Energy Levels and Atomic Spectra
A Physics MOSAIC
MIT Haystack Observatory RET 2010
Background Image from NASA
Observed Phenomena
Found on Wikipedia, User Jeff Kubina, Creative Commons
Image from NASA.gov
Blackbody Radiation
• A blackbody is a hypothetical object that is a
perfect emitter of all light and electromagnetic
radiation.
• The observed phenomena on the previous slide are
difficult to explain with classical physics. The failure
of the classical models to explain observed
behavior was called the ultraviolet catastrophe.
• A couple of (quantitative) relationships observed in
blackbody radiation
– I (total intensity) proportion to T4
– lmax (wavelength of peak intensity) proportional to 1/T
From webExhibits, www.webexhibits.org/causesofcolor. Creative Commons
Quantization of Energy
• The solution to the UV catastrophe was the
assertion (by Planck) that EM radiation comes
only in discrete packets of energy (called
photons), and the energy of these packets is
proportional to the frequency of the EM
radiation.
• This quantization was further verified by Einstein
(photoelectric effect), Compton (Compton shift),
and was used by Bohr in his model of the atom.
Important Equation
E  hf  hn
• The energy of a photon is equal to E = hf, where h is
Planck’s constant, h = 6.626 x 10-34 J·s.
• Frequency is sometimes abbreviated with f and
sometimes with the Greek letter n (“nu”).
• Because c = lf, and c is the speed of light in a vacuum =
299,792,458 m/s, the energy is also E = hc/l.
Relation Between Energy and
Frequency
• Thus, we can express a photon in terms of energy,
wavelength, or frequency and figure out any of
the others.
• That is,
– Energy is proportional to the frequency of the
radiation.
– Energy is indirectly proportional to the wavelength of
the radiation.
Bohr Model of the Atom
• You may recall that positive and negative charges
attract.
• The most energetically favorable position for the
positive nucleus and the negative electron is as
close together as possible.
• The lowest energy state for the electron is closest
to the nucleus and called the ground state.
• Energy levels further from the nucleus have lower
energies.
Bohr Model of the Atom
• The big idea of the Bohr Model is that only specific,
discrete orbits of electrons around the nucleus are
allowed by nature.
• This means that only some specific energies are
allowed. This is another way of saying the electron
energies are quantized.
• The energy level of an orbit is referred to with a
number, n, where n = 1 corresponds to the ground
state, n = 2 corresponds to the first excited state, etc.
• In general, the higher the n, the further the
electron’s orbit from the nucleus.
How Much Energy?
• The amount of energy associated with each
electron orbit depends on…
– the distance of the electron from the nucleus (energy
level) (STRONGLY)
– the number of protons in the nucleus (STRONGLY)
– the number of neutrons in the nucleus (WEAKLY)
– the number of additional electrons orbiting the atom
(STRONGLY)
– the mass of the nucleus (VERY WEAKLY)
Changing Energy Levels
• In order for an electron to go from one energy
level to another, a photon with an amount of
energy equal to the difference must be
released or absorbed.
• Because the amount of energy associated with
each orbit depends on the properties of the
atom, we can determine what atom produced
each photon by measuring its energy.
E  hf 
hc
l
 E final  Einitial
Changing Energy Levels in Bohr Model
= hf
From Wikipedia, GNU Free Documentation
(Very Famous) Hydrogen Transitions
From Wikipedia, original user Dorottya Szam, translated by OrangeDog, Creative Commons/GNU
Other Types of Energy
• Molecules will also have energy levels that are
quantized associated with their rotations and
oscillations. Rotations for a simple molecule are
shown below.
• In order to go from one energy state to another, a
photon must be absorbed or emitted.
Rotational Energy and Photons for
Molecules
Image from NASA
Production of Spectrum
• As Newton discovered, when white light is shined through a
prism, it is split into its constituent wavelengths, forming a
rainbow. (This is due to dispersion.)
• White light can also be split into a spectrum using a
diffraction grating.
• Because atoms will absorb or emit specific frequencies, the
rainbow produced is not always continuous.
Image from NASA
What Can The Spectrum Teach Us?
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•
•
•
•
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Type of Material
Chemical Composition
Temperature
Radial Velocity
Density
Presence of Magnetic Fields
Types of Spectra
Image from NASA
Kirchhoff’s (Other) Laws:
How to Determine Type of Material
• Kirchhoff describes the method of production of
each of the spectra shown on the previous slide.
– A luminous object (solid or dense gas) emits a
continuous spectrum.
– A rarefied luminous gas emits an emission (brightline) spectrum.
– A cool gas illuminated by a luminous object will
produce an absorption (dark-line) spectrum.
• Why?
• What type of spectrum will most stars produce?
Relationship Between Emission and
Absorption Spectra
• Remember that an emission spectrum is caused by
rarefied gas emitting the characteristic wavelengths
associated with the atoms in the gas.
• Remember also that an absorption spectrum is
caused by rarefied gas being illuminated by a
continuous source and “removing” the characteristic
wavelengths associated with the atoms in the gas.
• These two spectra, then, are sort of opposites;
depending on the point of view, one may see a dark
line spectrum or a bright line spectrum coming from
a cloud of dust.
Spectra From Space
Why do stars exhibit absorption
spectra, while supernova remnants
exhibit emission spectra?
Spectrum of CasA, from NASA
From Sloan Digital Sky Survey/Sky Server
Image from NASA (Composite of Hubble/Spitzer/Chandra)
Characteristic Spectra:
How to Determine Chemical Composition
• Recall that the energy associated with each atomic or molecular
transition depends on the properties of atom or molecule.
• This means that the presence of a spectral line of that energy (or
wavelength or frequency) indicates that it is present in the
sample being studied.
Hydrogen
Helium
Images from NASA
The Solar Spectrum
• We can analyze the spectrum from the sun and determine which
elements and molecules are present in great detail.
• This is how helium was discovered (and how it got its name).
• With careful measurement and modeling, relative abundances of
each atom or molecule can also be determined.
From NASA
Two Ways to Determine Temperature
• You have already seen that the overall profile of
the blackbody curve is characteristic of
temperature. This is one method to determine
the temperature of a sample that is
approximately a blackbody.
• Another way to determine the temperature of a
star (or other sample) uses the fact that the
relative strength of the lines from different
atoms depends on temperature in predictable
ways. For example, molecules only appear in
colder stars. Why?
Another Way to Determine
Temperature
From Sloan Digital Sky Survey
Spectral Classes
• For historical reasons, spectra from stars are classified
according to the strength of their hydrogen Balmer
absorption lines, with A having the strongest Balmer lines.
• Remember that Balmer lines come from transitions of
hydrogen’s electron from the second (n = 2) energy level.
• As seen in the previous slide, hydrogen lines are weak in
both very hot stars and very cool stars, but for different
reasons. Why?
• In order of temperature, the stellar classes are, from
hottest to coolest:
O
B
A
F
G
K
M
Historical Perspective
• Annie Jump Cannon was employed at Harvard to catalog stellar spectra in the
early 1900’s.
• She developed the classification system still used today, and worked with
several women (the “Harvard computers”) to classify many stars with their
eyes alone.
Library of Congress Image, Public Domain,
found via Wikipedia
Public Domain Images
Doppler Effect:
How to Determine Velocity
• As you may recall from studies of waves, when there is relative
velocity between the source and observer of a wave, there is a
change in perceived frequency.
• If the source and observer are moving apart, the frequency will
appear lower and the wavelength will appear longer.
• If the source and observer are moving towards each other, the
frequency will appear higher and the wavelength will appear
shorter.
Image from Wikipedia, Public Domain
Determining Relative, Radial Velocity
• The Doppler effect results in a change of perceived
frequency due to relative motion between the source and
observer.
• We know the frequency of an atom’s spectral line when it
is at rest very well.
• Therefore, we can determine the speed of an object along
our line of sight if we can measure a shift in the observed
frequency.
– Redshift: frequencies are lower than they would be at rest,
resulting from the source and observer moving apart from
each other.
– Blueshift: frequencies are higher than they would be at rest,
resulting from the source and observer moving towards each
other.
Redshift Example
Image from Wikipedia, Georg Wiora (Dr. Schorsch) created this image from the original Public Domain JPG.
Doppler Broadening:
How to Determine Density
• We just saw that objects moving towards us are
blueshifted and objects moving away from us are
redshifted.
• This is true at an atomic level, as well.
• In a very dense sample of atoms, the atoms will collide
with each other often, and some will end up moving away
from us and others will end up moving towards us,
resulting in some atoms producing frequencies slightly
lower than the rest value and other producing frequencies
slightly higher than the rest value.
• The effect of this is a broadening of the spectral line.
• A similar sort of broadening occurs when objects are at
high temperatures.
Doppler Broadening Example
©Swinburne University of Technology, used with permission
Spectra From Earth’s Atmosphere:
MOSAIC
• Earth’s troposphere and stratosphere contain
99% of the ozone in the atmosphere, but are very
dense.
• This means that the spectral lines coming from
these parts of the atmosphere are very broad.
• The ozone in the mesosphere is not very dense,
so it’s spectral line is more narrow.
• This is how the MOSAIC system is able to detect
it, effectively looking through the stratosphere
and troposphere.
MOSAIC spectrum
• This line corresponds to a rotational transition
of the ozone (O3) molecule, with a central
frequency of 11.0725 GHz.
Nighttime Measurements
Daytime Measurements
Zeeman Effect:
How to Measure a Magnetic Field
• Electrons have intrinsic angular momentum, and that
angular momentum creates a very small magnetic field.
• Therefore, when an electron is in the presence of another
(external) magnetic field, it has slightly more or less energy
depending on whether the magnetic fields are aligned (less
energy) or not aligned (more energy).
• This results in a splitting of the spectral line, since some
electrons making a particular transition will release or
absorb a photon with slightly more or less energy than in
the absence of the magnetic field.
Zeeman Effect Example
Image from NASA