April 3, 2007, jeb

Outline

• Absorption and Emission Lines
• Kirchhoff's Laws
• Astronomical Applications
• Particle Nature of Light: Photons
• Bohr Model of the Atom
• Spectral Analysis - Chemical ID
• The Message of Starlight

The Importance of Spectroscopy


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

Absorption and Emission Lines

 

The electromagnetic radiation received from an object in space is composed of many different wavelengths

• Spectrum of the star Procyon


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

Kirchhoff's Laws 


In 1859 German physicist Gustav Kirchhoff summarized the observed relationships among the three types of spectra (continuous, emission line, and absorption line)


• A luminous dense object produces a continuous spectrum


• A low-density, hot gas emits a series of bright emission lines


• a cool, thin gas absorbs certain wavelengths from a continuous spectrum, producing absorption lines

Astronomical Applications



By the late 19th century, spectroscopists were making many detailed measurements of the radiation from space, identifying the elements of the stars

Some unfamiliar lines appeared in the solar spectrum

It was assumed this must be due to an unknown element, which was called helium after the Greek word helios meaning Sun.

Nearly 30 years after it was discovered in the Sun's spectrum, helium was discovered on Earth in 1895.

Particle Nature of Light: Photons



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)

E = h f

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

Bohr Model of the Atom

 

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:
• helium and carbon

Molecules
A model of the carbon-monoxide (CO) molecule, as an example of the dynamics of molecules.


The spectra of molecules are quite different from those of the atom


• hydrogen spectra from molecular hydrogen (H₂) and atomic hydrogen

Spectral Analysis -> Chemical ID 



Each chemical element produces its own unique set of spectral lines.

These spectral lines serve as a "fingerprint"
- revealing the elements from which they are emitted, as well as the properties of the emitting object, such as temperature, speed, and density.


A spectrograph is an optical device that records a spectrum. 

Old fashioned spectrograph
• Light dispersed by prism 
• Deficiencies:
  • uneven spread of frequencies
  • uneven absorption of frequencies

Modern Device
• based on diffraction grating
• thousands of closely spaced parallel lines cut into glass
• as light passes through a grating, diffraction causes the different colors to be separated

Chemical ID

The emission spectra of some well known elements.

The visible spectrum of the Sun.

The emission and absorption lines of Sodium.



From the observed spectrum (analyzed with a spectrograph) we can determine the chemical elements involved.


Spectrum of the hot gases in a nearby star-forming region, the Omega Nebula (M17)

Spectroscopic Thermometer
Many properties of the spectra reveal temperature
• peak frequency or wavelength of continuous spectra
• lines
• line intensities
• line widths

Measurement of Radial Velocity
• Doppler effect will shift the spectral lines
  • Example of Doppler shift

Line Broadening
• Line broadening is caused by the environment in which the emission or absorption occurs
  • Example of the broadened line
  • Thermal broadening
  • Rotational broadening
  • Collisional broadening
  • Broadening by magnetic fields (Zeeman effect)

The Message of Starlight

Summary

• 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
• Atoms
  • positively charged heavy nucleus
  • orbited by electrons
  • explains how atoms can produce emission and absorption spectra
• Photons
• Molecules
• Spectral Analysis