Astronomy 1 – Fall 2014 CLM - Fall 2014 Lecture 4; October 14 2014

Previously on Astro-1 Planets appear to move on the sky mostly West to East but occasionally with “retrograde motions” The ancients thought that the Earth was at the center of the solar system and that planets moved in spheres around the Earth epicycles explained retrograde motion In the modern Heliocentric model, the planets go around the sun (copernican model) What pieces of evidence show that the Geocentric model is false? Kepler’s Laws The orbits of planets are ellipses A planet’s speed varies along the orbit The period of the orbit is related to the size of the orbit CLM - Fall 2014

Previously on Astro-1 Newton’s Laws of Motion: Inertia Relation between force and acceleration Action/Reaction Inertial and gravitational mass Newton’s Law of gravity The orbits of planets Tides CLM - Fall 2014

Today on Astro-1 The nature of light. Properties of light emitted by opaque sources. Spectral lines CLM - Fall 2014

Is the speed of light finite? Galileo tried, but couldn’t measure it. In 1676 Olaus Rømer noticed that the measurements of the eclipses of Jupiter’s moons were systematically off, depending on how distant Earth was from Jupiter. From this he deduced the speed of light (in terms of AU). Figure 5-1 Rømer’s Proof That Light Does Not Travel Instantaneously Thetiming of eclipses of Jupiter’s moons as seen from Earth depends on the Earth-Jupiter distance. Rømer correctly attributed this effect to variations in the time required for light to travel from Jupiter to the Earth. CLM - Fall 2014

Properties of Waves Example: Interference

Young’s Double-Slit Experiment Illustrates that Light is a Wave Figure 5-5 Young’s Double-Slit Experiment (a) Thomas Young’s classic double-slit experiment can easily be repeated in the modern laboratory by shining light from a laser onto two closely spaced parallel slits. Alternating dark and bright bands appear on a screen beyond the slits. CLM - Fall 2014

Light is Electromagnetic Radiation But what “wiggles” to make the wave? In 1860 James Clerk Maxwell showed that all forms of light consist of oscillating electric and magnetic fields that move through space at a speed of 3.00 × 105 km/s or 3.00 × 108 m/s. This figure shows a “snapshot” of these fields at one instant. Figure 5-6 Electromagnetic Radiation All forms of light consist of oscillating electric and magnetic fields that move through space at a speed of 3.00 105 km/s 3.00 108 m/s. This figure shows a “snapshot” of these fields at one instant. The distance between two successive crests, called the wavelength of the light, is usually designated by the Greek letter (lambda). CLM - Fall 2014

Frequency and Wavelength of an Electromagnetic Wave ν = frequency of an electromagnetic wave (in Hz – a Hertz is one cycle per second) c = speed of light, 3×108 m/s λ = wavelength of the wave (in meters) Example: What is the frequency of visible light at 540 nm? CLM - Fall 2014

Color of Light Depends on Its Wavelength

Newton used this experiment to prove that prisms do not add color to light but merely bend different colors through different angles. It also proved that white light, such as sunlight, is actually a combination of all the colors that appear in its spectrum. 4 Newton’s Experiment on the Nature of Light In a crucial experiment, Newton took sunlight that had passed through a prism and sent it through a second prism. Between the two prisms was a screen with a hole in it that allowed only one color of the spectrum to pass through. This same color emerged from the second prism. Newton’s experiment proved that prisms do not add color to light but merely bend different colors through different angles. It also proved that white light, such as sunlight, is actually a combination of all the colors that appear in its spectrum.

What about “invisible light What about “invisible light?” Around 1800 British astronomer William Herschel passed sunlight through a prism and held a thermometer just past the red end of the visible spectrum. The thermometer registered a temperature increase, indicating there was “infrared” light that we could not see. CLM - Fall 2014

Why is the Sky Blue? CLM - Fall 2014 Box 5-4 Light Scattering a) Why the sky looks blue CLM - Fall 2014

Why is the Sunset Red? CLM - Fall 2014 Box 5-4 Light Scattering (b) Why the setting Sun looks red CLM - Fall 2014

Human Eye is Sensitive to a Small Part of the Electromagnetic Spectrum

…but you are familiar with ‘invisible light’ It’s only invisible to the human eye.

The Doppler Shift: The Wavelength of Light is Affected by the Relative Motion between the Source and the Observer

Doppler Shift Equation Dl / l = v / c Dl = wavelength shift l = wavelength if source not moving v = speed of the source along the line of sight c = speed of light = 3e5 km/s

Demo: Doppler Shift of Sound Waves (iclicker Question) A speaker is whirled around on a rope. The sound from the speaker will do the following. Rise to higher frequency as the speaker moves towards the listener. Fall to lower frequency as the speaker moves away from the listener. Fall to lower frequency as the speaker moves towards the listener. Rise to higher frequency as the speaker moves away from the listener. Get louder as the speaker approaches the listener and get softer as the speaker moves away. Get louder as the speaker moves away and get softer as the speaker moves towards the listener. Both A & C

Why did the moon turn orange-red during the lunar eclipse Why did the moon turn orange-red during the lunar eclipse? (iclicker Question) The moon emits orange-red light because of its temperature. Red light was scattered towards the moon by the earth’s atmosphere. The earth emits red light, and we saw that light reflecting off the moon. The light emitted by the moon was red because of the moon’s Doppler shift. Sunlight passing through earth’s atmosphere was illuminating the moon. The blue light had been removed by scattering. CLM - Fall 2014

The Light Emitted by Opaque Sources “ Blackbody Radiation” CLM - Fall 2014

An opaque object emits electromagnetic radiation according to its temperature

Temperature is a measure of the average speed of the atoms in an object.

Temperature Units Box 5-1 Temperatures and Temperature Scales Astronomers use the Kelvin temperature scale. The “degrees” are the same as the Celsius system, only with 273 added, and they aren’t called degrees (just K). The are no negative numbers – “absolute” zero is the coldest possible temperature. CLM - Fall 2014

Hotter Objects Emit More Light Each curve shows the intensity of light at every wavelength that is emitted by a blackbody at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000 K curve is actually about 1000 times greater than the peak intensity for the 3000 K curve. Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve. CLM - Fall 2014

The Hotter the Object the Bluer Its Light Wien’s Law for a blackbody λmax = wavelength of maximum emission of the object (in meters) T = temperature of the object (in Kelvins). (The K and m above are units of Kelvins and meters). Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve.

Definition of a blackbody A blackbody is an idealized object that absorbs all radiation falling on it. It does not reflect light, instead it re-emits light. The temperature of the radiation it emits is determined by the average speed of the atoms in the object. A blackbody does not have to look black! The Sun is nearly a blackbody. Most things in everyday life (people, furniture, etc.) are too cool to emit visible light, so you can’t see them in the dark. Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve. CLM - Fall 2014

Cosmic Microwave Background. The CMB is a “perfect” Blackbody COBE FIRAS 1989; T=2.725 K CLM - Fall 2014

Demo: Spectrum of an Incandescent Light Bulb Passing electrical current through the wire in a lightbulb causes the wire to heat up. How will the light change as the current is increased? The light will remain white but get brighter. It will become brighter and bluer. It will become fainter and bluer. It will become brighter and redder. It will become fainter and redder. CLM - Fall 2014

Seeing in the Dark (iclicker Question) Suppose you want to build a camera that can see people in the dark. Approximately what wavelength does your camera need to be able to image? X-Rays Ultraviolet Light Optical Light Infrared Light Radio signals CLM - Fall 2014

An Infrared Portrait Human temperature in K = 273+37 = 310K This is in the infrared! In this image made with a camera sensitive to infrared radiation, the different colors represent regions of different temperature. Red areas (like the man’s face) are the warmest and emit the most infrared light, while blue-green areas (including the man’s hands and hair) are at the lowest temperatures and emit the least radiation. Figure 5-10 An Infrared Portrait In this image made with a camera sensitive to infrared radiation, the different colors represent regions of different temperature. Red areas (like the man’s face) are the warmest and emit the most infrared light, while blue-green areas (including the man’s hands and hair) are at the lowest temperatures and emit the least radiation. (Dr. Arthur Tucker/Photo Researchers) CLM - Fall 2014

Energy Flux Energy is usually measured in Joules (J). One joule per second is a Watt (W) – a measure of power. Flux is the amount of energy passing through one square meter every second.

Stefan-Boltzmann Law F = σT4 The Stefan-Boltzmann Law gives the flux of a blackbody of a given temperature. F = σT4 T = Temperature in Kelvins The value of the Stefan-Boltmann constant σ (a constant)= 5.67×10-8 W m-2 K-4. Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve. CLM - Fall 2014

Energy, Energy Flux & Power Let’s Check that You’ve Got It In the movie The Matrix – people are used as batteries. If the average human’s bodily surface area is 1.7 m2, and has an average temperature of 37°C, how much energy per second (power) does a person radiate? Answer. Treating a person as a blackbody, use the Stefan-Boltzmann law to determine the energy radiated per second per square meter, then multiply by the body’s surface area to get the energy radiated per second. Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve. Human temperature in K = 273+37 = 310K F = σT4 = (5.67×10-8 W m-2 K-4)(310 K)4 = 524 W m-2 Power = 524 W m-2 (1.7m2) = 891 W About the power of a toaster! CLM - Fall 2014

Power Radiated by Stars (iclicker Question) Why is a red giant much brighter than a red dwarf? Red giants are hotter than red dwarfs. The Stefan-Boltzmann Law tells us that the surface of a red giant emits more energy flux. The Stefan-Boltzmann Law tells us that the surfaces of all red stars emit the same energy flux. Red giants are bigger than red dwarfs, so they have more surface area. Both C & D. CLM - Fall 2014

Spectra are the “fingerprints” of atoms and molecules. CLM - Fall 2014

Stellar Spectra Have Spectral Lines Figure 5-12 The Sun as a Blackbody This graph shows that the intensity of sunlight over a wide range of wavelengths (solid curve) is a remarkably close match to the intensity of radiation coming from a blackbody at a temperature of 5800 K (dashed curve). The measurements of the Sun’s intensity were made above the Earth’s atmosphere (which absorbs and scatters certain wavelengths of sunlight). It’s not surprising that the range of visible wavelengths includes the peak of the Sun’s spectrum; the human eye evolved to take advantage of the most plentiful light available. CLM - Fall 2014

The Sun’s Spectrum In 1814 Joseph von Fraunhofer magnified the solar spectrum seen through a prism, and found hundreds of dark lines. Figure 5-13 The Sun’s Spectrum Numerous dark spectral lines are seen in this image of the Sun’s spectrum. The spectrum is spread out so much that it had to be cut into segments to fit on this page. (N. A. Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF) CLM - Fall 2014

What causes spectral lines? The structure of atoms CLM - Fall 2014

Rutherford’s Experiment Figure 5-19 Rutherford’s Experiment Alpha particles from a radioactive source are directed at a thin metal foil. This experiment provided the first evidence that the nuclei of atoms are relatively massive and compact. Rutherford’s Experiment CLM - Fall 2014

Rutherford’s model of the atom. Today we know this is not exactly correct – electrons do not orbit the nucleus, but the basic idea is right -- protons and neutrons exist in the nucleus, and electrons are outside of it. Figure 5-20 Rutherford’s Model of the Atom Electrons orbit the atom’s nucleus, which contains most of the atom’s mass. The nucleus contains two types of particles, protons and neutrons. CLM - Fall 2014

“Light is also a Particle” Planck’s Law “Light is also a Particle” or E = Energy of a photon h = Planck’s constant = 6.625×10-34 J s c = speed of light λ = wavelength of light ν = frequency of light Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve. CLM - Fall 2014

What is the Energy of a Photon? Example: DNA molecules are easily broken when hit with ultraviolet light at 260 nm. How much energy does a single photon at this wavelength have? 7.6 x 10-19 J 7.6 x 10-17 J 7.6 J 5.7 x 10-49 J 7.6 x 1019 J Figure 5-11 Blackbody Curves Each of these curves shows the intensity of light at every wavelength that is emitted by a blackbody (an idealized case of a dense object) at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000-K curve is actually about 1000 times greater than the peak intensity for the 3000-K curve. CLM - Fall 2014

The Bohr model of the atom Niels Bohr 1885-1962 Was a postdoc with Rutherford. In 1912, to explain discrete nature of spectral lines, hypothesized that electron orbits are quantized (quantum mechanics!). Bohr and Einstein, 1925 CLM - Fall 2014

The quantum nature of light is related to the quantum nature of atoms! Figure 5-23 The Absorption and Emission of an H Photon This schematic diagram, drawn according to the Bohr model, shows what happens when a hydrogen atom (a) absorbs or (b) emits a photon whose wavelength is 656.3 nm. (a) Atom absorbs a 656.3-nm photon; absorbed energy causes electron to jump from the n = 2 orbit up the n = 3 orbit (b) Electron falls from the n = 3 orbit to the n = 2 orbit; energy lost by atom goes into emitting a 656.3-nm photon CLM - Fall 2014

We still call these Balmer lines. In 1885 Swiss schoolteacher Johann Jakob Balmer, by trial and error, created a formula that can predict where lines of hydrogen fall in the spectrum of a star. We still call these Balmer lines. Figure 5-21 Balmer Lines in the Spectrum of a Star This portion of the spectrum of the star Vega in the constellation Lyra (the Harp) shows eight Balmer lines, from H at 656.3 nm through H (H-theta) at 388.9 nm. The series converges at 364.6 nm, slightly to the left of H. (NOAO) R = Rydberg constant = 1.097×107 m-1 n = any integer greater than 2 CLM - Fall 2014

The Balmer series and fomula. R = Rydberg constant = 1.097×107 m-1 Bohr figured out the physical explanation for Balmer’s formula – the spectra from stars depends on the structure of atoms! Figure 5-22 The Bohr Model of the Hydrogen Atom In this model, an electron circles the hydrogen nucleus (a proton) only in allowed orbits n 1, 2, 3, and so forth. The first four Bohr orbits are shown here. This figure is not drawn to scale; in the Bohr model, the n 2, 3, and 4 orbits are respectively 4, 9, and 16 times larger than the n 1 orbit. N = lower orbital n = higher orbital

Electron Transitions in the Hydrogen Atom The same wavelength occurs whether a photon is emitted or absorbed. Figure 5-24 Electron Transitions in the Hydrogen Atom This diagram shows the photon wavelengths associated with different electron transitions in hydrogen. In each case, the same wavelength occurs whether a photon is emitted (when the electron drops from a high orbit to a low one) or absorbed (when the electron jumps from a low orbit to a high one). The orbits are not shown to scale. CLM - Fall 2014

CLM - Fall 2014 Figure 5-25 Energy-Level Diagram of Hydrogen A convenient way to display the structure of the hydrogen atom is in a diagram like this, which shows the allowed energy levels. The diagram shows a number of possible electron jumps, or transitions, between energy levels. An upward transition occurs when the atom absorbs a photon; a downward transition occurs when the atom emits a photon. (Compare with Figure 5-24.) CLM - Fall 2014

Every Element Has a Unique Set of Spectral Lines Box 5-5 Atoms, the Periodic Table, and Isotopes The number of protons in an atom’s nucleus is the atomic number for that particular element. The chemical elements are most conveniently listed in the form of a periodic table (shown in the figure). Elements are arranged in the periodic table in order of increasing atomic number. With only a few exceptions, this sequence also corresponds to increasing average mass of the atoms of the elements. Thus, hydrogen (symbol H), with atomic number 1, is the lightest element. Iron (symbol Fe) has atomic number 26 and is a relatively heavy element. All the elements listed in a single vertical column of the periodic table have similar chemical properties. For example, the elements in the far right column are all gases under the conditions of temperature and pressure found at the Earth’s surface, and they are all very reluctant to react chemically with other elements. Atomic number is the number of protons in an atom. CLM - Fall 2014

CLM - Fall 2014 Figure 5-15 Various Spectra These photographs show the spectra of different types of gases as measured in a laboratory on Earth. Each type of gas has a unique spectrum that is the same wherever in the universe the gas is found. Water vapor (H2O) is a compound whose molecules are made up of hydrogen and oxygen atoms; the hydrogen molecule (H2) is made up of two hydrogen atoms. (Ted Kinsman/Science Photo Library) CLM - Fall 2014

The Ring Nebula is a shell of glowing gases surrounding a dying star. Nitrogen & Sulpher Hydrogen & Oxygen

Spectroscopy Reveals the Chemical Composition of Celestial Objects Figure 5-17 Iron in the Sun The upper part of this figure is a portion of the Sun’s spectrum at violet wavelengths, showing numerous dark absorption lines. The lower part of the figure is a corresponding portion of the emission line spectrum of vaporized iron. The iron lines coincide with some of the solar lines, which proves that there is some iron (albeit a relatively small amount) in the Sun’s atmosphere. (Carnegie Observatories) CLM - Fall 2014

Kirchoff’s Laws 1. A hot, dense object such as a blackbody emits a continuous spectrum covering all wavelengths. 2. A hot, transparent gas produces a spectrum that contains bright (emission) lines. 3. A cool, transparent gas in front of a light source that itself has a continuous spectrum produces dark (absorption) lines in the continuous spectrum. CLM - Fall 2014

Figure 5-16 Continuous, Absorption Line, and Emission Line Spectra A hot, opaque body (like a blackbody) emits a continuous spectrum of light (spectrum a). If this light is passed through a cloud of a cooler gas, the cloud absorbs light of certain specific wavelengths, and the spectrum of light that passes directly through the cloud has dark absorption lines (spectrum b). The cloud does not retain all the light energy that it absorbs but radiates it outward in all directions. The spectrum of this reradiated light contains bright emission lines (spectrum c) with exactly the same wavelengths as the dark absorption lines in spectrum b. The specific wavelengths observed depend on the chemical composition of the cloud. CLM - Fall 2014

CLM - Fall 2014

CLM - Fall 2014 Figure 5-14 The Kirchhoff-Bunsen Experiment In the mid-1850s, Gustav Kirchhoff and Robert Bunsen discovered that when a chemical substance is heated and vaporized, the spectrum of the emitted light exhibits a series of bright spectral lines. They also found that each chemical element produces its own characteristic pattern of spectral lines. (In an actual laboratory experiment, lenses would be needed to focus the image of the slit onto the screen.) CLM - Fall 2014

Spectral Lines (iclicker Question) Professor Martin used a spectrograph on the Keck telescope to observe a distant galaxy. She detected 2 absorption lines from sodium atoms. The wavelengths she measured were 0.22 nm bluer than the wavelengths of 589.0 and 589.6 nm where she expected to find the lines. What should she conclude? There are cool clouds between the observer and the galaxy. There gas between the galaxy and the observer is hotter than the galaxy. The gas clouds are moving away from the galaxy towards the observer. The gas clouds are falling into the galaxy. Both A and C

Structure of Atoms Most of the mass of ordinary matter resides in the A) electrons and nuclei, shared equally B) nuclei of atoms C) electrons around the nuclei of atoms D) energy stored within the atom in electromagnetic forces E) Atoms have no mass. CLM - Fall 2014

Summary What is light? Light is electromagnetic radiation An opaque object emits light according to its temperture. Wien’s law: max (in meters) = (0.0029 Km)/T. The Stefan-Boltzmann law: F = T4. What are photons? light can have particle-light properties. Particle energy: E = h = hc/ Kirchoff’s Laws A hot body produces a continuous spectrum A hot transparent gas produces emission lines Cool transparent gas in front of a hot body produces absorption lines CLM - Fall 2014

Summary Why is the sky is blue and sunsets red? Blue light is more strongly scattered by the atmosphere than red light What are stars and interstellar gas made of? Mostly Hydrogen, He, Oxygen, Carbon What causes spectral lines? Atomic structure CLM - Fall 2014

Homework – Due 10/20/14 On your own: answer all the review questions in chapter 5 To TAs: answer questions, 5.34 (Note that Io’s surface temperature is -150o C and not 2150o C), 5.37, 5.43, 5.44 CLM - Fall 2014