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Radiation
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and
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Spectroscopy
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March 31, 2013, jeb
Outline
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We learn about the stars by studying the electromagnetic
radiation that they emit.
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Visible light is one particular type of electromagnetic radiation.
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The types of electromagnetic radiation are:
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radio
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infrared
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visible light
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ultraviolet
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X rays
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Gamma rays
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Electromagnetic radiation is a
wave with a wavelength and an amplitude.
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The frequency of a wave is related to its velocity
and wavelength through the formula
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wavelength x frequency = velocity |
- wavelength is measured in units of length
- meters
- millimeter (mm) = 0.001 m = 10-3 m
- micrometer (&mu m) = 0.000001 m = 10-6 m
- nanometer (nm) = 0.000000001 m = 10-9 m
- frequency is expressed in units of inverse time (1/sec)
- called Hertz (1 Hz = 1/sec)
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Since electromagnetic radiation (or waves) travel
at the speed of light
300,000 kilometers/second
- 1 kilometer(km) = 1000 m = 103 m
we have a relationship
between wavelength and frequency.
| wavelength x frequency = 300,000 km/sec |
- The
electromagnetic spectrum ranges from radio waves
at one extreme to gamma rays at the other extreme.
- Radiation is composed of "photons" (packets of electromagnetic radiation)
- the "photons" are "particles"
- Einstein was awarded the Nobel Prize for understanding that light (and electromagnetic radiation) is composed of these "particles" ("photons")
- the "photons" have energies related to the "color" or wavelength
- short wavelengths -> higher energies
- long wavelengths -> lower energies
- So light is both a wave, and particles.
- This property is known as "wave-particle duality," a basic element of the quantum theory of physics
- Visible light
can be split
into its components by a prism.
- the bending of light in going through the prism results from REFRACTION
- long wavelengths (red) are refracted less than short wavelengths (blue
and violet)
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The
entire
electromagnetic spectrum shows the frequencies and wavelengths of the
types of electromagnetic radiation.
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The atmosphere blocks much of the electromagnetic
radiation from space.
This is referred to as atmospheric "opacity".
There are "windows" of transparency
in the radio and visible parts of the spectrum.
Electromagnetic Radiation is generated by the
movement of charged particles
Nature's primary charged particles are:
- Proton (positive charge)
- Electron (negative charge)
Electromagnetic Waves
- Changing electric fields are accompanied by
magnetic fields
- The Earth has a
magnetic field
- The Earth's magnetic field is relatively static, not a wave
On Earth, we generate radio waves (a form of Electromagnetic Radiation)
by moving electrons along an antenna
A blackbody radiator is a perfect radiator of light
that absorbs and re-emits all radiation incident on it.
Its light output depends only on its temperature.
The sun and stars emit radiation like a blackbody following
the Blackbody
spectrum.
- This curve is known as the blackbody curve, or the Planck curve.
As an object (a blackbody) is heated, the radiation it
emits will always be described by the blackbody
spectrum for the temperature of the body, with the curve peaking to
higher and higher frequency.
Wien's Law
The maximum wavelength of radiation emitted by a blackbody
is inversely proportional to the temperature:
max wavelength ~ 1/Temperature
Stefan's Law
The total amount of energy emitted by a blackbody
is proportional to the 4th power of the temperature:
Wien's Law and Stefan's Law are evident in the changes
in the blackbody
spectrum with temperature.
Examples of the
blackbody spectra from cosmic objects:
(a.) a cool, invisible galactic gas cloud, Rho Ophiuchi (T=60 K)
(b.) a dim, young star in the Orion Nebula (T=600 K)
(c.) the Sun, with a surface temperature of 6000 K
(d.) a globular cluster of bright stars, Omega Centauri (T=60,000 K)
The farther away an object is the fainter it appears.
We refer to the amount of radiation for the star at our
location as the apparent brightness.
The apparent brightness of a star is inversely
proportional to the square of its distance:
apparent brightness ~ 1/(distance)2
This Law results from the spreading
of the energy in the radiation.
Electromagnetic radiation (of any type) always travels through diffuse
space at the same speed, the speed of light:
300,000 kilometers/second
The observed speed will not depend on relative motion.
However, the wavelength of the light does change with
relative motion.
Stars moving
away from us appear red-shifted and stars moving
toward us appear blue-shifted.
This can be illustrated
by considering the wave crests of the wave motion.
Spectroscopy allows scientists to infer the nature of matter at great
distances
- the chemical composition of distance stars can be revealed
- also, important information on the origin, evolution, and destiny of stars in
the universe has been discovered
The electromagnetic radiation received from an object in space
is composed of many different wavelengths
Splitting the incoming radiation into its component wavelengths is
a vital step in the process of analyzing the radiation to obtain
information about the distant object
A spectroscope is a device for splitting a beam of radiation
into its component frequencies and delivering them to a screen or detector
for detailed study
Simple
spectroscope
Source of continuous radiation gives rainbow, while hydrogen
gas emits spectral lines
Emission
spectra of some well-known elements.
Illustration
of formation of absorption lines
Comparison of the absorption
and emission lines of sodium
Dark absorption
lines of the Sun
In 1859 German physicist Gustav Kirchhoff summarized the observed relationships
among the three types of spectra (continuous, emission line, and absorption
line)
Light and other types of electromagnetic radiation
travels in packets of energy, named "photons"
An Electromagnetic wave is made of many photons
The energy of a photon is proportional to its frequency
(this is a key fact in explaining the spectral lines - see below)
where E is energy (in Joules)
h is Planck's constant
(h = 6.63 x 10 -34Joule seconds)
and f is frequency in 1/sec, or Hz.
Photon energies are very small
For example, for visible light (0.5 &mu m), f = 6 x 1014 /sec
So, E = 4 x 10-19 Joules
typical approximate energies
heat from 1 pound of wood = 30 MegaJoules = 3 x 107 Joules
kinetic energy carried by a flying housefly = 10-7 Joules
Energy of particle emitted by radioactive uranium nucleus = 6 x 10-13 Joules
kinetic energy carried by molecule in air = 4 x 10-21 Joules
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The structure of the atom explains the formation of spectral lines
This model was set forth by the Danish physicist Neils Bohr in 1912
The early
concept of the hydrogen atom pictured the electron in a well-defined
orbit circling a central proton. The orbits are said to be quantized,
since only certain orbits are possible, and therefore only certain
energy states of the atom are possible.
- the state of lowest energy - the ground state - is the "normal"
condition of the electron
- if an electron energy exceeds a maximum allowed energy in the
atom, it will leave the atom, and the atom will be ionized
- the electron can exist only in certain well defined energy states,
orbitals
The modern
view of the hydrogen atom thinks of the electron as a "cloud"
surrounding the proton in the nucleus, but only certain clouds are possible,
so the orbital energies are still quantized.
Photons (the quantum of electromagnetic radiation) can
be absorbed
or emitted by an atom, boosting the electron to an excited
state (on absorption) or bring the electron to a lower energy state (on
emission).
Since only certain energy states of the atom are allowed, only certain
wavelengths of photons are emitted or absorbed, explaining the spectral
lines.
More details of Hydrogen
More complex atoms:
Molecules
The spectra of molecules are quite different from those of the atom
- There are many forms of electromagnetic radiation
- visible light, radio, ultraviolet, etc.
- wave characterized by period, wavelength, and amplitude
- frequency is reciprocal of the period
- Moving electric charges generate radiation
- Radiation moves through empty space at the speed of light
- 300,000 kilometers per second
- Blackbody radiation laws based on temperature
- Inverse square law
- Doppler effect
- A spectroscope splits radiation into its component frequencies
- Many hot objects emit continuous spectrum
- A hot gas may produce an emission spectrum, with emission lines
- A continuous beam passing through a cool gas produces an absorption spectrum
- Kirchhoff's Laws
- luminous dense object -> continuous spectrum
- low-density, hot gas -> emission line spectrum
- cool, thin gas absorber -> absorption line spectrum
- Photons
- E = hf
- visible light, E = 4 x 10-19 Joules
- Atoms
- positively charged heavy nucleus
- orbited by electrons
- explains how atoms can produce emission and absorption spectra
- Molecules
