# The Origin and Nature of Light How is this Radiation Emitted

### The Origin and Nature of Light

All objects emit radiation, in the form of electromagnetic waves. This radiation is a direct result of the motions

(vibrations) of charged particles within the object.

The hotter an object is …

• the higher its temperature

• the higher its level of internal motions or vibrations

• the more light it radiates

### How is this Radiation Emitted?

• Natural objects emit radiation at a wide range of

wavelengths (or frequencies)

• The intensity (strength) of this emission is generally

different at different wavelengths

• This can be depicted by plotting the object’s spectrum,

which shows how its intensity varies with wavelength

– the plural of spectrum is spectra

### Observing Spectra

What do the spectra of astronomical objects look like?

To answer this question, astronomers use an instrument called a spectrograph (or spectrometer):

• The purpose of a spectrograph is to split incoming light

into its components at different wavelengths

• This can be done using a prism or diffraction grating

• When attached to a telescope, a spectrograph is usually

accompanied by a detector (e.g., a CCD) which is used

to record the spectrum

1

• Many objects emit radiation in a distinctive pattern

• Definition: a blackbody absorbs and re-emits all

• All blackbody spectra have the same characteristic shape

• Each blackbody has an intensity peak (maximum) at a

specific wavelength (or frequency)

• Different blackbodies have intensity peaks at different

wavelengths

• The actual wavelength of the peak can tell us about the

temperature of a blackbody

### The Kelvin Temperature Scale

When we measure temperatures in astronomy, we use the

Kelvin temperature scale, rather than Celsius.

• The lowest point on the Kelvin scale is called absolute

zero

– this is referred to as zero degrees Kelvin (0 K)

– this is the lowest temperature theoretically possible,

since all motion ceases at absolute zero

– 0 K ~ –273 degrees Celsius

2

### The Kelvin Temperature Scale

• A change in temperature of 1 K is equal to a change of

1 degree Celsius

– water freezes at 273 K (0 C)

– water boils at 373 K (100 C)

### Wien’s Law

The relationship between temperature (T) in Kelvins and the wavelength of maximum intensity (• max

) for any blackbody is given by Wien’s Law:

• • max

= 0.29

--------------;

T where • max is in cm

### Wien’s Law

• this tells us that • max is inversely proportional to T

– light from hot objects peaks at short wavelengths

– light from cool objects peaks at long wavelengths

• this explains why a fire’s embers become redder (longer

wavelength) as they cool off

3

### Applying Wien’s Law to the Sun

Wien’s Law has many useful applications in astronomy.

For example, we can use it to estimate the temperature of the Sun’s surface, which acts like a blackbody.

• Wien’s Law can be rearranged to give;

T = 0.29

-----------

• max

• The intensity of sunlight peaks at about 500 nm

– • max

= 500 nm

– there are 10 7 nm in 1 cm

### Applying Wien’s Law to the Sun

• so, • max

= 500 nm

------------------------

(10 7 nm/cm)

5 x 10 –5 cm

• T = (0.29 cm•K)/(5 x 10 –5 cm) = 5800 K

• This agrees well with other measurements of the Sun’s

surface temperature

### Surface Area and Luminosity

We can also relate the temperature of a blackbody to its surface area and luminosity …

• The rate at which energy is emitted from an object is

called its luminosity (L)

– luminosity is energy emitted per unit time

• The luminosity of a blackbody depends on its

temperature (T)

• The luminosity of a blackbody also depends on its

surface area (A)

– larger objects have greater surface areas

4

### Stefan’s Law

In 1879, Austrian physicist Josef Stefan performed some experiments, and showed how luminosity, surface area, and temperature are related for blackbodies:

• He found that luminosity is directly proportional to

surface area

– larger blackbodies are more luminous

• He found that luminosity is directly proportional to

temperature to the fourth power

– hotter blackbodies are much more luminous

• These findings are now known as Stefan’s Law:

L ~ AT 4

### Spectra

Wien’s Law and Stefan’s Law tells us about the overall properties of blackbodies. However, the detailed appearance of most spectra tells us much more…

• Most natural objects do not radiate as perfect blackbodies

• Instead, distinctive features can be seen in their spectra

• For example, in 1814, optician Joseph von Fraunhofer

noticed that the Sun’s spectra has many dark lines,

corresponding to reduced radiation at specific

wavelengths

### Spectral Lines

• These dark features are called spectral lines

• The specific wavelengths at which these features are

found are not random, but are typically seen in many

different spectra

• Chemists discovered that they could produce distinct

sets of spectral lines by heating different chemical

elements

e.g., hydrogen, oxygen, calcium

• We now know that each chemical element produces its

own unique set of spectral lines

5

### Types of Spectra

Observed spectra can be divided into three general types:

continuous spectra show a smooth variation of intensity

with wavelength, often roughly in the shape of a

blackbody

absorption line spectra are similar to continuous spectra,

but are missing radiation at certain specific wavelengths

– each of these features is called an absorption line

emission line spectra are lacking in radiation at most

wavelengths, with the observed radiation occurring only

at certain specific wavelengths

– each of these features is called an emission line

### Kirchhoff’s Laws

In 1859, German physicist Gustav Kirchhoff was able to describe how these different types of spectra arise. His findings are now known as Kirchhoff’s Laws:

1) A hot object or a hot, dense gas produces a continuous

spectrum

– no spectral lines are present

– this is a blackbody spectrum

2) A low-density hot gas produces an emission line

spectrum

### Kirchhoff’s Laws

3) A cool gas in front of a continuous source of light

produces an absorption line spectrum

6

### The Atom

Kirchhoff’s Laws describe the circumstances under which different spectra arise. However, they do not explain why.

For this, we must study the atom itself.

• It has long been suspected that all matter consists of a

common set of “building blocks”

• Since ancient times, these hypothetical units have been

referred to as atoms

• Early in the 20th century, scientists performed

experiments, and verified that this is indeed true

• Atoms were found to be made up of protons, neutrons,

and electrons

### The Structure of the Atom

Each chemical element has atoms with a unique mix of protons, neutrons, and electrons. However, all atoms have the same basic structure …

• Protons and neutrons are found in the innermost region

of the atom, called the nucleus

– the total number of protons and neutrons determines

which element it is

• Electrons orbit around the nucleus

– each electron is about 2000 times less massive than

a proton or neutron

• Atoms are primarily empty space!

### Relating Light and Atoms

• Each electron is located at a specific energy level

– the attraction between the electron (negative) and

the nucleus (positive) keeps the electron there

• Sometimes an electron will move spontaneously to a

lower energy level

– to compensate for this loss in energy, a photon of

light will be emitted from the atom

7

### Relating Light and Atoms

• Sometimes an atom will absorb a photon of light

– to compensate for this gain in energy, an electron

will move to a higher energy level

• A photon’s energy equals the energy lost or gained

this determines the wavelength of the photon

### Why Do We See Spectral Lines?

If electrons were allowed in any energy level, all spectra would be continuous. The distinct nature of spectral lines indicates that not all levels are allowed.

• In 1913, Danish physicist Niels Bohr devised an

explanation for the existence of spectral lines

– this is now known as the Bohr model of the atom

• He discovered that electrons can occupy only certain

specific energy levels (or orbits) within atoms

• This is due to the quantization of angular momentum

### Energy Levels

• An electron usually occupies the lowest energy level

that is available

– the lowest energy level of all is called the

ground state

– an electron can stay in the ground state for a long

time

• When a photon is absorbed, the electron moves to a

higher energy level

– this is called an excited state

– an excited state generally doesn’t last very long

– the electron will eventually move back down to a

lower energy level, such as the ground state

8

### Understanding Kirchhoff’s Laws

The Bohr model of the atom provides a natural explanation for Kirchhoff’s Laws:

1) A blackbody emits radiation at all wavelengths, giving

a continuous spectrum of light

2) A low-density hot gas emits photons at very specific

wavelengths when electrons move to lower allowed

energy levels

### Understanding Kirchhoff’s Laws

3) A cool gas in front of a continuous source of light

absorbs photons at very specific wavelengths as

electrons are bumped up to higher energy levels

– while these photons do eventually get

re-emitted, they are scattered in random

directions

### The Doppler Effect

While spectral lines occur at very specific wavelengths, we will generally observe them at somewhat different wavelengths, due to the Doppler effect …

• Light sources that are moving towards us have their

– this is called a blue-shift

• Light sources moving away from us have their radiation

shifted to longer wavelengths

– this is called a red-shift

• This effect was first explained by Christian Doppler in

1842, and is known as the Doppler effect

9

### The Strength of the Doppler Effect

We now know in which direction wavelengths are changed by the Doppler effect. However, it is just as important to determine the strength of this effect…

• The strength of the Doppler effect is directly proportional

to the relative speed of the wave source and the observer

– the faster the relative speed, the stronger the effect

• The strength of the Doppler effect is inversely proportional

to the wave speed

– the faster the wave speed, the smaller the effect

– this explains why the Doppler effect is more

noticeable for sound waves than light waves

### The Use of Spectra in Astronomy

• By identifying patterns of spectral lines associated with

different chemical elements, astronomers can determine

the chemical makeup of distant stars and galaxies

• The relative abundance of different ions yields a

measurement of a star’s surface temperature

• The width of spectral lines provides measures of rotation,

turbulence, and magnetic fields

• The Doppler shift of a spectrum provides a measure of

the speed of distant stars and galaxies, relative to us

10