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Radiation and Radiation and SpectraSpectra

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Lite Question

What does it mean to see something?

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Astronomy and Light (1)Most of the celestial objects studied in astronomy are completely beyond human reach The astronomers gain information about them almost exclusively through the light and other kinds of radiation received from them

Light is the most familiar form of radiation, which is a general term for (electromagnetic) waves

Because of this fact, astronomers have devised many techniques to decode as much as possible the information that is encoded in the often very faint rays of light from celestial objects

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Astronomy and Light (2)If this “cosmic code” can be deciphered, we can learn an enormous amount about astronomical objects (their composition, motion, temperature, and much more) without having to leave Earth or its immediate environment! To uncover such information, astronomers must be able to analyze the light they receive

One of astronomers’ most powerful tools in analyzing light is spectroscopy

This is a technique of dispersing (spreading out) the light into its different constituent colors (or wavelengths) and analyzing the spectrum, which is the array of colors

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Astronomy and Light (3) Physicists have found that light and other types radiation are generated by processes at the atomic levelThus, to appreciate how light is generated and behaves, we must first become familiar with how atoms workOur exploration will focus on one particular component of an atom, called electric charge

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Electric ChargeMany objects have not only mass, but also an additional property called electric charge, which can be traced to the atoms that the objects are made of In the vicinity of an electric charge, another charge feels a force of attraction or repulsion

This is true regardless of whether the charges are at rest or in motion relative to each otherThere are two kinds of charge: positive and negativeLike charges repel, and unlike charges attract

If the charges are in motion relative to each other, another force arises, which is called magnetism

Although magnetism was well known for millennia, its being caused by moving charges was not understood until the 19th century

Thus, the electric charge is responsible for both electricity and magnetism

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The Atom and the NucleusEach atom consists of a core, or nucleus, containing positively charged protons and neutral neutrons, and negatively charged electrons surrounding the nucleus

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Isotopes of HydrogenThe hydrogen atom is the simplest, consisting of only one proton and one electronAlthough most hydrogen atoms have no neutrons at all, some may contain a proton and one or two neutrons in the nucleus The different hydrogen nuclei with different numbers of neutrons are called isotopes of hydrogen

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Electric and Magnetic FieldsIn physics, the word field (or force field)is used to describe the action of forces that one object exerts on other distant objects

For example, the Earth produces a gravitational field in the space around it that controls the Moon’s orbit about Earth, although they do not come directly into contact

Thus, a stationary electric charge produces an electric field around it, whereas a moving electric charge produces both an electric field and a magnetic fieldSimilarly, a magnet is surrounded by a magnetic field

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James Clerk Maxwell (1)Maxwell (1831-1879), born and educated in Scotland, unified the rules governing electricity and magnetism into a coherent theory

It describes the intimate relationship between electricity and magnetism with only a few elegant formulasAlso, it allows us to understand the nature and behavior of light

Before Maxwell proposed his theory, many experiments had shown that changing magnetic fields could generate electric fields

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James Clerk Maxwell (2)Maxwell’s theory led to a hypothesis:

If a changing magnetic field can create an electric field, then a changing electric field can create a magnetic field

The consequences of his hypothesis: Changing electric and magnetic fields should trigger each otherThe changing fields should spread out like a wave and travel through space at a speed equal to the speed of light

Maxwell’s concluded:Light is one form of a family of possible electric and magnetic disturbances which travel called electromagnetic radiation or electromagnetic waves

Experiments later confirmed Maxwell’s prediction

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Electromagnetic Radiation (1)Electromagnetic (EM) radiation has some of the characteristics that other types of waves have, such as wavelength, frequency, and speed (see next slide) Unlike most other kinds of waves, however, EM waves can travel through empty space (vacuum)

Sound waves cannot travel through vacuum

The speed of light, and other EM radiation, is constant in empty space

All forms of radiation have the same speed of 299,800 kilometers/second in vacuum This number is abbreviated as c

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Wave Characteristics The wavelength () is the size of one cycle of the wave in space

It is also the distance from one crest (or one trough) to the nextCommon units for are meter (m), nanometer (nm), and angstrom (A)

The frequency (f) of the wave indicates the number of wave cycles that pass per second

The unit for frequency is hertz (Hz)

The speed (v) of the wave indicates how fast it propagates through space

Common units for v are m/s, km/hour, and miles/hour

v = f x

-8

-6

-4

-2

0

2

4

6

8

0 5 10 15 20

Distance (m)

Wav

e A

mpl

itude

Wavelength

The electric and magnetic fields oscillate at right angles to each other and the combined wave moves in a direction perpendicular to both of the electric and magnetic field oscillations.

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Electromagnetic Radiation (2) Visible light (what your eye detects) has a range of wavelengths from 4000 angstroms to 7000 angstroms (or from 400 nm to 700 nm)

1 angstrom = 10-10 meter

Different wavelengths of light are perceived by the eye as different colorsWhite light is a combination of all the colors

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Refraction of LightWhen light rays pass from one transparent medium (or a vacuum) to another, the rays are bent or refractedThe refraction angle depends the wavelength (color)

In other words, light rays of different colors are bent differently

Incidence angle

Refraction angle

Incidence angle

Refraction angle

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Dispersion by RefractionThe separation of light into its various colors is called dispersionWhite light passing through a prism undergoes dispersion into different colors

What is produced is a rainbow-colored band of light called a continuous spectrum

First discovered by Newton

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EM Radiation Carries EnergyThe types of radiation, from the highest to lowest energy, are

Gamma raysX-raysUltraviolet (UV)Visible lightInfrared (IR)Radio waves

Microwaves are high-energy radio waves

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Electromagnetic SpectrumThe EM spectrum is the entire range of wavelengths of EM radiation, including the visible spectrum

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Period/Frequency Examples

Phenomenon Period FrequencyEarth's Orbit around Sun 365 days 0.00273973 /day

31536000 s 3.171E-08 HzEarth Rotation 1 days 1 /day

86400 s 1.1574E-05 HzElectrical Power (US) 0.01666667 s 60 HzLight(Blue) 1.6667E-15 s 6E+14 Hz

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Visible Light (1)Since the speed of light is v = c = 3 x 108 m/s, the formula v = f x becomes

c = f x

c = f x can be rewritten as f = c/ = c/f

Light with a smaller wavelength has a higher (larger) frequencyLight with a longer wavelength has a lower (smaller) frequency

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Visible Light (2)

color (angstroms) f (*1014 Hz) Energy (*10-19 J)

violet 4000 -   4600 7.5 -   6.5 5.0 -   4.3

indigo 4600 -   4750 6.5 -   6.3 4.3 -   4.2

blue 4750 -   4900 6.3 -   6.1 4.2 -   4.1

green 4900 -   5650 6.1 -   5.3 4.1 -   3.5

yellow 5650 -   5750 5.3 -   5.2 3.5 -   3.45

orange 5750 -   6000 5.2 -   5.0 3.45 -   3.3

red 6000 -   8000 5.0 -   3.7 3.3 -   2.5

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Electromagnetic Radiation Reaching Earth

Not all wavelengths of light from space make it to Earth’s surface

Only long-wave ultraviolet (UV), visible, parts of the infrared (IR), and radio waves make it to surface

More IR reaches elevations above 9,000 feet (2,765 meters) elevation

This is one reason why modern observatories are built on top of very high mountains

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Earth’s AtmosphereBlocks gamma rays, X-rays, and most UV

Good for the preservation of life on the planet…An obstacle for astronomers who study the sky in these bands

Blocks most of the IR and parts of the radio Astronomers unable to detect these forms of energy from celestial objects from the groundMust resort to very expensive satellite observatories in orbit

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Electromagnetic Spectrum and Earth’s Atmosphere

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Lite Question

Is light a wave or a particle?

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Max Planck’s PhotonPlanck (1858-1947) discovered that if one considers light as packets of energy called photons, one can accurately explain the shape of continuous spectraA photon is the particle of electromagnetic radiationBizarre though it may be, light is both a particle and a waveWhether light behaves like a wave or like a particle depends on how the light is observed

This depends on the experimental setup!

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A Continuous SpectrumThis is a continuous band of the colors of the rainbow, one color smoothly blending into the next

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Albert Einstein’s Photon Energy Interpretation

A few years after Planck's discovery, Einstein (1879-1955) found a very simple relationship between the energy of a light wave (photon) and its frequency (f)

Energy of light = h × fHere h = 6.63 × 10-34 J·sec is a universal constant of nature called Planck's constant

Alternatively, energy of light = (h × c)/

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Blackbody RadiationA blackbody is an idealized object which absorbs all the electromagnetic radiation that falls on it, reflecting none of the incoming radiation

In other words, a blackbody is a perfect absorber of radiation, thus “appearing black”

When a blackbody is heated, it emits EM radiation very efficiently at all wavelengths

A blackbody is thus an excellent emitter of radiation

Though no real object is a perfect blackbody, most celestial bodies behave very much like a blackbody when it comes to emitting radiation

In other words, they produce radiation spectra that are very similar to the spectrum of blackbody radiation

Therefore, understanding the blackbody spectrum allows us to understand the radiation from celestial objects

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Blackbody Spectrum (1)These graphs show that the higher the temperature of a blackbody, the shorter the wavelength at which maximum power is emitted

Power is the amount of energy released per second

The wavelength (max) at which maximum power is emitted by a blackbody is related to its kelvin temperature (T) by max = 3 x 106/T

This relationship is known as Wien’s law

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Blackbody Spectrum (2)These graphs also show that a blackbody (BB) at a higher temperature emits more power at all wavelengths than does a cooler BBThe total power emitted per unit area (F) by a BB is proportional to its kelvin temperature (T) raised to the fourth power, namely F T4

This is known as the Stefan-Boltzmann law

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Star Color and

TemperatureLessons learned

from blackbody radiation can be used to estimate the temperature of stars and other celestial bodiesThus, the dominant color and the brightness of a body can give us some idea about its temperature

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Discrete SpectraA close examination of the spectra from the Sun and other stars reveals that the rainbow of colors in their spectra has many dark lines, called absorption lines

They are produced by the cooler thin gas in the upper layers of the stars absorbing certain colors of light produced by the hotter dense lower layers

The spectra of hot, thin (low density) gas clouds are a series of bright lines called emission linesIn both of these types of spectra you see spectral features at certain, discrete wavelengths (or colors) and nowhere else

Absorption and Emission Line Spectra

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Spectra (1)The type of line spectrum you see depends on the temperature of the thin gas

If the thin gas is cooler than the thermal source in the background, you see absorption linesSince the spectra of stars show absorption lines, it tells you that the density and temperature of the upper layers of a star is lower than the deeper layersIn a few cases you can see emission lines on top of a continuous spectrum — this is produced by a thin gas that is hotter than the thermal source in the background

The spectrum of a hydrogen-emission nebula (= gas or dust cloud) is just a series of emission lines without any continuous spectrum because there are no stars visible behind the hot nebulaSome objects produce spectra that are a combination of a continuous spectrum, an emission-line spectrum, and an absorption-line spectrum simultaneously!

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Spectra (2)

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The Bohr AtomNiels Bohr (1885-1962) developed a model of the atom that provided the explanation for discrete-line spectra in the early 20th centuryIn the model, an electron can be found only in energy orbits of certain sizesAlso, if the electron moves from one orbit to another, it must absorb or radiate energy

The absorbed or radiated energy can be in the form of a photon or an energy exchange with another atom

This model sounded outlandish, but numerous experiments confirmed its validity

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Bohr’s Model of the AtomThe massive but small positively-charged protons and massive but small neutral neutrons are found in the tiny nucleusThe small negatively-charged electrons move around the nucleus in certain specific orbits (energies)

An electron is much lighter than a proton or neutronIn a neutral atom the number of electrons equals the number of protons

The arrangement of an atom's energy orbits depends on the number of protons and neutrons in the nucleus and the number of electrons orbiting the nucleusEach type of atom has a unique arrangement of the energy orbits and, therefore, produces its own unique pattern of emission or absorption lines

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How Emission Line is Produced

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Spectral “Signatures” of Hydrogen and Helium

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How Absorption Line is Produced

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Doppler Effect When Source and Observer are in Relative

Motion

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No Doppler Effect When Source and Observer are not in

Relative Motion

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Doppler Effect in Radar Guns

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Doppler Shift in Spectra

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Doppler Shift in Radiation Graphs (1)

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Doppler Shift in Radiation Graphs (2)