1AST 2010: Chapter 47 Jul 2005

Radiation & Spectra

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 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 wavesBecause 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 the 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 Many 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

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Detour: the Atom and the Nucleus

Each 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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Detour: 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

Electric ChargeIn 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, not until the 19th century did scientist understand that it was caused by moving charges

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

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Electric and Magnetic Fields

In 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 conclusion:Light is one form of a family of possible electric and magnetic disturbances which travel and are called electromagnetic radiation or electromagnetic waves

Experiments later confirmed Maxwell’s prediction

Lite Question

What other What other waves do you waves do you

know?know?

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

Sound waves cannot travel through vacuumAlso unlike other types of waves, light and other EM waves travel in empty space (vacuum) at the same speed, which is the speed of light

The speed of light is 299,800 kilometers/second This number is usually 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/hourv = f x

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Electromagnetic WaveThe electric and magnetic fields of an EM wave 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

Animation

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Visible SpectrumVisible light (the EM radiation that the human eye detects) has a range of wavelengths from 4,000 angstroms to 7,000 angstroms (or from 400 nm to 700 nm)

1 angstrom = 10-10 meterDifferent wavelengths of light are perceived by the eye as different colorsWhite light is a combination of all the colors

Simulations for combining light of different colors When light rays pass from one transparent medium (or a vacuum) to another, they are bent or refracted

The refraction angle depends on the wavelength (color)In other words, light rays of different colors are bent differentlySimulation

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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 spectrumSimulation

First discovered by Newton

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EM Radiation Carries EnergyObjects in the universe send us an enormous range of EM radiationThe 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

Simulation

Visible Light 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/ or = c/fThus, light with a larger wavelength has a lower frequency, and light with a smaller wavelength has a higher frequencyIn the visible spectrum, red colors have the largest wavelengths (lowest frequencies), whereas blue and violet colors have the smallest wavelengths (highest frequencies)

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Electromagnetic Radiation Reaching Earth Not all wavelengths of light from space make it to

Earth’s surfaceOnly long-wave ultraviolet (UV), visible, parts of the infrared (IR), and most radio waves reach the surfaceMore IR reaches elevations above 9,000 feet (2,765 meters)

The blocking of gamma rays, X-rays, and most UV by the Earth’s atmosphere

is good for the preservation of life on the planetbut poses an obstacle to astronomers studying the sky in these bands

Consequently, astronomers unable to detect these types of radiation from celestial objects using ground-based instruments must perform their observations from high mountaintops, high-flying airplanes, and spacecraft

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Electromagnetic Spectrum & Earth’s Atmosphere

Lite Question

Is light a wave Is light a wave or a particle?or a particle?

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

A continuous spectrum is formed whenever a solid, liquid, or very-dense gas gives off radiation

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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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Albert Einstein’s Photon Energy

InterpretationA 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)/ Thus, a high-energy EM wave has a high frequency and a small wavelength

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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 and, therefore, “appears black”

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

A blackbody is thus an excellent emitter of radiationThough 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 secondSimulation

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

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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Line Spectra (1)If a thin (low density) gas is heated until it glows with its own light, the spectrum is not continuous, but consists of a series of separate bright lines called emission lines

The lines imply that the atoms of the gas can emit only certain discrete wavelengths (colors) of light

The gas of each particular element (such as hydrogen, or sodium) produces an emission line spectrum that has a specific pattern of lines unique to that element and thus serves as its unique spectral signature

No two elements have the same patterns

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Line Spectra (2)A 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

The combination of dark lines and continuous spectrum is called the absorption line spectrum The underlying continuous spectrum is produced by the hotter and denser gas in the stars’ inner layersThe dark lines are produced by the cooler and thinner gas in the stars’ outer layers, and imply that the atoms of the gas can absorb only certain discrete wavelengths (colors) of light

The gas of a particular element can produce both emission and absorption line-spectra

Absorption &

Emission Line

Spectra

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Three Kinds of SpectraSince each element has its own spectral signature in the pattern of absorption or emission lines we observe, spectral analyses can reveal some information about the composition of the Sun and other stars

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The Bohr AtomNiels Bohr (1885-1962) developed a model of the atom that provided the explanation for 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 emit energy

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

SimulationThis 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 its own 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 & 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

Animations (for sound waves)

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Doppler Effect in Radar Guns

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Doppler Shift in Spectra