and
Spectroscopy

## Outline

### Light and Electromagnetic Radiation Generation of Electromagnetic Radiation Blackbody Radiation Astronomical Applications Inverse Square Law Doppler Effect Importance of Spectroscopy Absorption and Emission Lines Kirchhoff's Laws Particle Nature of Light: Photons Bohr Model of the Atom Summary

• We learn about the stars by studying the electromagnetic radiation that they emit.

• Visible light is one particular type of electromagnetic radiation.

• The types of electromagnetic radiation are:
• infrared
• visible light
• ultraviolet
• X rays
• Gamma rays

• Electromagnetic radiation is a wave with a wavelength and an amplitude.

• The frequency of a wave is related to its velocity and wavelength through the formula

• wavelength x frequency = velocity

• wavelength is measured in units of length
• meters
• millimeter (mm) = 0.001 m = 10-3 m
• micrometer (μm) = 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)

• 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.

• 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
• like gamma rays
• 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)

• The entire electromagnetic spectrum shows the frequencies and wavelengths of the types of electromagnetic radiation.

• 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

On Earth, we generate radio waves (a form of Electromagnetic Radiation) by moving electrons along an antenna
Some Demonstrations

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.

# Astronomical Applications

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)

# Inverse Square Law

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.

# The Doppler Effect

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.

# 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

# 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)

# 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 μm), 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:
Molecules
The spectra of molecules are quite different from those of the atom

# Summary

• 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