Credit/Permission: For text, © David Jeffery. For figures etc., as specified with the figure etc. / Only for reading and use by the instructors and students of the UNLV astronomy laboratory course.
This is a lab exercise without observations.
But for reference, see Sky Map: Current Time Las Vegas and weather.
Sections
We touch on the following topics:
Some of the
Tasks can be completed ahead of the lab period.
Doing some of them ahead of lab period would be helpful.
However, you can print a copy ahead of time if you like especially if
want to do some parts ahead of time.
You might have to compensate for updates in this case.
The Lab Exercise itself is NOT printed in the lab ever.
That would be killing forests
and the Lab Exercise is designed to be an active web document.
General remarks about quiz prep are given at
Quiz Preparation: General Instructions.
For DavidJ's lab sections, the quiz prep is doing all the items listed here and self-testing with the
Prep Quizzes and Prep Quiz Keys
if they exist.
However to complement and/or supplement the reading, you should at least
read the intro of a sample of the articles
linked
to the following keywords etc.
so that you can define and/or understand some keywords etc. at the level of our class.
A further list of keywords which you are NOT required to look at---but it would be useful to do so---is:
To prolong the lifetimes of these
spectral tubes,
the manual recommends that they
be cycled on and off in 30 second periods (30 s on and 30 s off).
According to the manual,
the helium spectral tube
and neon spectral tube
can be run continuously longer than other
spectral tubes, but
it is probably best to stick to the 30 second periods for simplicity in instructions
to the students.
The spectroscope is explicated
in the figure below
(local link /
general link: spectroscope.html)
and the
diffraction grating
in the figure below that
(local link /
general link: diffraction_grating.html).
Read the over the two figures. Have you done so?
Y / N
In this task,
we study the continuous spectrum
of the incandescent light bulb.
The
continuous spectrum
is to good approximation a blackbody spectrum
which we studied theoretically in
Lab 8: Stars: Blackbody Spectra.
For an explication of blackbody spectra,
see Blackbody file:
blackbody_spectra.html.
Sub Tasks:
In this task,
we consider further the
continuous spectrum
of the
incandescent light bulb.
Recall,
continuous spectrum
is to good approximation a blackbody spectrum
which we studied theoretically in
Lab 8: Stars: Blackbody Spectra.
For an explication of blackbody spectra,
see Blackbody file:
blackbody_spectra.html.
Sub Tasks:
Answer:
End of Task
In this task, we study the
line spectra
produced by a dilute gases
in spectral tubes.
A line spectrum consists of
a discrete set of spectral lines
that are sort of the images of the
slit aperture
of the spectroscope.
We discuss line spectrum theoretically
below in section
Quantized States and
section Grotrian Diagrams and Atomic Transitions.
Sub Tasks:
You should be cautious with the
spectral tubes
and absolutely do NOT touch exposed glass: it can be HOT.
Also the voltage of
the spectral tubes is very high, and
so be very cautious about anything that might be an
electrical conducting surface.
Except for the sodium spectral tube,
the spectral tubes
should be cycled on and off in 30 second periods (30 s on and 30 s off).
This just helps extend their lifetimes.
The only molecule currently available is
carbon dioxide (CO_2).
The other gases are
noble gases
(which ordinarily do NOT form
molecules)
or hydrogen (H)
(which at ordinary room
temperature
would be molecular hydrogen (H_2),
but in the spectral tube
is sufficiently hot to be
atomic hydrogen (H_I) gas).
Answer: Y/N
The formation of stellar spectra
is explicated in the two figures below
(local link /
general link: spectrum_formation.html;
local link /
general link: spectrum_formation_stellar.html).
Read the over the two figures. Have you done so?
Y / N
As simplified synthetic
solar spectrum
(in image representation) with the
Fraunhofer lines is displayed in the
figure below
(local link /
general link: fraunhofer_lines.html).
The Fraunhofer lines are the most
prominent and first discovered solar
absorption lines.
Since they were discovered before they could be identified with
atoms
and
molecules, they were designated by letters.
The letters have stuck.
Sub Tasks:
Note that classification of stars by
stellar spectra
(more specifically their
absorption line spectra)
is the best empirical way (i.e., way based on observation) of classifying
stars.
The stellar spectrum
is a direct observable and contains a wealth of information about
a star.
The spectral types
are discussed in the context of the
HR diagram
in the figure below
(local link /
general link: star_hr_lum.html).
Sub Tasks:
Have you read it?
Y / N
Sub Tasks:
The CLASSIFICATION WINDOW has three graphs of
Intensity versus Wavelength
with wavelength in
angstroms (Å).
Note 1 nm = 10 Å and the
visible band fiducial range = 4000--7000 Å.
A list of standard
main-sequence stars
will appear at the right of the CLASSIFICATION WINDOW.
The list is NOT complete: NOT all
spectral subtypes
are shown:
usually only
spectral subtype
0 and 5.
You will have to
interpolate as best you can
to classify the
spectral subtypes
NOT listed.
Maybe with some imagination, classification to
spectral subtypes
1--3 and 6--9 is possible.
The sprectra of highlighted standard star on the list and the one below it are
displayed, respectively, in the top and bottom graphs.
The spectra are
absorption line spectra.
The troughs are the absorptions in the intensity representation of a sprectrum.
Scroll through the available standard star spectra by clicking on the standard star name:
O star
to M star.
Things you can do with the
CLASSIFICATION WINDOW (CW) and SPECTRAL LINE TABLE (SLT):
It's spectrum will be shown on the middle graph.
Go File/Display/Show Difference.
The top graph will show the standard star spectrum and
the bottom graph shows the difference spectrum: i.e.,
top spectrum minus the middle spectrum.
Now scroll up and down the standard star list.
When the difference is as flat as possible as judged by eye,
you have the best fit of a standard star to HD 124320.
What if you have two equally good fits.
These must be for adjacent standard stars?
Then HD 124320 must lie between those two standard stars in
spectral type
In fact, HD 124320 gets about an equally good fit from the A1 star and the A5 star.
So one interpolates to find the
subtype.
It seems HD 124320 is a bit closer to A1 than A5, and so our estimate is A2.
We enter A2 for HD 124320 in
Table: Best Fit Spectral Types below.
In this task, you answer questions about the
catalog-identified star
you classified
in Table: Best Fit Spectral Types
in Task 8.
Recall that all these stars
are main-sequence stars.
Sub Tasks:
In this and the following sections, we delve a bit into the details
of energy levels
and atomic transitions.
Atoms,
molecules,
and ions
(which are
electrically charged
atoms
and
molecules)
have quantized internal energy states
(which are usually called energy levels) for their bound
electrons.
The states actually have many
characterizing parameters, but the
energy
that they have (relative to some convenient
zero-point energy) is usually key one,
and hence the common name energy levels.
This is dictated by quantum mechanics---which is
the best verified of all physics theories.
There are mistakes in calculations and in
experiments, but
no anomally has ever resisted attack.
It would cause an astonishing
paradigm shift if there
ever was a truly wrong prediction by
quantum mechanics.
Alas, quantum mechanics is very
hard to apply, and so there are vast realms where we CANNOT extract an answer from it.
But there are lots of realms where can get answers, at least approximate ones.
Why are the
energy levels quantized.
Well in quantum mechanics, particles
have a wave nature as well as
particle nature.
This fact has the name the wave-particle duality.
The wave function
of a particle (given the conventional symbol Ψ which is the
Greek letter
Psi vocalized "si")
determines the distribution of positions the particle has and everything else one can know about the particle.
So the particle is spread out in space.
Just accept it.
This is true at the macroscopic level too.
For example, consider
standing waves on a
vibrating string
as illustrated in the animation
in the figure below
(local link /
general link: standing_waves.html).
Concert A
(frequency 440 Hz)
is the general muscial tuning
standard for musical pitch.
Say you had a 1-meter vibrating string
emitting concert A
sound
as its
fundamental.
What is the phase velocity
of the vibrating string waves?
Note you have to give a numerical value and its
unit.
HINT: You will have to have read over
section Quantized States to this point---as you should
have---and you
will have to do a little
algebra on the
frequency
formula in the figure above
(local link
general link: standing_waves.html)
to get a formula with v_phase = something
in algebraic symbols.
Note also that units
are treated just like
algebraic symbols since they are
algebraic symbols.
The classic example of a quantized
quantum mechanical system is the
quantum harmonic oscillator.
A macroscopic classical physics
harmonic oscillator is illustrated for fun
in the animation in the figure below
(local link /
general link: harmonic_oscillator.html.
The figure below
(loca link /
general link: qm_harmonic_oscillator.html)
describes the
quantum harmonic oscillator.
Say a quantum harmonic oscillator
does a transition between the n=7 and the n=3
energy levels and emits
a photon (a particle of
light) that carries away the lost
energy.
In units of ħω, how much
energy does the
photon have?
HINT: You will have to use the
formula shown in the figure above
(loca link /
general link: qm_harmonic_oscillator.html).
The figure below
(local link /
general link: atom_diagram_abstract.html)
gives an abstract diagram of
an atom undergoing an
atomic transition
(i.e., a transition between energy levels).
They look like fuzzy little balls.
And there is a good reason for this.
They are fuzzy little balls.
They just don't have sharp edges.
As a result images of
atoms do NOT
tell a lot about the states of
atoms: i.e.,
their energy level structure.
So people often use standard abstract diagrams
to understand atomic
energy level structure.
The most standard are Grotrian diagrams
which we take up below in
section Grotrian Diagrams.
In the figure below
(local link /
general link: atom_gold.html)
is an image of gold---you see
fuzzy little balls.
The vertical axis represents
energy.
All the other characterizing parameters
(usually called quantum numbers)
are absorbed into columns.
The energy levels
are represented by points or horizontal line segments in the appropriate column.
Possible
atomic transitions
are represented by oblique lines---except usually in the important cases
of atomic hydrogen
or hydrogenic atoms.
Atomic transitions
within columns are usually
forbidden transition---they can
happen, but NOT by strong process---the strong process is forbidden---weaker processes
may occur.
The energy units used for
Grotrian diagram are
either or both of the
electron-volt (eV) = 1.6021766208(98)*10**(-19) J
(the natural unit)
and the
inverse centimeter (cm**(-1))
(a rather pointless unit).
The electron-volt
(equal to 1.602176565(35)*10**(-19)
joules) is
a microscopic unit of energy.
It is the
natural unit
for
energy levels
since
atomic transitions
of outer
electrons
are typically
1 eV to within 2 orders of magnitude.
We examine
Grotrian diagrams
and atomic transitions
in the subsections below.
The hydrogen
is the most abundant
element
in the
observable universe.
So it's important.
The Grotrian diagram
for neutral hydrogen (H I)
is shown in the figure below
(local link /
grotrian_01_00_H_I.html).
Atomic transitions
(AKA lines)
that emit to absorb photons are often
called
called atomic lines or
just lines---for reasons
we'll get to below.
The strength of a
line
is vaguely speaking its effect on the ambient
electromagnetic radiation field.
The effect could be either emission or absorption from the
ambient
electromagnetic radiation field.
How strong a line
is depends on many things---too many to go into here in glorious detail.
But a key thing is how low in
energy
the
energy levels
that form the upper and lower states of the
line.
The lower the energy of
these energy levels,
the stronger the line tends to be.
This is because the lower the energy
of the energy level,
the more atoms
are occupying that energy level usually.
The
ground-state
energy level
is usually the overwhelmling most occupied
energy level.
The lower the temperature,
the more the lower
excited-state
energy level occupation.
The excited-state
energy levels are those
with energy above the
ground-state
energy level.
In fact, at most temperatures
the occupation decreases rapidly as one
as goes up in energy
of energy level.
Forbidden lines
do actually occur
(i.e., these atomic transitions
happen), but the main process is forbidden, and so the
forbidden lines tend to be weak.
However, forbidden lines
connecting to the ground state
tend to be the strongest forbidden lines.
They tend to be very important when only
forbidden lines connect to the
ground state from the lowest
energy levels.
Those energy levels
tend to have high occupation whereas
the allowed atomic lines
come from low-occupation higher
energy
energy levels.
So the allowed atomic lines
can become weak compared to the
forbidden lines in this case.
Sub Tasks:
Visible light
is the range of
electromagnetic radiation (EMR)
that the human eye is sensitive to.
The fiducial range for visible light in
wavelength is
0.4--0.7 μm = 400--700 nm = 4000--7000 Å.
In fact, the actual range depends on conditions and individual characteristics.
Under ideal conditions for those with very sensitive
human vision,
we have
extreme human
visible range ≅ 310--1050 nm.
Below we show a schematic diagram
(local link /
general link:
human_luminosity_function.html)
of the average human eye
luminosity function.
What do you estimate to be the strongest and weakest
atomic hydrogen lines
in emission in the
visible band (fiducial range 0.4--0.7 μm)
extending the fiducial range a bit?
HINT: Recall
Task 6,
subsection Strong Atomic Transitions,
and the neutral hydrogen
Grotrian diagram shown in the figure above
(local link /
grotrian_01_00_H_I.html).
_____________________ , _____________________
The de Broglie relation
for calculating
photon energy
from photon
wavelength is
What is the photon energy range
visible light (fiducial range 0.4--0.7 μm)
using the fiducial range.
Helium is the 2nd most abundant
element
in the
observable universe.
So it's important.
The Grotrian diagram
for neutral helium (He I)
is shown in the figure below
(local link /
grotrian_02_00_He_I.html).
The lower energy level
of the He I 5876 Å line
is the upper energy level
of the _____________________ line which is in the
________________ wavelength band.
HINT: You need to consult the
Grotrian diagram of
He I above
(local link /
grotrian_02_00_He_I.html).
Calcium
is an abundant
metal
in the
observable universe.
Just accept it.
In stars,
absorption lines
arising from the ground state
of singly ionized calcium (Ca II)
are particularly important.
The Grotrian diagram
for singly ionized calcium (Ca II)
is shown in the figure below
(local link /
grotrian_20_01_Ca_II.html).
Atomic lines that arise from the
ground state of their parent
atom are usually very strong because the
ground state is usually overwhelming the
most occupied of any energy level.
Now the
Ca II H & K lines
and the Ca II 7291 Å and
7323 Å lines
both arise from the ground state
of Ca II.
However, the Ca II H & K lines are
usually much stronger. EXPLAIN why with the short answer in sentence form.
HINT:
You should read over subsection
Strong Atomic Transitions
and
Grotrian diagram of
Ca II
(local link /
general link: grotrian_20_01_Ca_II.html).
The strengths of atomic lines
in astrophysical spectra depends among many other things on the
abundances of the
elements that give rise to them.
Actually, the
cosmic composition
is well known in certain respects.
The figure below
(local link /
general link: solar_composition.html)
explicates the situation.
Above about what
atomic number Z would you expect
the elements
to have relatively weak
spectral lines in
astrophysical spectra? Why?
HINT: You should consult subsection
The Cosmic Composition
and the
solar composition figure above
(local link /
general link: solar_composition.html)
and note where there is a general decline to a definite lower abundance behavior
(excluding just the small Z region 1--6: i.e.,
hydrogen (H) to
carbon (C)).
Note that the expectation of weaker
spectral lines for high enough Z
is just a general one.
Intrinsic properties of some atoms for
the high Z region
may make some of their spectral lines
very strong in some circumstances.
Do the preparation required by your lab
instructor.
Keywords:
absorption line spectrum,
atomic spectral lines,
Clea Stellar Spectra software,
color index
(AKA color),
diffraction,
diffraction grating,
diffraction grating formula,
electromagnetic spectrum,
emission line spectrum,
Fraunhofer lines,
gas-discharge lamp
(e.g., sodium-vapor lamp),
gooseneck lamp,
Grotrian diagram,
Hertzsprung-Russell diagram,
hydrogen Balmer lines,
incandescent light bulb,
Kirchhoff's 3 laws of spectroscopy,
light,
luminosity,
main sequence,
Moore & Merrill 1968, Partial Grotrian Diagrams,
Na D lines,
OBAFGKM stellar classification,
photopic vision,
photosphere,
objective-prism spectroscopy,
prism,
Schmidt camera
(AKA Schmidt telescope),
scotopic vision,
spectral lines,
spectral tube
(Geissler tube or sometimes
gas-filled tube),
spectral types,
spectroscope (AKA spectrometer),
spectroscopy,
stellar classification,
visible light,
white light,
Wien's law,
etc.
Hm.
We should currently have:
Task Master:
EOF
In this section, we will do
spectroscopy
on hot substances and study their spectra.
___________________________________________________________________________
| | | |
400 500 600 700
There should be set out some subset of the following
spectral tubes:
___________________________________________________________________________
| | | |
400 500 600 700
___________________________________________________________________________
| | | |
400 500 600 700
___________________________________________________________________________
| | | |
400 500 600 700
___________________________________________________________________________
| | | |
400 500 600 700
_________________________________________________
Table: An Incomplete List of Fraunhofer Lines
_________________________________________________
Fraunhofer line Species Wavelengths
designation (nm)
_________________________________________________
A O_2 759.370
B
C
D_1
D_2
D_3 or d
F
G'
G_1
G_2
h
H
K
_________________________________________________
In this section, we consider
spectral types
and classify
stellar spectra according to those
spectral types.
Star Spectral Type Photospheric
/Luminosity Temperature
Class (K)
Alcyone B7III 12753(147)
Aldebaran
Barnard's Star
Betelgeuse
Capella
Mizar A2V 9000(200)
Polaris
Procyon
Rigel
Sirius
Sun
61 Cygni
Note: Mizar is
a tricky case since it consists of
a double star with component
"stars"
Mizar A
and
Mizar B
and each component "star" is a
spectroscopic binary:
Mizar A
consisting of
Mizar Aa
and Mizar Ab;
Mizar B
consisting of
Mizar Ba
and Mizar Bb.
Mizar A
is much brighter than
Mizar B
and both its
binary companions are
A2V stars with
photospheric temperature
T = 9000(200) K.
_______________________________
Table: Best Fit Spectral Types
_______________________________
Star Spectral Type
_______________________________
HD 124320 A2
HD 37767
HD 35619
HD 23733
O 1015
HD 24189
HD 107399
HD 240334
HD 17647
BD +63 137
HD 66171
HZ 948
HD 35215
Feige 40
Feige 41
HD 6111
HD 23863
HD 221741
HD 242936
HD 5351
SAO 81292
HD 27685
HD 21619
HD 23511
HD 158659
_______________________________
In the above sections, we have made use of the concepts of
quantized energy levels
and atomic transitions.
Quantum mechanics
is never wrong.
"Quantized" means that the energy levels form
a discrete set like integers and
NOT a continuum like
real numbers.
In quantum mechanics
at particle is NOT all at one place, but is in a
continuum
superposition of positions.
Now having a wave nature naturally
leads to quantization if the system/particle is bound---i.e., the particle
CANNOT travel to infinity.
Actually, electrons
in atoms are usually NOT much like
quantum harmonic oscillators,
but many quantum mechanical systems
approximate
quantum harmonic oscillators.
The standard abstract diagrams for atoms
are Grotrian diagrams.
The hydrogen atom
and hydrogenic atoms
are special cases because they have
many energy levels of the
same energy
(i.e.,
degenerate energy levels).
The
degenerate energy levels
are just shown as one combined level and the set of combined levels
just makes one column.
The atomic transitions
are now between the combined levels and are represented by vertical lines.
The zero energy
of Grotrian diagram is
conventionally
chosen to be the ground state
energy---which
in a fundamental sense is NOT zero, but
a non-zero zero-point energy.
I think this is because
accurate values for the
zero-point energy may be
hard to obtain and
knowing what those values are is often NOT needed.
The occupation of
energy levels is determined
often by temperature.
One conclusion of the above discussion is that
atomic transitions
with the lower energy level
being the ground state
are often very strong.
Unless those
atomic transitions
are forbidden lines.
What is the color
of near ultraviolet (UV) 300--400 nm)
and near infrared (IR) 700--1400 nm?
The source doesn't say, but I suspect just
violet and
red, respectively
(see Wikipedia: Light:
Electromagnetic spectrum and visible light).
E = hc/λ = (1.23984193 eV-μm)/(λ_μm) ,
where h is the Planck constant,
c is the vacuum light speed,
λ is wavelength,
and
λ_μm is wavelength in microns.
"Metal" is used here in
its astro-jargon sense
which means any element NOT
hydrogen or
helium.
Calcium is also an important ingredient
in many contexts including
life as we know it.
This section is only
for remote instruction.
Goodnight all.
Post mortem comments that may often apply specifically to
Lab 10: Stellar Spectra: