Astronomy 161: An Introduction to Solar System Astronomy Prof. Richard Pogge, MTWThF 2:30

# Lecture 24: Matter & Light

## Key Ideas:

Temperature (Kelvin Scale)
• Measures internal energy content.
Kirchoff's Laws of Spectroscopy:
• A hot, dense object produces a continuous spectrum(blackbody spectrum).
• A hot, low-density gas produces an emission-line spectrum.
• A cool, dense gas produces an absorption-line spectrum.

## The Interaction of Light & Matter

Light & Matter can interact in a number of different ways:
• Matter can transmit light (glass, water).
• Matter can reflect light.
• Matter can gain energy by absorbing light.
• Matter can lose energy by emitting light.
The last two (absorption and emission) bear on the internal energy of the matter.

## Temperature

Temperature is a measurement of the internal energy content of an object.
Solids:
Higher temperature means higher average vibrational energy per atom or molecule.
Gases:
Higher temperature means more average kinetic energy (faster speeds) per atom or molecule.

## Absolute Temperature

At high temperatures:
Atoms & molecules move very rapidly.
At cooler temperatures:
Atoms & molecules move more slowly.
If it gets cold enough, all motion will cease. How cold is "cold enough"?
• Corresponds to a temperature of -273° Celsius (-459° F).
• Called "Absolute Zero".
Realistically, this represents an ultimate lower limit that is physically unobtainable (you can get close, but you never get exactly to it).

## Kelvin Temperature Scale

An absolute temperature system in which the temperature is directly proportional to the internal energy.
• Developed by British physicist William Thomson, First Lord Kelvin (19th century)
• Uses the Celsius degree, but a different zero temperature

Kelvin Absolute Temperature Scale (K):

• 0 K = Absolute Zero
• 273 K = pure water freezes (0° Celsius)
• 373 K = pure water boils (100° C)
The principal advantage of the Kelvin scale compared to the more familiar Celsius and Fahrenheit scales is that temperature measured in Kelvins is directly proportional to the amount of internal energy in an object. If you double the internal energy, you double the temperature in Kelvins. This is why the Kelvin scale is said to measure absolute temperature. Both the Celsius and Fahrenheit systems are difficult to use for relating the absolute energy content of objects because they are tied arbitrarily to the freezing and boiling points of water on the surface of the Earth.

We will primarily use the Kelvin scale in this course (and Astronomy 162), but will occasionally use Celsius (with Fahrenheit equivalents) where we are talking about planetary temperatures.

## What is a Spectrum?

A spectrum is the distribution of photon energies coming from a light source:
• How many photons of each energy are emitted by the light source?

Spectra are observed by passing light through a spectrograph:

• Breaks the light into its component wavelengths and spreads them apart (dispersion).
• Uses either prisms or diffraction gratings.

## Kirchoff's Laws of Spectroscopy

1. A hot solid or hot, dense gas produces a continuous spectrum.
2. A hot, low-density gas produces an emission-line spectrum.
3. A continuous spectrum source viewed through a cool, low-density gas produces an absorption-line spectrum.

German physicist Gustav Kirchoff (1824-1887) formulated these laws empirically during the mid-19th century. While they adequately describe the different kinds of spectra that are observed, they do not explain why these spectra appear in these circumstances. A physical explanation had to wait until the 20th century for the development of quantum mechanics and modern atomic theory.

A Blackbody is an object that absorbs all light.
• Absorbs at all wavelengths.

As it absorbs light, it heats up.

• Characterized by its Temperature.

It is also the perfect radiator:

• Emits at all wavelengths (continuous spectrum)
• Energy emitted depends strongly on the Temperature.
• Peak wavelength also depends on Temperature.
Blackbody Spectra for three Temperatures: 10000K, 8000K, and 6000K.

## Stefan-Boltzmann Law

Energy emitted per second per area by a blackbody with Temperature (T):
s is Boltzmann's constant (a number).

In Words:

"Hotter objects are Brighter at All Wavelengths"
Note the relative brightnesses at each wavelength for the three different-temperature blackbodies above.

## Wien's Law

Relates peak wavelength and Temperature:
In Words:
• "Hotter objects are BLUER"
• "Cooler objects are REDDER"
Note the wavelength of peak brightness for the three different-temperature blackbodies above.

## Examples

Person: Body Temperature = 310 K

Sun: surface temperature = 5770 K

## Emission-Line Spectrum

A hot, low-density gas, in which the atoms are relatively isolated from each other, will emit an emission-line spectrum:

• Only emits light at particular wavelengths, giving the appearance of bright, discrete emission lines.
• There is no light emitted between the emission lines.

19th chemists century noticed that each element, heated into an incandescent gas in a flame, emitted unique emission lines.

• Mapped out the emission-line spectra of known atoms and molecules.
• Used this as a tool to identify the composition of unknown compounds.
• They did not, however, understand how it worked.

## Absorption-Line Spectrum

Light from a continuous spectrum through a vessel containing a cooler gas shows a continuous spectrum from the lamp crossed by of dark absorption lines at particular wavelengths.:

• The wavelengths of the absorption lines correspond exactly to the wavelengths of emission lines seen when the gas is hot!
• Light is being absorbed by the atoms in the gas.

## Why does it work?

Why does each element have a characteristic line spectrum?