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Lecture 8: The Hydrogen Atom
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| Astronomy 1101/1103 |
Terry Herter, Cornell University
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Lecture
Topics
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The Spectrum of Hydrogen Ionization of atoms Learn how these emissions and absorptions are useful to astronomy.
- Each element, ion, or molecule has a unique signature
- These signatures are the Rosetta Stone of Astronomy
21-cm Emission from Hydrogen |
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The Spectrum
of
Hydrogen
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Hydrogen has one electron, so it is the simplest of the elements in terms of its spectrum. Like other elements Hydrogen has discrete emission or absorption lines which result when the electron move between energy levels.
- Note, to move "up" a level, a photon of exactly the correct energy (or wavelength) is required.
The Hydrogen atom can emit and absorb light at discrete wavelengths in the ultraviolet, visible, infrared, and radio. In the visible the lines are called the Balmer lines. |
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Hydrogen
Balmer
Spectrum
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A schematic representation of the hydrogen Balmer spectrum is show below.
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Aside (In case you are interested)
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The Balmer series derives its name from Johann Jacob Balmer who (in 1885) found a series that fits wavelengths of the set of four emission lines (Ha, Hb, Hg, Hd) from hydrogen discovered by Anders Ångström. Ångström found the first three lines in 1862 and by 1871 had discovered a fourth line and measured the wavelengths to high accuracy. Balmer was not a spectroscopist or even an experimentalist. He was a high school teacher for girls in mathematics and interested in numerology. A friend suggested he work on the problem! In 1890 Johannes Robert Rydberg generalized Balmer's formula to cover other hydrogen spectral lines (and also introduced the concept of the wave number, which is the reciprical of the wavelength). Rydberg also applied the concept to akali metals and other elements. Of course, none of this explained where the series came from. This was left to Niels Bohr and quantum mechanics. |
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Hydrogen
Energy
Levels
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| The energy level diagram for hydrogen is given below. The various hydrogen spectral "series" are defined by their ending (bottom) level, e.g. for the Lyman series all electronic transitions go to level one, while for the Balmer series all electrons go to level two. 
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Aside (In case you are interested)
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| There are names for series where the electron goes to levels 3, 4, 5, or 6 that are respectively called the Paschen, Brackett, Pfund and Humphreys series. |
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Energy
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The energies in atoms are usually expressed in electron volts (eV).
For instance, the energy difference between n=2 and n=1 in H is 10.2 eV. Since E = hc/l, l = 1216 A
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Aside (In case you are interested)
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| The electron volt is defined as the work required to move an electron through a potential difference of 1 volt. In "electrostatics" the force on a charged particle is given by F = q E, where q = charge and E is the electric field strength. For a uniform electric field, V = E d where V is the electric potential (measured in volts) and d is the distance moved (note that the electric field has units of volts/meter). Then we have Energy = F d = q V. |
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Hydrogen
Spectral
Lines
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The spectral lines in the ultraviolet are call the Lyman series. In the visible these are called the Balmer series.
Series |
Designation |
Transition
(Levels) |
Wavelength |
Lyman (UV) |
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Lya |
2-1 |
1215.7 A |
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Lyb |
3-1 |
1025.7 A |
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Lyg |
4-1 |
972.53 A |
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... |
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limit |
infinity-1 |
911.5 A |
Balmer (visible) |
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Ha |
3-2 |
6562.8 A |
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Hb |
4-2 |
4861.3 A |
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Hg |
5-2 |
4340.5 A |
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... |
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limit |
infinity-2 |
3646.0 A |
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"Transition" indicates the change in energy level (designated by the principle quantum number) of the electron. For instance, 3 - 1 implies the electron falls from n = 3 to n = 1 in the atom. The term "limit" indicates the limit to reach the continuum (see below). If a photon has more energy than this threshold (shorter wavelength) it can ionize hydrogen. |
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Spectral
Line
Notes
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Key Features of the Atoms
The energy levels get closer together as the quantum numbers get larger.
The greater the difference between the quantum numbers, the larger the energy of the photon emitted or absorbed.
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The
Continuum
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If an electron is given enough energy (via a photon or by other means) it can escape the atom. The electron is then "unbound" and the quantization of energy levels disappears.
The continuum is shown schematically in the energy level diagram below, above the n = infinity principle quantum number. Photons with energy exceeding 13.6 eV can promote the electron into the continuum -- freeing the electron from the hydrogen atom.
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Ionization
and
Ions
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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. Though adding an extra electron also creates an ion, it is much more difficult and rare. Many atoms in space are ionized. Fortunately each ion has its own spectral signature. |
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Hydrogen
Ionization
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The ionization energy of hydrogen is 13.6 eV. Ionizing an electron from the ground state (n = 1) of hydrogen requires photons of energy 13.6 eV or greater.
=> l < 912 A
Ionized hydrogen is just a proton by itself! |
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Helium
Ions
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All elements can be ionized by removing one or more electrons. The example of helium is shown below. 
It takes progressively more energy to remove successive electrons from an atom.
- That is, it is much harder to ionize He II than He I.
Note: You can not have He IV! |
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Notation |
Astronomers use the following notation to indicate the ionic state of an atom.
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Suffix
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Meaning
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Examples
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I
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neutral
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He I, O I
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II
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once ionized
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He II, O II
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III
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twice ionized
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He III, O III
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IV
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three times ionized
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O IV, Ne IV
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Spectral
Signatures
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Spectral Signatures: Astronomy's Rosetta Stone
The set of spectral lines associated with a given ion are unique and are of fundamental importance to astronomy. We call this the "spectral signature" of an ion. Allows the identification of elements across the galaxy and universe.
- With spectral signatures we can identify oxygen, carbon, iron, etc.
In addition these signatures provide information on:
- Chemical composition of the stars
- Abundances of the elements
- Physical conditions of the gases such as densities and temperatures
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Emission
from
Solids
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Solid materials have a continuous spectrum rather than a discrete one. This is different from individual atoms. Examples:
- Tungsten filament light bulb - continuous
- Fluorescent lamp - discrete
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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.
The figure below illustrates the "spin flip" that cause the emission of a 21-cm photon.
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A 21-cm photon is emitted when poles go from being aligned to opposite (a spin flip).
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This emission from a small number of H-atoms is very weak, but hydrogen is very plentiful in space.
- So we see a lot of 21-cm radiation from our galaxy.
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