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Homework #2

Homework #2. Homework #2 is due Thursday, September 20. Quiz #1 Notes. High Score: 20/20 (100%) Average: 15.8/20 (79%) Median: 16/20 (80%). Chapter 5 Light and Matter: Reading Messages from the Cosmos. Light. Light is a form of radiative energy.

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Homework #2

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  1. Homework #2 Homework #2 is due Thursday, September 20.

  2. Quiz #1 Notes High Score: 20/20 (100%) Average: 15.8/20 (79%) Median: 16/20 (80%)

  3. Chapter 5Light and Matter: Reading Messages from the Cosmos

  4. Light Light is a form of radiative energy. Light provides our only means of learning about very distant objects. • White optical light is made up of many different colors – extend concept to all forms of light

  5. Color and Reflection Objects appear to have certain colors because their surface preferentially reflects certain colors, while absorbing other colors. • But there is more to light than the human eye can see!

  6. What is the electromagnetic spectrum? In physics, when we speak of “light”, we mean all parts of the electromagnetic spectrum – optical light, ultraviolet, infrared, X-rays, gamma-ray, radio…… “Optical” or “visible” light is that small part of the electromagnetic (EM) spectrum that our human eyes happen to be sensitive to (dogs and cats can see UV light!). Only difference between “optical” light and X-rays, ultraviolet, etc. is energy/wavelength of EM wave….otherwise they are the same phenomenon.

  7. What is the electromagnetic spectrum? Optical light is just one small part of the EM spectrum that our eyes our sensitive to – all travel as an electromagnetic wave

  8. Is light a wave or a particle? • Light propagates through a medium and undergoes interference when passing through a slit like a wave – it’s a wave! • Light comes in small quantized packets called photons – it’s a particle! • Light is an electromagnetic wave anda particle – wave-particle duality • Profound truth of quantum mechanics (electrons also exhibit both wave and particle behavior).

  9. Waves • A wave is a pattern of motion that can carry energy without carrying matter along with it

  10. Properties of Waves • Wavelength is the distance between two wave peaks (unit: centimeter, for example - denoted ) • Frequency is the number of times per second that a wave vibrates up and down (unit: Hertz =1/seconds) - denoted ) wave speed = wavelength x frequency For light:  *  = c (speed of light) where c = 3 x 1010 cm/s

  11. Wavelength and Frequency of Light wavelength x frequency = speed of light = constant Longer wavelength, smaller frequency Shorter wavelength, larger frequency

  12. Example Red light has a wavelength of 6000 Å (Angstroms). What is its frequency? Note: 1 Å = 10-8 cm = 10-10 m = 0.1 nanometer  = c /  = 3 x 1010 cm/s / 6000 Å 1 Å = 10-8 cm • = 3 x 1010 cm/s / 6000 x 10-8 cm  = 5 x 1014/s = 5 x 1014 Hz

  13. Particles of Light • Particles of light are called photons, which are massless. • Despite being a particle, photons have a wavelength and a frequency (and energy and momentum). • The energy of a photon depends on its frequency.

  14. Light, Energy, and Power • Light is a form of radiative energy. • Unit of Energy: Joule (physics) or ergs (astro) 1 Joule = 1 Newton m = 1 kg m2/s2 1 erg = 1 dyne cm = 1 g cm2/s2 = 10-7 J • We can measure the flow of energy in light in units of watts: 1 Watt = 1 Joule/s = 107 ergs/s • A Watt is a unit of Power (and Luminosity)

  15. Wavelength, Frequency, and Energy E = h x = photon energy h = 6.626 x 10-27 ergs s = 6.626 x 10-34 Joule s h = Planck’s constant (universal constant) Energy of a 6000 Å photon? E = 6.63 x 10-27 ergs s * 5 x 1014 Hz E = 3.32 x 10-12 ergs

  16. A red laser pointer has a power of 1 milli-Watt when active. Red light has a wavelength of 6000 Å. How many photons per second are emitted by the laser pointer?1 milli-Watt = 10-3 Watts = 104 ergs/s104 ergs/s / 3.32 x 10-12 ergs/photons= 3 x 1015 photons/s

  17. The higher the photon energy • The longer its wavelength. • The shorter its wavelength. • Energy is independent of wavelength.

  18. The higher the photon energy • The longer its wavelength. • The shorter its wavelength. • Energy is independent of wavelength. E = hx, but  = c / l, soE = h* c / l So if E goes up, wavelength l goes down.

  19. The electromagnetic spectrum Wavelength More particle-like Gamma rays X-rays Ultraviolet Optical Infrared Microwave Radio Frequency Energy More wave-like Each part of EM spectrum interacts differently with matter.

  20. Which type of light travels the fastest? • Radio • optical • X-ray • Gamma-ray

  21. Which type of light travels the fastest? • Radio • optical • X-ray • Gamma-ray Trick question! They all travel at the speed of light (3 x 1010 cm/s).

  22. Only Some Light Gets Through the Atmosphere • Optical • Some Infrared • Radio Early astronomy obviously focused on optical light.

  23. Properties of Thermal Radiation Hotter objects emit more light at all frequencies per unit area (Stefan-Boltzmann Law). Hotter objects emit photons with a higher average energy (Wien’s Law). Thermal radiation is also called blackbody radiation. Any solid, liquid, or thick gas (including you) with with a non-zero temperature will emit like a blackbody

  24. Blackbody (Planck’s Law) I(,T) =2h3/c2 * 1/(eh/kT -1) Peak frequency (and wavelength) dependent on temperature T Hotter blackbodies emit more energy (per unit area) at all frequencies/wavelengths. Linear Scales Log Scales

  25. Blackbody (Planck’s Law) I(,T) =2h3/c2 * 1/(eh/kT -1) or equivalently, since I(,T) d = I(λ,T) dλ I(λ,T) =2hc2/λ5 * 1/(ehc/λkT -1) How to find the maximum of this function?

  26. Blackbody (Planck’s Law) I(,T) =2h3/c2 * 1/(eh/kT -1) or equivalently, since I(,T) d = I(λ,T) dλ I(λ,T) =2hc2/λ5 * 1/(ehc/λkT -1) How to find the maximum of this function? Differentiate I(λ,T) with respect to λ, and set equal to zero. Some math…. λmaxT = constant

  27. Wien’s Law Peak wavelength λmax T = 0.29 cm Kelvin Know this law…… Linear Scales Log Scales

  28. Wien’s Law What is the peak wavelength of the surface of the Sun? For Sun T = 5800 K Peak wavelength λmax T = 0.29 cm Kelvin λmax = 0.29 cm Kelvin / 5800 K = 5 x 10-5 cm = 5000 Å (yellow light) Human eye sensitivity peaks near this wavelength.

  29. Properties of Blackbody (Thermal) Radiation Color of metal poker changes from dull red to red to orange, and then eventually to white as metal heats up  Wien’s Law

  30. Humans Emit (Infrared, Not Optical) Light! • The human body has a temperature of 310 K. • Peak emission happens in the infrared. • Night vision goggles work by detecting the infrared blackbody emission from your body. optical (light on) optical (light off) infrared (lights off)

  31. Blackbody (Planck’s Law) How much energy does a blackbody emit per unit area? Integrate Planck curve over all frequencies and all solid angles Integrate I(,T) =2h3/c2 * 1/(eh/kT -1) from =0 to =∞ and over all solid angles. Some math…. emitted energy per unit area per time = constant * T4

  32. Stefan-Boltzmann Law A blackbody is the maximum power (luminosity) that an object can emit per unit area S = Energy/time/area = T4 Where S is in units of ergs/s/cm2  note this is per area! (or Watts/cm2) • = Stefan-Boltzmann constant = = 5.67 x 10-5 ergs/cm2/s/K4 = 5.67 x 10-8 J/m2/s/K4

  33. Stefan-Boltzmann Law A blackbody is the maximum power (luminosity) that an object can emit per unit area S = Energy/time/area = T4 Where S is in units of ergs/s/cm2  note this is per area! (or Watts/cm2) Both a 6000 K star and a 6000 K small hunk of metal emit the same amount of luminosity per unit area same S Must know size of object to convert the power per unit area to a total luminosity.

  34. If the Sun suddenly becomes 3 times hotter: • its luminosity will increase by 9 • its luminosity will increase by 27 • its luminosity will increase by 81

  35. If the Sun suddenly becomes 3 times hotter: • its luminosity will increase by 9 • its luminosity will increase by 27 • its luminosity will increase by 81 Assuming it stays the same size….if the Sun also changed size, the luminosity will change further

  36. Which object has a higher luminosity? • A 3000 K star • A 6000 K star • Not enough info given

  37. Which object has a higher luminosity? • A 3000 K star • A 6000 K star • Not enough info given Without knowing the size of each star, we cannot calculate the luminosity of the star (only the power per unit area)

  38. Amended Stefan-Boltzmann Law Total Luminosity = energy per unit area per time * surface area L = S * area= T4 * 4R2 where R is the radius of the blackbody. L in units of ergs/s • bigger objects emit more light at a given temperature A 6000 K star and a 6000 K small hunk of metal emit radically different luminosities because of their radically different sizes  much different L

  39. What is the structure of matter? Electron cloud is much bigger (100,000x) than nucleus  atom is nearly all empty space (although nucleus contains >99% of mass of atom)! The atom Atoms are composed of protons, neutrons and electrons. Protons carry positive charge in nucleus Neutrons are uncharged and reside in the nucleus too (about same mass as proton) Electrons carry negative charge in electron cloud surrounding nucleus – # electrons = # protons in a neutral atom (very small mass compared to proton)

  40. Atomic Terminology • Atomic number = # of protons in nucleus • Atomic mass number = # of protons + neutrons (Hydrogen-1) (Helium-4) (Carbon-12) It’s the number of protons that makes an element (hydrogen, helium, carbon, etc.) what it is…..

  41. Atomic Terminology • Isotopes: atoms with the same # of protons but different # of neutrons # of protonsdetermine the chemical properties, not neutrons  above isotopes are all carbon and behave chemically like carbon

  42. More Terminology • Molecules: consist of two or more atoms joined together chemically (H2O, CO2) CO2 – carbon dioxide

  43. What are the phases of matter? • Familiar phases: • Solid (ice) • Liquid (water) • Gas (water vapor) • Phases of same material behave differently because of differences in chemical bonds. • Bonds break by heating  heat gives extra kinetic energy to the atoms/molecules

  44. Phase Changes • Ionization: stripping of electrons, changing atoms into plasma (+ and – ions) • Dissociation: breaking of molecules into atoms • Evaporation: breaking of flexible chemical bonds, changing liquid into solid • Melting: breaking of rigid chemical bonds, changing solid into liquid

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