Download star charts

ASTRONOMY 130
SPECTRA
PURPOSE: To learn how various types of spectra are formed and how they can be used to
classify stars. To observe the spectra of different elements and learn how they can be
identified.
PROCEDURE: Use the spectra of different elements and different spectral classifications to sort
stars into different spectral types.
LIGHT
Light is a form of electromagnetic radiation which has a characteristic wavelength (color)
and frequency, but in some ways, light also behaves as though it were composed of particles. A
name has been given to these particles or bundles of electromagnetic energy; they are called
photons. A photon has energy but no mass. There is a relationship between the energy of a
photon and its wavelength or frequency:
E  hf 
hc

because f  c, where c is the speed of light. The term h is called Planck’s constant.
We can see that, since h and c are constants, the relationship between energy and
wavelength is inverse, that is; the greater the energy, the smaller the wavelength. If the energy is
large, the wavelength is short - blue light and if the energy is small, the wavelength is long - red
light. For every value of the energy E, there is one and only one value of wavelength or
frequency.
KIRCHOFF’S LAWS
There are several ways to produce light, but the kinds of spectra emitted fall into two
categories: a continuous spectrum consists of all possible wavelengths. A line spectrum may be
of two types: bright line (or emission line) spectra are produced when light of only a few discrete
wavelengths are present. A dark line (or absorption line) spectrum occurs when discrete
wavelengths are missing from a continuous spectrum.
Kirchoff discovered the three basic laws which describe the emission or absorption of
light:
(1) An incandescent solid, liquid, or highly compressed (or highly ionized) gas emits a
continuous spectrum.
(2) An incandescent gas which is neither compressed or ionized emits a bright line or
emission spectrum.
(3) A relatively cool gas in front of a hot continuous source produces an absorption
spectrum whose absorbed wavelengths are the same as those that would be emitted if
the gas were heated.
THE SPECTROSCOPE
A device which enables us to see the lines produced by the gases in stars, is the
spectroscope. There are two basic types: prism and grating. We will be using the grating type.
Take care not to touch the grating with your hands.
You will observe a variety of spectra with your spectroscope. Record your
observations on Exercise sheet 1. Carefully draw the spectrum you observe, giving the
proper relationship between the lines as well as their colors.
FORMATION OF SPECTRAL LINES
In order to understand how stars are classified by their spectra, we need to take a look at
the process that produces the spectral lines that are unique to each element. We will use, as our
example, the hydrogen atom which is the simplest of all the atoms.
The simple Bohr model of the hydrogen atoms is a solar-system like arrangement in
which a tiny negatively charged electron orbits the heavy positive proton in the nucleus.
Figure 1.
electron
1
2
3
4 5
proton
Permitted Orbits
It has been discovered that there are only certain orbits which the electron may occupy;
the areas between these permitted orbits are never occupied by electrons. Recently is has become
convenient to talk about energy levels instead of orbits.
Figure 2.
6
5
4
3
2
1
Orbits
Energy Levels
Energy levels are analogous to orbits: an electron may occupy one of these levels, but not
the area between. Because of the opposite charges between electron and proton, the electron, if
left alone, will tend to occupy the lowest energy level (nearest the proton) or innermost orbit.
This is called the ground state or first energy level. An electron at this level has a minimum
amount of energy.
Electrons can also occupy higher or excited levels, but it takes energy to pull the electron
away from the proton. Therefore, for an electron to pull the electron to occupy the first excited
state, or level 2, it is necessary to supply an amount of energy equal to the energy difference
between the two levels. If more or less than this amount is supplied, the electron will not jump to
level 2. The transition to the higher level can only be made if a bundle of energy (a photon),
equal to the energy level difference, is supplied.
Figure 3.
n = 4, E4
Third Excited State
n = 3, E3
Second Excited State
Energy difference E3 - E1
n = 2, E2
First Excited State
Energy difference E2 - E1
n = 1, E1
Ground State
An excited atom is one in which the electrons are not in the ground state, but at some
higher level (that is, energy has been supplied to the atom). If left alone, the electrons will tend to
jump back down to the ground level (where they have minimum energy). That is, because of the
attraction between the electron and proton, the electron would like to give up its excess energy
and drop back to the ground state. But to do so, it must give up that excess energy. Therefore,
when an electron jumps back down to the ground state, it radiates away the energy used to boost
it to the higher level. This energy leaves the atom as a photon.
Figure 4.
n = 4, E4
n = 3, E3
n = 2, E2
Energy given off E3 - E1
n = 1, E1
Suppose we have a warm cloud of hydrogen gas. Since it is warm, many of the atoms will
be excited (electrons will be in higher energy levels). If an atom with an excited electron is left
alone, the electron will jump down to a ground state, and radiate away energy, thus producing an
emission line. Let us consider two cases, one atom with an electron in level 3, another with an
electron in level 2.
Figure 5.
n=3
n=2
E21 = E2 - E1
E31 = E3 - E1
n=1
In an energy level diagram, the spacing between levels is proportional to the energy difference
between the levels. The energy difference between level 3 and 1 is greater than the energy
difference between level 2 and 1. Therefore, the photon given off by a 3-1 jump produces “bluer”
wavelength light than the 2-1 jump. The 2-1 jump produces a redder wavelength photon than the
3-1 jump.
Emission lines are a result of downward jumps of electrons within the atom which
produce photons at the specified wavelength (or color).
The hydrogen atom, because of its simplicity, has been exhaustively studied. Now we
consider three separate cases of downward jumps by electrons:
(1) all downward jumps end up in the ground state (LYMAN series)
(2) all downward jumps end up in the first excited state, level 2 (BALMER series)
(3) all downward jumps end up in the second excited state, level 3 (PASCHEN series).
FIGURE 6.
n=6
E6
E5
E4
n=5
n=4
n=3
LYMAN SERIES
E3
n=2
E2
n=1
E1
BALMER SERIES
PASCHEN SERIES
In the second case, each jump to the second level is shorter than the shortest jump (2-1) in
the first case. The energy is less, and therefore the photon is redder (has a larger wavelength).
The reddest photon is produced by the shortest jump, 3-2. The bluest jump is 6-2, and its photon
is still redder than the reddest Lyman series line. This second series of lines is called the Balmer
Series, and is important because most of the lines are in the visible part of the spectrum.
In general, this principle applies to other atoms as well; atoms with more protons and
electrons. Each element has a characteristic set of lines in the visible part of the spectrum, and the
position of these lines can be calculated by knowing the configuration of the electrons involved.
Identification of these characteristic lines in the spectra enables us to determine what elements
are present and what the temperature is.
Suppose we have a cloud of cold hydrogen has with most of its electrons in the ground or
first excited state. If there is a source of continuous light behind the cloud, this source produces
photons at all wavelengths. Now some of these photons will have exactly the amount of energy
corresponding to that need for upward transitions within the hydrogen gas atoms. If a photon
comes along with the correct amount of energy to an electron from the first to third level it will
be absorbed by the atom, and the spectrum is now missing one wavelength (corresponding to the
energy of the absorbed photon).
The electron now in level 3 will jump back down if left alone, but the photon emitted will
probably leave the atom in some different direction and will not be seen. It is also possible that
another photon may come along and knock the electron completely out of the atom. The atom is
then called ionized. In either case, that initial photon, and the wavelength corresponding to it, is
lost. Therefore, a dark line appears in the continuous spectrum at the position of the missing
wavelength.
THE SPECTRA OF STARS
Stellar spectra are usually absorption spectra. The hot, dense gas of the interior of the
stars produce the continuous spectrum, but in the outer regions , atmospheres of stars act as a
(comparatively) cool gas in front of a hot continuous source. Depending on the composition of
the gas, absorption lines will be formed as photons are caught by the atoms of the gas. Although
stars are mostly hydrogen, they also contain many other elements, and each of the elements has
the ability to produce an absorption spectrum. For the above reasons, the typical stellar spectrum
will show lines of many elements.
Figure 8.
H
He He
Mn
Ca Ca
H
H
Fe
H
Fe
Hydrogen Balmer lines are easily seen in the spectra of stars, but in some stars, these lines
seem weak compared to the lines of other elements. In other stars, the Balmer lines are dominant.
To understand what it is that determines the relative “strength” of spectral lines, imagine that we
have a cloud consisting of 100 atoms of hydrogen gas.
If that gas is cold, most of the 100 atoms will have their electrons in the lowest energy
level. Suppose that, due to collisions or other random effects, 4 of the atoms have electrons in the
second energy level, then of the 100 atoms, only 4 are capable of contribution to the Balmer
lines, since only 4 have electrons which can make the upward jumps from the second energy
level.
If the gas is warmer, more of the atoms will have “excited” electrons; electrons which are
not in the ground state, but in some higher level. Many of these electrons will be in the second
energy level and many more atoms will contribute to the Balmer lines as upward transitions
occur. The lines will be stronger than in the first case of only 4 atoms forming the Balmer Series.
As the temperature increases, more atoms will have their electrons in very high energy
levels and some may have lost their electrons completely. We can plot the strength of the Balmer
lines as a function of temperature. Figure 9 is a graph of the ratio of atoms with electrons in level
2 to all other atoms. See Figure 9.
Figure 9.
For the graph in Figure 9, notice that temperature increases to the left. We expect to see
Hydrogen Balmer lines to reach peak intensity in stars having a surface temperature of about
10,000 K. The same kind of principle can be applied to other elements found in stars. At various
temperatures, some lines will be weak, others strong. See Figure 10.
We come to the conclusion that the differences in spectra from star to star are due to
differences in temperature. In fact, if all stars have the same chemical composition (same
percentage of each element), then differences in the spectra are caused by temperature only (for
stars of about the same size).
THE SPECTRAL SEQUENCE
From the above discussion, it should be possible to organize or classify the stars
according to their spectral change with temperature. Such a scheme has been worked out, and
letters have been assigned to the various classes. The sequence is O-B-A-F-G-K-M, which can be
remembered by the phrase: “Oh, be a fine girl, kiss me!” Further, each class is subdivided into
ten parts, so class A includes A0, A1, A2, ......, A9 and then F0.
The hottest stars are bluish-white O type, with temperatures of about 50,000 K. The
coldest are the red M type, with temperatures of about 3000 K. The sun is a yellow G2 star, with
a temperature of about 6000 K.
You will receive an objective prism spectrogram of a group of stars. A number of
spectra have been marked and with the aid of a set of standard spectra, you are to place the
stars in their proper spectral class. The results will be recorded on Exercise Sheet 2.
Questions:
1. What type of spectrum did the light bulb produce?
2. How many hydrogen lines did you see? Identify them by the jumps they made between energy
levels.
3. Why is a narrow slit used for most spectroscopes instead of an ellipse or half moon?.
4. What type of spectrum should the moon produce?
5. For each of the spectral classes, list the temperature and the color of a star that has that class.
6. Determine the spectral class and the color of the following stars: Sirius, Rigel, Aldebaran,
Capella, Regulus, Arcturus, Deneb, Vega, Procyon, Spica, Antares, and Betelgeuse.
Exercise Sheet 1
SPECTRA
V
Type
Source
Type
Source
Type
Source
Type
Source
Type
Source
Type
Source
Type
Source
Type
Source
R
Exercise Sheet 2
SPECTRAL CLASSIFICATION
1.
16.
.
2.
17.
.
3.
18.
.
4.
19.
.
5.
20.
.
6.
21.
.
7.
22.
.
8.
23.
.
9.
24.
.
10.
25.
.
11.
26.
.
12.
27.
.
13.
28.
.
14.
29.
.
15.
30.
.