Chapter 2 Light and Matter Reading assignment: Chapter 2
Stars and galaxies are too far for us to send a spacecraft to study them (in our lifetimes). All we can receive from stars and galaxies is light But there is much we can learn by studying the LIGHT they emit! Such as chemical composition, temperature, speeds, etc. Radio Light Visible Light X-ray Light (Antennae galaxies NGC 4038/4039, Corvus constellation)
Active Galaxy NGC 5128 (Radio source Centaurus A. Located in the constellation of Centaurus. A means the first radio source discovered in that constellation) Radio Light Centaurus A Visible Light
Centaurus A Infrared Light Visible Light
Questions: Light and radiation How astronomers learn about the chemical elements that made up stars and galaxies? How do they know about the temperature of planets, stars and galaxies? How do they know about the speed at which they are moving? The answer: Through the interpretation of light or the electromagnetic radiation received from these objects. Electromagnetic radiation refers to waves in which the energy is carried in the form of oscillating electric and magnetic field. Visible light is a particular type of electromagnetic radiation visible to the human eye. Radio, infrared, ultraviolet, X-rays and Gamma rays are electromagnetic radiation or light but invisible to the human eye The difference between all these types of electromagnetic radiation is the wavelength (or the frequency)
Light behave like a wave or a particle (This is called the duality of the behavior of light ) Let us take a look to the behavior of light as a wave The pebble cause the water to move up and down but there is no displacement of water away from the point where the pebble hit the water. But the information (and energy) is carried from place to place without physical movement of material in radial direction. The twig moves up and down. Energy is transferred to the twig.
Wave characteristics Parameters that describe a wave: Wavelength Amplitude Frequency Wave speed
Wavelength (λ) (Unit of length: m, cm, nm, ) Distance between successive wave peaks Period (Units of time: s) Time between the passing of wave crests Frequency (f) Number of vibrations per unit time (Unit: Hertz, Hz = 1/s). Multiples: khz, MHz Frequency = 1/ Period or Period x Frequency = 1 Wave Speed (Units of velocity: km/s, m/sec) Wave Speed = Wavelength x Frequency In the case of light, c is the speed: c = wavelength x frequency c = λ x f λ = wavelength (lambda) f = frequency Important: Light at all wavelengths travels in vacuum at the same speed: c = 300,000 km/s
Electrically charged particles and electromagnetic waves Electrons have - charge Protons have + charge Both have electric fields + - attract, ++ and - - repel The changing position of a charged particle creates waves called electromagnetic waves The electromagnetic waves travels through empty space eventually interacting with a distant charged particle. Visible light is an electromagnetic wave
Magnetism Effect on electric charges Moving electric charges also produce Magnetic fields. Example: electric current passing through a coil. Another example: electric motors and alternators Another interesting example: The Earth s magnetic field is produced by the spinning of charges in the liquid metal core of the Earth. Conversely, magnetic fields force charged particles to move.
Accelerated charges (electrons, protons) produce: An electromagnetic wave is composed of two oscillating fields, an electric field and a magnetic field perpendicular to each other Ripples in the ElectroMagnetic (E&M) field = E&M Waves = LIGHT!
Wavelength means COLOR 400nm 500nm 600nm 700nm Visible light ranges in wavelength from ~400 to ~700 nanometers.
Electromagnetic Spectrum Microwaves, cooking communication heat detected by our eyes sunburn penetrate tissue most energetic
Visible light is a small part of the EM spectrum.
Did you ever wonder why astronomers put telescopes on mountaintops or in space?
The temperature scale Comparison of Kelvin, Celsius and Fahrenheit scales The scale most used in sciences, physics and astronomy is Kelvin. The unit is kelvin (K)
The atoms and molecules that make up matter are in constant motion. Atoms and molecules are normally neutral (No electric charge). The temperature of an object measures the amount of microscopic motion of the particles. The kinetic energy is E = ½ m v² The higher the temperature, the faster the particles move (larger v) and the larger the kinetic energy. When the charged particles change their state of motion (change in speed, direction, acceleration), electromagnetic radiation is emitted. Blackbody Radiation
Thermal Radiation Blackbodies, like stars, incandescent light bulbs and irons, emit this characteristic spectrum of light. A body at a temperature higher than 0 K will emit as a blackbody. (No emission if the temperature of a body is 0 K) The intensity peaks at a given frequency and fall off to lesser values above and below that frequency. This plot is in logarithmic scale. The intensity and frequency scales appears compressed Blackbody Spectrum: Peak of intensity
Blackbodies with different temperatures look like this: Hotter blackbodies are brighter and bluer. (nm : nanometer; 1 nm = 10^-9 m)
An example: The spectrum of the Sun
Wien s Law Hotter bodies radiate more strongly at shorter wavelengths (i.e. they re bluer). Cooler bodies radiates more at longer wavelengths (i.e. they are redder) There is a wavelength at which the intensity of the radiation reaches a maximum ( max ) max = 0.29 cm T (K) Using this equation we can measure a star s temperature from its spectrum!
Stefan s Law Hotter blackbodies are brighter overall (at every wavelength). where: F = total radiative flux (total energy radiated per second) = constant F = T 4 The total radiated flux or total energy radiated per second is proportional to the area under the black body curve Also note that the total energy radiated per second is proportional to the fourth power of an object s temperature Example: If the temperature T of a body is increased to 2T, the total energy radiated per second is increased to (2T) 4 = 16 T 4
Important properties of blackbodies a different temperatures max max shift to shorter wavelengths if the temperature T increases The total energy emitted increases as T to the fourth power The energy emitted at a single wavelength in larger as the T increases
Application of Stefan s and Wien s Laws The plot is in linear scale Stefan s Law max =242 nm Increasing the temperature from 6,000 K to 12,000 K of a black body will increase the total radiated flux (Total energy radiated per second) by a factor of 16 The total radiated flux is proportional to the area under the curve. The area under the 12,000 K curve is 16 times larger than the area under the 6,000 K curve Wien s Law max = 2,900,000(nm)/T (K) The max shift from the visual, around 483 nm (green-yellow, for a 6,000 K) to around 242 nm (ultraviolet for a 12,000 K). max =483 nm
The temperature of the stars and the Sun (Flu x) Radiation from the Sun Radiation of three stars at three different temperatures
Stellar Colors Reddish coolest stars (~3000 K) Orange-ish Sun (~6000 K) Yellowish Bluish hottest stars (~50,000 K) Stars, light bulbs, irons, etc., are ~Blackbodies with different colors, depending on their temperature. A Blackbody is a perfect emitter and absorber, whose temperature defines how much light it emits at each wavelength.
Comparison of blackbody curves from four astronomical objects Cloud of interstellar dust T= 60 K Nebula T = 600K Sun T = 6,000 K Globular cluster (including white dwarfs) T= 60,000 K Binary Star Albireo, β (Beta) Cygni For the Gator fans: The Gator star! Temperature of the orange-yellowish star = 4,080 K Temperature of the blue star = 13,200 K
Spectroscopy (Analysis of Spectra) Light can be separated into different wavelengths (separated in colors) to produce a spectrum. The instrument used to produce and analyze a spectrum is known as a spectroscope It consist of a opaque barrier with a slit to produce a narrow beam of light, a prism or a diffraction grating and a detector (it can be the eye) or a screen to project the spectrum.
Continuous Spectrum
Emission Line Spectrum
Emission Line Spectra Each element produces its own unique pattern of lines
Absorption Line Spectrum
Absorption Line Spectra Spectrum of the Sun The H (Hydrogen) letter followed by a Greek letter are used for the Balmer series (Visible H lines).
Three Types of Spectra Continuous Emission Lines Absorption Lines
Kirchhoff s Laws of Radiation (Published in 1859) Kirchhoff s First Law Hot, dense gases or solids produce a continuous spectrum. Emits light at all wavelengths Example: Light bulb filament Continuous Spectrum
Kirchhoff s Second Law A hot, low-density gas when exited ( by an electric current or UV emission) produce an emission line spectrum. These lines are characteristic of the chemical composition of a gas The lines are the fingerprints of the chemical element. They are unique to the element. Examples: Neon signs, Sodium vapor street lamps, emission nebulae Emission Line Spectrum
Kirchhoff s Third Law A Low-density cool gas in front of a hot continuous source produces an absorption line spectrum. These lines are characteristic of the chemical composition of the gas For the same gas, the absorption lines occur at the same wavelengths of the emission lines Example: The Sun, stars Absorption Spectrum
Summary of Kirchhoff s Laws: 1 2 3 How can we explain the lines that appear in discrete emission or absorption spectrum? Using Kirchhoff s laws we can describe the phenomenon but do we have a theory to explain it?
The Nature of Atoms Three subatomic particles makeup an atom: 1. Proton - positive charge 2. Neutron (proton+electron) no charge 3. Electron - negative charge The nucleus is composed of protons and neutrons. Like charges repel so a large amount of force is required to keep the protons in the nucleus together. mass of proton mass of neutron 1836 x mass of electron Atoms are mostly empty space! And, since all matter is made up of atoms, matter is mostly empty space!! Atoms are neutral, they have no electric charge (equal number of electrons and protons) If an atom loses or gains an electron, it acquires an electric charge. It is said to be ionized and it is therefore an ion. Atoms can bond with other atoms of the same kind or different kind to form molecules. Example: Molecular Oxygen, O₂ ; Water, H₂O
Each atom of a given element contains a specific number of protons and electrons thus making that element unique.
Bohr s Hydrogen Model Niels Bohr In 1913, Bohr developed a model of the atom that provided the first explanation of the hydrogen s spectral lines e - p + Electron orbits the proton (i.e. nucleus) kept in place by the Coulomb Force (F c ). 1 F c R 2 How does this structure lead to unique emission and absorption lines?
Bohr s Model Electrons can only be in particular orbits (energy states). Excited state (higher energy) Ground state (lowest energy) Energy is quantized (Quantum Mechanics). Excitation requires energy to be added to the atom De-excitation - energy is released from the atom e p
electrons gain energy nucleus R 2 R 3 E 2 E 3 R 1 R 2 R 1 E 1 lose energy R3 DE = E 3 -E 1 Electron needs to gain energy to move from R 1 to R 3 (excited). Electron needs to lose energy to move from R 3 to R 1 (de-excited). How does the electron get the energy it needs to become excited? 1. Collisions between atoms can excite electrons to higher energy levels. Passing an electric current (applying a high voltage to a low density gas)will make atoms collide. 2. The absorption of energy from light can excite electrons.
What s going on? Light can behave as a particle. Albert Einstein Light energy must be carried in packets called photons. Einstein was awarded the Nobel Prize in 1921 for his theory of the photoelectric effect. The effect can be explained if light is considered as a particle (photons) Photon energy 1/wavelength Photon energy frequency Light Intensity = # photons arriving/second Low energy photons cannot cause e - ejections. High energy photons cause ejection of e - (can ionize an element)
Quantum Mechanics: Atoms can only absorb or emit photons with energies exactly equal to the energy difference between electron orbits. The energy of a photon is related to the wavelength: E ph 1/ f E ph = h f = h c/ (f = c/ ) h is the Planck s constant Larger orbital jumps shorter wavelength photons. (Larger orbital jumps have larger energy levels) Important: A radio photon has long wavelength (low frequency) and low energy A gamma ray photon has short wavelength (high frequency) and high energy
The energy of the photon must be precisely equal to DE. E p DE E p = DE Photon absorbed photon emitted E p = DE
The Hydrogen atom Atoms of different elements have unique energy level structures. The figure on the left, shows some of the energy levels of Hydrogen Every e - transition corresponds to a unique wavelength. Ionization = ejection of e -. Balmer The figure at the bottom shows the Balmer series of Hydrogen. Part of the lines of this series are in the visible part of the spectrum. Hydrogen Balmer series Hγ Hβ Hα
Examples of spectra of different elements. Every element (atom) emit or absorb a particular set of lines. It has a unique signature or fingerprint of that element
Bohr s Hydrogen Atom In modern quantum mechanics: Electrons are not just particles, but also waves, without exact locations.
The Doppler Effect Moving sources, like fire trucks and race cars, change the pitch of the sound (siren) as they go by. The pitch is higher (higher frequency) when they are approaching and lower (lower frequency) when they are moving away. This is an example of Doppler effect in sound waves
Doppler effect Motion along the line of sight (radial motion) produces a Doppler effect No Doppler effect if the motion is perpendicular to the line of sight
Doppler effect in electromagnetic waves Electromagnetic waves also show a Doppler effect. Light emitted by a moving object also present the Doppler effect v/c = Δ / = ( shift - rest)/ rest v is the radial velocity of an object c is the speed of light Δ = ( shift - rest) is the change in wavelength shift is the shifted or observed wavelength rest is the wavelength at rest
The Doppler Shift Stationary source: Moving source:
An example of a body emitting the Balmer series of hydrogen Red shift and blue shift of hydrogen Balmer series lines Important! If the body emitting the Balmer series is receding (moving away from observer), the lines are shifted to the red part of the spectrum. The spectrum is said to be red shifted. The body do not necessarily looks red If the body is approaching the observer, the lines are shifted to the blue part of the spectrum. The spectrum is said to be blue shifted. The body do not necessarily looks blue
Obtaining the rotation of an object from the width of the Doppler lines We will assume that the object is not approaching or receding from the observer. It is only rotating. If the object (a planet, a star or a galaxy) is rotating, the side approaching the observer will be blue shifted. The side moving away form the observer will be red shifted. The line emitted from the center will have no shift. As a consequence, the line will be wider that it would if the object had no rotation. The rotation rate of the object can be determined by measuring the width of the spectral lines
The Zeeman Effect A single emission lines can split into two or more under the presence of magnetic field The presence of magnetic field split the energy levels of an atom Splitting of an emission line in a sunspot due the presence of magnetic field in the sunspot
What can we learn from spectroscopy? The chemical composition by matching the spectral lines with laboratory spectra of atoms. The temperature by matching overall spectral shape with blackbody curve (Wien s law). The line-of-sight velocity by determining the Doppler shift. The rotation rate by measuring the broadening of spectral line due to Doppler shift. The pressure of the gas in the emitting region due to broadening of spectral lines. The greater the pressure, the broader the line The magnetic field (Zeeman effect) which splits a single line into two or more lines