Lecture 8: Radiation Spectrum. Radiation. Electromagnetic Radiation

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1 Lecture 8: Radiation Spectrum The information contained in the light we receive is unaffected by distance The information remains intact so long as the light doesn t run into something along the way Since the Earth is not special (according to the Copernican hypothesis), we hypothesize that the physical laws we observe on Earth operate in the same way everywhere Radiation Even from such an enormous distance, the light from the Andromeda galaxy tells us about the stars there The color of the light is related to the temperature of the stars emitting it Electromagnetic Radiation 1

2 Radiation Light versus Water When you drop a rock in the pond, the waves are oscillations of the water height They propagate only to the edge of the pond Electromagnetic waves are oscillations of the EM field that are carried with the radiation The oscillating E field produces an oscillating M field, and viceversa! The waves are self-propagating! Hence, no background fluid is required. This is kind of weird Radiation The wavelength λ is the distance between two peaks: The frequency f is the number of peaks passing a fixed location per second: 2

3 Radiation The time between passage of successive peaks at a fixed location is called the period of the wave: λ period = c The frequency f is related to the period by f = Combining these relations gives c f = λ 1 period (seconds) (cycles per second: Hz) speed of light (universal constant) λ f = c Radiation Photoelectric Effect The quantization of radiation energy was deduced by Albert Einstein in order to explain the photoelectric effect: For red light, no electrons are ejected from the metal plate For blue light, slow electrons are ejected For ultraviolet (UV) light, fast electrons are ejected 3

4 Photoelectric Effect The observations raised an interesting question: If radiation energy is deposited continuously, then why don t we see very slow electrons leaving the plate when we shine red light? The answer is that energy must be deposited is discrete amounts that increase in proportion to the frequency of the radiation E = h f The electrons in the plate absorb energy from a single photon The energy of a photon of red light is too small to kick an electron out of the metal plate Einstein won the Nobel Prize for this work in 1921 Radiation We measure the wavelength of visible light using Angstroms, with 1 Angstrom = 10-8 cm Blue light has a wavelength of about 4,000 Angstroms Red light has a wavelength of about 7,000 Angstroms The energy in radiation is quantized (divided) into small units of energy called photons The minimum energy is contained in one photon, with energy E = h f where h is Planck s constant Each photon has energy Radiation E = h The energy E is related to the wavelength λ by h c E = λ Hence, the energy decreases with increasing wavelength Therefore, blue light has a higher energy than red light blue light has a higher frequency than red light blue light has a smaller wavelength than red light f c f = λ 4

5 Doppler Effect The observed wavelength of radiation depends on the speed of the source relative to the observer This is called the Doppler Effect A stationary observer see the rest wavelength (color) of the light Doppler Effect An observer moving away (receding) from the source sees stretched-out light (longer wavelength; REDSHIFT) A receding observer sees a longer wavelength, lower frequency, and lower energy, since c f = λ E = h f Doppler Effect An observer moving towards (approaching) the source sees compressed light (shorter wavelength; BLUESHIFT) An approaching observer sees a shorter wavelength, higher frequency, and higher energy, since c f = λ E = h f 5

6 Doppler Effect The emitted (rest frame) and observed wavelengths are related by v λ observed= λ emitted 1 + c where v is the relative velocity of the observer and the source and c is the speed of light The observed wavelength is smaller than the emitted wavelength if v is negative (approaching observer) The observed wavelength is larger than the emitted wavelength if v is positive (receding observer) If we know both wavelengths, then we can measure the relative speed v 6

7 Radiation Spectrum The radiation spectrum is the curve of brightness as a function of frequency (or wavelength) Brightness (intensity) is the amount of energy radiated by photons at the selected frequency (or wavelength) Radiation Spectrum Different objects can be brighter at different frequencies (or wavelengths) The shape of the radiation spectrum is usually related to the temperature of the object Black-Body Radiation The spectrum emitted from a body by virtue of its temperature is called black-body radiation or Planck radiation 7

8 Radiation Spectrum Visible radiation corresponds to temperatures in the range 4,000 K (red hot) to 7,000 K (blue hot) For the Planck curve, the wavelength of peak brightness determines its color 8

9 Radiation Spectrum As an object heats, the sequence of colors displayed is: dull red; bright red; bright yellow; bright blue; white The hotter an object, the higher the frequency of the brightness peak The hotter an object, the lower the wavelength of the brightness peak The hotter an object, the brighter it appears at ALL frequencies 9

10 Wien s Law The hotter an object, the lower the wavelength of the brightness peak The value of the peak wavelength λ peak is related to the temperature by Wien s law: T = λ peak Where λ peak is measured in Angstroms and T in Kelvins Temperature scales: Water freezes at 273 K Water boils at 373 K Room temperature is about 300 K 7 Wien s Law Example: A red star has λ peak =7,000 Angstroms and therefore T red =4,000 K Example: A blue star has λ peak =4,000 Angstroms and therefore T blue =7,000 K Example: A yellow star has λ peak =5,000 Angstroms and therefore T yellow =6,000 K 10

11 Stefan s Law Stefan s Law The total energy radiated at all frequencies (all wavelengths) of the Planck (black-body) curve is given by Stefan s Law: 4 F = σ T Where σ is Stefan s constant and F is the flux (energy per second per square cm) Hence, hotter objects radiate much more energy than cooler objects Example: a star with 3 times the temperature of another star radiates 3x3x3x3=81 times more energy! Emission of Radiation An electron at rest has a radial electric field: When an electron is jiggled, its electric field wiggles : Oscillating Charge Animation 11

12 Emission of Radiation An oscillating electron produces an oscillating electric field, which drives an oscillating magnetic field according to Maxwell s equations The frequency of the radiation is the same as the frequency of the electron s motion Emission of Radiation The frequency of the radiation is the same as the frequency of the electron s motion The frequency is connected with the temperature of the object The hotter the object, the faster the random motions, and the higher the frequency of the radiation This object has hotter and colder regions 12

13 Emission of Radiation Particles at low temperatures produce low-frequency radiation Emission of Radiation Particles at high temperatures produce high-frequency radiation 13

14 Many Different Temperatures Atmospheric Blockage Radiation propagates forever unless it is absorbed by something along the way The Earth s atmosphere is opaque to most radiation Atmospheric Blockage Radio waves are reflected by the ionosphere Microwaves are absorbed by water molecules in Earth s atmosphere X-ray, ultraviolet, and gamma-ray radiation is blocked by the ozone layer (these are harmful forms of high-energy radiation) Observational high-energy astronomy must be performed in space using satellites 14

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