energy released as the
electron drops from one level to another is put into
kinetic energy of the collision.
– Recombination- the opposite of ionization. An ion
captures an electron and becomes one stage less
ionized. A photo is given off with energy
corresponding to the energy lost by the electron as it is
captured.
The formation of a continuous spectrum: a great puzzle of
the 19th century.
The continuous spectrum is produced in part by electrons that
are not necessarily confined to bound orbits, but are relatively
free to wander around. Also, in the case in a solid or gas
under high pressure, atoms and molecules bound together by
electric fields and shared electrons store energy in this
binding and can release it in the form of radiation. Together,
these processes can give rise to photons of any amount of
energy and thus give rise to photons of a continuous range of
wavelengths. However theoretical attempts in the 19th
century to predict the relative likelihood of various energy
photons being produced, that is, to account for the shape of
the spectrum emitted by a glowing solid, failed. It predicted
that the spectrum would rise forever into the ultraviolet. This
was called the ultraviolet catastrophe.
The solution to the spectrum of continuous radiation:
Planck’s theory of black body radiation.
Planck needed to use the new theory of quantum
mechanics to do the problem correctly. He defined a
new type of object- a black body- as an object
capable of emitting or absorbing any wavelength
without any hindrance: a perfect emitter or absorber.
Using quantum theory, he derived the spectrum of a
black body and showed that its shape only depended
on temperature. He thus theoretically provided the
basis for Wien’s and Stefan-Boltzmann’s Law, which
we will now turn to.
Illustration of black body radiation at different
temperatures:
Wien’s law: an empirical law.
The wavelength of maximum light output from a
black body depends inversely on the temperature.
max
C
 , where C is a constant and T is the temperature.
T
The hotter an object is, the bluer its maximum light
output becomes.
Stefan-Boltzmann Law:
The amount of radiation emitted per unit area of a
black body goes up as the fourth power of the
temperature. Doubling the temperature results in 16
times as much energy output per unit area.
E   T , where  is a constant.
4
With these physical principles and ideas, we are
now ready to investigate the nature of the stars!