Blackbody Radiation

Problems

practice

  1. Write something.
  2. Write something.
  3. Write something.
  4. Combine the speed of light (c), gravitational constant (G), and the reduced planck constant (ℏ) so as to generate the planck units of …
    1. length
    2. mass
    3. time
    Add boltzmann's constant (k) to the list and generate the planck unit of …
    1. temperature
    Combine your results and generate the planck units of …
    1. acceleration
    2. force
    3. momentum
    4. energy
    5. power
    6. pressure
    7. density
    8. angular frequency
    Include the coulomb law constant (1/4πε0) and generate the planck units of …
    1. charge
    2. current
    3. voltage
    4. resistance

conceptual

  1. Pigments are used to give color to paint (on a house or on an artist's canvas), fibers (in clothing, carpeting, or tapestries), and glaze (on ceramic pottery or mosaic tiles).
    1. Why does red pigment appear red? Why does blue pigment appear blue?
    2. How does the energy of a photon of red light compare to the energy of a photon of blue light?
    3. Which pigment is most likely to fade first when exposed to sunlight, red or blue? Justify your answer.
  2. Three related questions.
    1. Why are ultraviolet, x‑rays, and gamma rays always regarded as harmful while infrared, microwaves, and radio waves are generally regarded as benign (by sensible people, anyway).
    2. In what sense can visible light be thought of as "just right" as an energy source for life (and other forms of chemistry) on earth?
    3. Under what circumstances could exposure to the generally benign electromagnetic waves listed in part a. be considered harmful?

numerical

  1. A microwave oven emits 700 W of radiation at a frequency of 2.45 GHz. How many photons does it generate per second?
  2. The filament of a 60 W incandescent light bulb has a temperature of 3300 K.
    1. Assume the filament is an ideal blackbody and determine the peak wavelength of its spectrum.
    2. Assume the peak wavelength is equal to the mean wavelength of all the photons emitted and determine the number of photons emitted per second.
  3. The world's most powerful laser is the Petawatt at Lawrence Livermore National Laboratory in California. At full energy of about 680 joules, the shots delivered by the Petawatt last a mere 440 femtoseconds. The resulting rapid dump of energy when applied to a small space is sufficient to knock neutrons loose from medium sized nuclei like gold or to split heavier nuclei like uranium in two. When applied to light nuclei like hydrogen, the power of the Petawatt could be used to initiate nuclear fusion (the process that powers the sun) in reactors on earth.
    1. What is the power of the Petawatt beam?
    2. What is the energy per photon assuming a wavelength of 1057 nm?
    3. How many photons are delivered per shot?
  4. A laser used in a fiber optic communication system operates at a wavelength of 635 nm, has a power output of 1 mW, and can transmit data at a rate of 2.5 gigabits per second. Compute the following quantities.
    1. The duration of a single pulse.
    2. The energy of a single pulse.
    3. The energy of a single photon.
    4. The number of photons in a single pulse.
  5. Complete the following table for different types of electromagnetic radiation. (If you need to reach for your calculator more than two times, you are doing the work the hard way.)

    energy per
    photon (eV)    		 energy per
    photon (J)    		 frequency
    (Hz)    		 wavelength
    (m)    		 type of
    radiation
    100 eV        
    103 eV        
    106 eV        


  6. Complete the following table for visible light.
     
      lowest frequency highest frequency
    color    
    wavelength (m)    
    frequency (Hz)    
    energy per photon (J)    
    energy per photon (eV)    
     

statistical

  1. led.txt
    Four physics students measured the voltage drop across a batch of light emitting diodes (LEDs) connected to a simple circuit. They used a spectrometer to measure the peak wavelength of the light emitted from each LED.
    1. Calculate the frequency (f) corresponding to the peak wavelength for each LED in hertz (Hz).
    2. Calculate the energy loss (E) of the electrons flowing through the LEDs in joules (J).
    3. Construct a graph of energy vs. frequency. Add a best fit straight line to the graph.
    4. Determine the value of Planck's constant (h) in joule seconds (Js).
  2. led.txt
    Four physics students measured the voltage drop across a batch of light emitting diodes (LEDs) connected to a simple circuit. They used a spectrometer to measure the peak wavelength of the light emitted from each LED.
    1. Calculate the inverse peak wavelength (λ−1) for each LED in inverse nanometers (nm−1).
    2. Calculate the energy loss (E) of the electrons flowing through the LEDs in electron volts (eV).
    3. Construct a graph of energy vs. inverse wavelength. Add a best fit straight line to the graph.
    4. Determine the value of Planck's constant times the speed of light (hc) in electron volt nanometers (eVnm).

The Physics Hypertextbook

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