Astronomy 100

Lectures

Table of Contents

Astro 114

Lecture 9
Black Body Radiation, Atoms, and Spectral Lines

Outline

Black Body Radiation
The Inverse Square Law of Light
Atoms and Electron Energy Levels
Absorption and Emission Lines

Terms to Know

black body radiation
continuum
Wien's Law
Stefan-Boltzmann law
absolute zero
inverse square law (of light)
atom
nucleus
proton
neutron
electron
ionization
emission line
absorption line

1. Black Body Radiation and Temperature

Everything in the Universe emits radiation all the time. This includes stars, planets, and people. Hot things emit lots of high energy ("blue") radiation, while cooler things emit little radiation at all, most of it low energy ("red"). This is expressed in two laws:

Wien's Law tells you about the color
_peak = 2.9 / T, with T in K (degrees Kelvin) and in mm
Stefan-Boltzmann Law tells you about the total amount of radiation
E T⁴

For the Sun, _peak = 2.9/6000 = 4.8 x 10^-4 mm, or 480 nm, corresponding to yellow-green. This is almost exactly the same wavelength to which the human eye is most sensitive. Why?

This thermal radiation from matter is called "black body radiation." It is caused by electrons in the matter emitting photons as they vibrate -- faster when hot, slower when cool. At absolute zero temperature, atoms stop vibrating completely, and only then are totally dark.

Black body spectra are smooth, or continuous, curves; such spectra are therefore known as continuum spectra.

A great deal of the light we collect from distant stars, galaxies, and quasars is black body radiation.

2. The Inverse Square Law of Light

As you get farther and farther from luminous objects (stars, planets, city lights), they appear to get fainter very quickly. To be precise, the intensity I, or amount of light received per second per cm², of an object at distance r is I 1/r². This is called the inverse square law of light , somewhat analogous to the inverse square law of gravity.

3. Atoms and Electron Energy Levels

Atoms consist of two parts: nuclei (containing protons and neutrons), and electron clouds, with one or more electrons orbiting the nucleus.

The electrons are analogous to planets going around the Sun, except for one big difference: they are allowed in only a few special orbits . Each electron orbit corresponds to a different energy level. The orbit closest to the nucleus has the lowest energy level. If the electron gains more energy (from a collision with another atom, or by absorbing a photon), it jumps to an orbit farther away from the nucleus. If it gains a lot of energy, it jumps so far from the nucleus that it escapes completely. This is called ionization , and the leftover nucleus (which may still have other electrons) is an ion.

To jump from one energy level to a higher one by absorbing light, an electron needs just the right energy photon to come along. Later, the electron will at some point emit one or more photons, with either the same energy as the one it absorbed, or with the energy corresponding to a different orbital jump. At the same time, the electron will drop back down to a lower energy orbit.

Each element (hydrogen, helium, oxygen, etc.) has different, distinct energy levels, depending on the number of protons in the nucleus and the arrangement of the electron cloud.

4. Absorption and Emission Lines

Gas is made of atoms (often arranged into molecules). Shine a light through a cloud of gas, pass the light through a prism, and what do you see? Some colors have been removed, or absorbed from the light by the gas! This is due to electrons in the gas "stealing" energy from the passing light. The colors correspond to the allowed energy levels of the electrons for that particular element. Since each element has special energy levels, each element has its own pattern of absorption lines that makes up a unique "fingerprint" in the spectrum.

If you turn the light off, the gas may still glow -- with the same colors that were removed before! These are called emission lines.