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Atoms and Spectra
Atoms and Spectra
Relativity and Astrophysics
Lecture 11
Terry Herter
Outline
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Bohr Model of the Atom
Electronic Transitions
Hydrogen Atom
Other elements – Spectral signatures
21-cm Hydrogen line
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Monday:
Tuesday:
02:00 – 04:00 pm
11:00 – 12:00 am
If you can’t make these, set
up an appointment.
Prelim
Wednesday, Sept. 23
Closed book and notes, will cover material through last Friday
Should know
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My office hours are:
Spacetime interval, fundamental postulates of Special Relativity,
simultaneity and other issues raise by relativity
Will have both qualitative and quantitative questions
Lorentz Transformation equations will be provided (if needed)
You may want to bring a calculator
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Atoms and Spectra
Where does light come from?
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It had been known during the 19th century that
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If we picture an electron as in orbit around the
nucleus, it should radiate light
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Changing direction is acceleration!
But if the electron radiated, it would lose energy and soon
spiral into the nucleus.
The world would collapse instantly!
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Accelerated charges produce light, and hence emit energy
Fortunately it doesn’t.
What is wrong with this picture?
Enter Quantum Mechanics (QM)
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Quantum Mechanics was developed during the revolution
which occurred in physics from 1900 - 1930.
Both Special Relativity and General Relativity were
developed during this time.
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The Bohr Model of the Atom
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Niels Bohr 1913:
Formulated 3 rules regarding
atoms.
1. Electrons can only be in
discrete orbits.
2. A photon can be emitted or
absorbed by an atom only
when an electron jumps from
one orbit to another.
3. The photon energy (E) equals
the energy difference
between the orbits.
E = hf = hc/
since c = f, and f = c/.
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Atoms and Spectra
Quantum Numbers (Q.N.)
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An electron can reside
in one of many orbits.
n = number of orbit
= Principal Q.N.
n = 1 is the lowest
energy state.
If n > 1, then the atom
is “excited.”
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Electronic “Orbits” in an Atom
n= 3
2
1
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Atomic Energy Levels
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Energy Level Diagram
4
3
2
Emission
Absorption
Energy
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n=1
4
3
2
1
A schematic
representation of the
orbital energy levels.
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Atoms and Spectra
Electronic Transitions
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An electron transition occurs when a electron
moves between to orbits.
When absorption of a photon occurs, an
electron goes up, e.g. from n=1 to n=2.
Emission of a photon occurs when an
electron moves down, e.g. from n=2 to n=1.
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Spectra from Atoms
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A spectrum is the intensity of light seen from an
object at different wavelengths.
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e.g. done by spectroscopy with a prism.
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Individual atoms, like H, show spectral lines, i.e. For
H, these are the Balmer lines in the visible.
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For a “Conversational” lecture on spectral lines see
http://www.colorado.edu/physics/2000/quantumzone/
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Atoms and Spectra
The Spectrum of Hydrogen
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H has one electron => simplest spectrum.
Discrete emission and absorption lines
 Need a photon of the correct energy to move up a level.
Spectral lines occur in ultraviolet, visible, infrared, and radio.
Visible lines called Balmer lines.
H H
H
H
...
4000
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5000
 (A) 
6000
7000
Note the discrete “lines” where there is emission.
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Hydrogen Energy Level Diagram
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4
3
12.75 eV
12.09 eV
H
H
2
H
10.20 eV
For instance, the energy
difference between n = 2 and
n = 1 in H is 10.2 eV.
Balmer Lines
Ly
Ly
The energies in atoms are
usually expressed in electron
volts (eV).
1 eV = 1.6 x 10-19 J
Ly
Since E = hc/
Lyman Lines
n=1
0 eV
Ground State = Lowest Energy Level
Lyman Lines - Ultraviolet
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Ly:
Ly:
Ly:
…
Balmer Lines - Visible
n=2  1,  = 1216 A
n=3 1,  = 1026 A
n=4 1,  = 973 A
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H:
H:
H:
…
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n=3 2,  = 6563 A
n=4 2,  = 4861 A
n=5  2,  = 4341 A
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Atoms and Spectra
Hydrogen Balmer Spectrum: Revisited
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4
3
12.75 eV
12.09 eV
H
H
2
H
Balmer Lines - Visible
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10.20 eV
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Balmer Lines
n=1
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0 eV
H H
n=3 2,  = 6563 A
n=4 2,  = 4861 A
n=5  2,  = 4341 A
H:
H:
H:
…
Notes: (1) The energy levels get closer
together as the quantum numbers get larger.
(2) The greater the difference between the
quantum numbers, the larger the energy of
the photon emitted or absorbed.
H
H
...
4000
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6000
5000
 (A) 
7000
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The “Continuum”
Continuum for free electrons
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The ionization energy of hydrogen is
13.6 eV. To ionize an electron from
the ground state (n=1) of hydrogen
requires photons of energy 13.6 eV or
greater. =>  < 912 A
2
If h > 13.6 eV, electron
can leave the atom.
13.6 eV
The energy of an electron
in the continuum is not
quantized (it’s continuous).
n=1
Ground State = Lowest Energy Level
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An electron in the continuum has escaped from the
proton.
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This can happen if the Hydrogen atom absorbs a
photon with energy (h) greater than 13.6 eV.
And the hydrogen atom is “ionized.”
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Atoms and Spectra
Ionization and Ions
Neutral
HeI
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Once
Ionized
HeII
Twice
Ionized
HeIII
If a photon has enough energy, it can ionize an atom,
i.e. promote an electron into the continuum.
An atom becomes an ion when one or more electrons
have been removed.
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Adding an extra electron also creates an ion but this is much
more difficult and rare.
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Notation
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Astronomers use the following notation to indicate the
ionic state of an atom.
Suffix
I
II
III
etc.
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Example
HeI, OI
HeII, OII
HeIII, OIII
Notes (on ionization):
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Meaning
neutral
once ionized
twice ionized
It takes progressively more energy to remove successive
electrons from an atom.
That is, it is much harder to ionize HeII than HeI.
Note: You can not have HeIV !
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Atoms and Spectra
Spectra of several elements
White Light
Hydrogen
Helium
Lithium
Beryllium
Boron
Carbon
Nitrogen
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Spectra of several elements
White Light
Hydrogen
Sodium
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Solid materials have a continuous spectrum rather
than a discrete one (somewhat like white light).
This is different from individual atoms.
Examples:
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Tungsten filament light bulb - continuous
Fluorescent lamp - discrete
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Spectral Signatures:
Astronomy’s Rosetta Stone
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Spectral signature:
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Each ion has a unique set of spectral lines associated with it.
This is of fundamental importance to astronomy, allowing the
identification of elements clear across the galaxy and
universe.
With spectral signatures we can identify oxygen, carbon,
iron, etc.
In addition these signature provides information on:
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Chemical composition of the stars
Abundances of the elements
Physical conditions of the gases
 Densities and Temperatures
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Hydrogen 21-cm Radiation
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An important spectral line in astronomy for measuring
the gas between stars is the 21-cm line of Hydrogen.
This is in the radio part of the spectrum.
The n = 1 level (ground state) of H is actually “split”
into 2 levels separated by a very small energy.
This splitting is due to the fact that the electron and
proton have intrinsic spin, i.e. they behave like small
magnets.
When the North poles are aligned the energy is
higher than when they are not.
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Atoms and Spectra
21-cm Radiation (cont’d)
Poles Aligned
(higher energy state)
N
Poles Opposite
(lower energy state)
N
N
S
S
S
N
S
A 21-cm photon is emitted when poles go from being
aligned to opposite (a spin flip).
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Hydrogen Energy Level Diagram – 21 cm line
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4
3
12.75 eV
12.09 eV
H
2
H
H
Balmer Lines
Ly
Ly
Ly
10.20 eV
Not to scale – greatly
magnified so we can
see it here!
Lyman Lines
n=1
Ground State = Lowest Energy Level
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This emission from a small number of H-atoms is very weak, but
hydrogen is very plentiful in space.
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We see lots of this radiation from our Galaxy and others. (Line first
detected in 1951)
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Note – the lifetime of the 21-cm hydrogen upper state is about 107 yrs,
whereas the lifetime of the n = 2 state is 10-9 seconds!
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21-cm emission
E = 6x10-6 eV
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