University of Michigan - Department of Astronomy

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Version: short


Principles of Spectroscopy

But say with what degree of heat.
Talk Fahrenheit, talk Centigrade.
Use language we can comprehend.
Tell us what elements you blend.

Robert Frost "Choose Something Like a Star"

Overview

Introduction

The Electromagnetic Spectrum

A photon is a small bit of electromagnetic energy sent across space. Higher energy photons vibrate faster than lower energy photons, so they have a higher frequency and shorter wavelength.

The electromagnetic spectrum

In the visible part of the electromagnetic spectrum, the lowest energy, longest wavelength photons are red, and the highest energy shortest wavelength photons are blue (notes astronomers tend to lump indigo and violet in with "blue.") Because of this relationship between color and energy, astronomers tend to talk about higher energy photos as being "bluer" and lower energy photons as being "redder".

The visible spectrum

Electrons absorbing and emitting photonsPhotons can be emitted or absorbed by electrically charged particles-- usually an electron. An electron looses a bit of energy if it emits a photon, and gains a bit of energy if it absorbs a photon. Electrons that aren't bound to a particular atom are "loose", and their energy is related to their speed: a loose electron will speed up if it gains energy and slow down if it looses energy.

Black-body/Thermal Emission and the Continuous Spectrum

A dense object contains many loose electrons, which can emit photons of any energy as long as the photon has less energy than the electron started with. As an object heats up, the electrons gain more kinetic energy, so they become able to emit more energy as photons. The light produced by a hot, dense object is called thermal emission and it contains photons of all energies. The resulting "rainbow" is called a continuous spectrum. The hotter the object becomes,the brighter the continuous spectrum becomes. This is described by the Stefan-Boltzmann Law:

f = σT4

f is the flux, the light energy emitted per unit area (a measurement of the brightness.) As the emitting object is heated, the flux increases as the temperature, T (measured in Kelvin, K), to the fourth power. Imagine you place two identical pokers in a fire, but you pull one out after only a few minutes, and leave the other one in until it is twice as hot as the other. The hotter one will be 24 or sixteen times brighter than the cooler one. σ is called the Stefan-Boltzmann constant, and has the value 5.67x10-8J m-2 K-4 and ensures the two sides are actually equal.

As the object heats up and the electrons get more energy, the energy of the typical photon emitted also increases. This means that the continuous spectrum gradually shifts toward shorter wavelengths (higher energies) and therefore looks bluer. This is described by Wien's Law, which says the peak wavelength times the temperature is constant:

λpeak * T = 0.29 cm K

which means that as the temperature, T, of the emitting object increases, the wavelength λpeak where the intensity of the light is the greatest must decrease. Note the constant here requires the wavelength be in cm, and T in Kelvins. A very hot poker will glow with a bluer (shorter wavelength) light while a cooler poker will glow with a redder light. It is important to note that this is only the peak wavelength: all the other colors are also emitted, up to a maximum energy. The human eye tends to be more sensitive to the colors red and blue, so things hot enough to peak in the yellow-green portion of the spectrum tend to appear "white hot."

Continuous Thermal Emission -- Blackbody CurvesTogether, these two laws describe blackbody radiation or thermal radiation. Any hot, dense, opaque object will produce a continuous spectrum across all wavelengths, with the total energy and dominant color dependant on the temperature. If there are two identical dense opaque objects, but one is warmer than the other, it will also emit more light (brighter) and more higher energy light. This is illustrated at the right. The maximum intensity corresponds to λpeak and a higher intensity is also a higher flux.

Remember, Wien's law and the Stefan-Boltzmann Law apply only to continuous thermal emission, which you only get from dense, opaque objects, like most solids and liquids and dense gases. To be a blackbody, the object must have loose electrons than can absorb or emit any photon.

What about electrons that are part of an atom?

Thin Gas - Emission Line and Absorption Line Spectra

In the Bohr model of the atom, electrons orbit a nucleus of protons and neutrons. Each orbit has a different potential energy, similar to how planetary orbits correspond to particular gravitational potential energies. But according to quantum mechanics, the electrons can only orbit in certain places, which means the electrons can only have certain orbital energies -- these allowed energies are called energy levels.

Energy level schematic

Electrons prefer to stay in low energy levels, but if they absorb a photon or gain energy some other way, they can "jump up" to higher energy levels. If it gains energy by absorbing a photon, it has to have exactly the correct amount of energy -- it has to exactly match the energy difference between the energy levels. Therefore, the atom can only absorb light at a few specific energies, or colors. This is called line absorption. Line absorption occurs when a low-density gas is in front of a hotter, continuous spectrum source. The cooler, low-density gas acts to block the photons which have the right wavelengths, while the other photons travel through the gas unperturbed. This leads to a generally bright spectrum, with dark lines at specific wavelengths. The missing colors are called spectral absorption lines and result in an absorption line spectrum.

The energy-level jumping can also happen in reverse. The electron can "fall down" from a higher energy level to a lower one, emitting a photon with energy equal to the difference between the levels. This is called line emission, because photons are emitted. The spectrum produced is a set of bright emission lines, so it is called an emission line spectrum. This can only occur in a low density gas viewed on its own or in front of a cooler background (if a hot, dense object is in the background, we see line absorption instead of line emission).

Notice that these two processes only involve photons with particular energies that match its energy levels. Since each atom or molecule has a different set of energy levels, each atom or molecule also has a unique set of spectral lines.

 

Kirchoff's Laws

Let's summarize what are known as "Kirchoff's Laws."

  1. A hot, dense gas (or a solid or liquid) has free electrons and will emit a continuous spectrum, with the brightness and typical color described by the Stefan-Boltzmann and Wien Laws.
  2. A low-density gas along the line of sight to a hotter continuous radiation source will absorb photons of specific energies, leaving an absorption line spectrum.
  3. A low-density gas viewed alone or in front of a cool background will produce an emission line spectrum.

Kirchoff's Laws, Illustraited

Some Final Notes

There is no distinct transition between "dense" and "thin" gases. Very thin gasses will have very narrow emission and absorption lines, denser gases will have wider lines, and gasses dense enough to be opaque will act as black bodies. Solids and liquids can be black bodies and still transparent. For example, a window is transparent in visible light, but it emits a continuous spectrum with a peak wavelength in the infrared range.

One photon by itself can't tell us much, but by looking at all the photons together, astronomers can gain information about the temperature, density, and chemical composition of any object we can observe. This is done by looking at the spectrum of the light -- the number of photons (i.e. the brightness) at each wavelength.  The characteristics of the spectrum tell us information about the sources of light.

As photons travel outwards from the center of the sun, where the density and temperature are high enough to allow fusion, they are constantly absorbed and re-emitted by the atoms in the sun.  Eventually they get to the outer edge of the sun, called the photosphere, which is where the sun changes from being opaque to being transparent. The photosphere, then, is the layer where all the photons we see originate. The transparent region above the photosphere is called the atmosphere of the sun and has two major layers. The cooler, thin layer above the photosphere is the chromosphere. Above that is the incredibly hot and thin Corona, which can only be seen during an eclipse or by using a device that blocks the light from the photosphere and chromosphere.

In this activity, you'll look at a couple different light sources, determine the type of spectrum each source produces, and consider what sort of information astronomers can get from that type of source.

Activities

 


updated: 1/12/12 by SAM. Original JPB, JP, MML

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