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Blackbody radiation and greenhouse effect 5.2 Lab: Optics 1 Part 1: Blackbody Radiation and the Greenhouse Effect Much of the light we see comes from atoms and molecules, which are so hot they vibrate and collide with high-energy motion. Every time an atom changes the direction it is moving, the acceleration of electrons at the exterior of the atom causes light to be emitted. Objects at temperatures like the surface of the sun emit light in the visible part of the spectrum. For a better understanding of what blackbody radiation is, read section 8.6 of the textbook (pp. 310–313), paying particular attention to the formula for the wavelength that is given the maximum power (p. 311) and example 8.4 which uses it. A good basic video explanation can be found in Why Do Hot Objects Glow? - Black Body Radiation . Two equations link Electromagnetic Energy ( E ) to Photon Frequency ( f ). To explain the relation between the blackbody spectrum and temperature (which remember is related to the amount of internal energy in a body), the energy of light had to be quantized using the equation: E = hf . This led to the recognition that while light is a wave it also has properties similar to particles. A particle of light is called a photon and it is localized in space as it moves at the speed of light ( 3 × 10 8 m s ). The letter h stands for Planck’s Constant and is a fixed number given as 6.63 × 10 − 34 J Hz or sometimes given with the unit Js . This is the energy in Joules of a photon with a frequency of 1 Hz. Higher frequencies have proportionately higher energies. Since the energy of photons is so small (even high energy gamma rays have energies that are still a tiny fraction of a Joule), a smaller energy unit is often used, called an electronVolt ( eV ), meaning the KE energy of a single electron accelerated by a 1 Volt electric field. Plank’s Constant in eV is h = 4.14 × 10 − 15 eV Hz . The second important equation is the relation between the wavelength of light that is most commonly emitted from a blackbody at a particular Kelvin temperature. λ = 0.0029 Km T If we use the relationship between wavelength, frequency, and the speed of light ( c = λf ) to express this as a frequency of peak emitted photons: 1

Blackbody radiation and greenhouse effect λ = 0.0029 Km T = c f Solving the right side for the frequency, we get f = c 0.0029 Km T = ( 1.034 × 10 11 Hz K ) T From this we see that the hotter the object, the higher the peak photon frequency. Traditionally, blackbody radiation charts have the photon wavelength along the horizontal axis, so higher energy light is on the left side. The textbook also gives an equation that shows that the power of the radiated light (the energy emitted per second) is proportional to the area of the object and to the Kelvin temperature to the 4 th power. To see the relationship between temperature and frequency of sunlight and light emitted by the earth itself, open the simulation Blackbody Spectrum : The graph shows the distribution of light in terms of wavelength. In this chart, the farther to the left, the higher the frequency and energy of photons emitted. The vertical direction represents intensity of light. (See Figure 8.38 on p. 312.) Check the boxes labeled “Graph Values” and “Labels” to see the specific wavelength of the peak intensity and in what part of the electromagnetic spectrum the wavelength falls. Set the temperature slider so the temperature is 5800 K , about the temperature of the surface of the sun. This should be the default temperature when the simulation opens. If you’ve set the “Graph Values” check box, the simulation should identify the wavelength of the peak intensity along the horizontal axis . We can also calculate this wavelength: λ = 0.0029 Km T . Record the wavelength of the peak intensity here. Make sure you’ve recorded the value along the horizontal axis, not the vertical axis! Sun @ 5800 K λ = 0.0000005 µm Convert to meters λ = 0.0000005 × 10 - 6 m Use scientific notation for the wavelength in meters. Note: the symbol e to stand for × 10 ❑ is not proper in expressing measurements in scientific notation except in calculators and spreadsheets. Incorrect 3e8; correct 3×10^8. Unit conversion: 1 µm = 1 × 10 − 6 m , so to convert µm to m replace the micrometer unit with 10 − 6 m . 2

Blackbody radiation and greenhouse effect Example: an incandescent light bulb has peak wavelength of 0.966 µm so converted to m this would be 0.966 × 10 − 6 m = 9.66 × 10 − 7 m . For reference, 1 µm is about the size of a speck of dust or a bacterium. Use this to calculate the frequency of the light : f = c λ = 3 × 10 8 m s λ ; If wavelength is in meters, frequency should come out in Hertz (Hz). Example: the peak frequency of the light bulb example would be 3 × 10 8 m s 9.66 × 10 − 7 m = 3.11 × 10 14 Hz . Frequency f = 0.5 Use scientific notation for frequency in standard units. If you have checked the “labels” checkbox on the simulation graph, it shows the parts of the electromagnetic spectrum along the top. Use that information to answer the next question. In what part of the electromagnetic spectrum is the peak of the graph? a Radio b Microwave c Infrared X d Visible e Ultraviolet f X-Ray g Gamma Ray Adjust the temperature to 300 K, ground temperature on a warm day. At first glance, it appears nothing is graphed for this low temperature. But if you adjust the scale of the graph , you can see the curve. At the bottom right of the graph are two magnifying glass icons, one + and one -. Click on the “minus magnifier” three times. Then click on the “plus magnifier” at the upper left of the graph until you can see the curve clearly (9 times) . Record the wavelength and calculate the frequency as before . Earth @ 300 K λ = 9.666666666667 × 10 -6 µm Convert to meters λ = 9.666666666666998 76e-6 m Frequency f = 9.659 Use scientific notation for quantities in standard units. 3

Blackbody radiation and greenhouse effect What part of the electromagnetic spectrum is the peak of the graph? a Radio b Microwave X c Infrared d Visible e Ultraviolet f X-Ray g Gamma Ray Note: the usual wavelength ranges of visible light and infrared light are given in the table below, following the usual frequency ranges. Check your calculated wavelength and frequency values to be sure you are in the right range. Type of radiation Low wavelength High Wavelength Visible 0.4 µm 0.8 µm 4.0 × 10 − 7 m 8.0 × 10 − 7 m Infrared 0.8 µm 1000 µm 8.0 × 10 − 7 m 1 × 10 − 3 m Low Frequency High Frequency Visible 4 × 10 14 Hz 8 × 10 14 Hz Infrared 3 × 10 9 Hz 4 × 10 14 Hz If your values in the table on page 2 and 3 do not fit with the regions of the spectrum indicated on the simulation graph, check your math. The X-ray and Gamma Ray parts of the spectrum are higher in frequency than visible light and shorter in wavelength. Few objects in the universe are hot enough to emit these types of radiation except in supernova explosions and other violent stellar events. Radio and Microwave radiation are only emitted by very cool objects and have low frequencies and long wavelengths compared to IR, visible, and UV light. Review the infographic on the next page. The entire spectrum is depicted, with illustrations as well, indicating their wavelengths when compared to physical objects. Also note the illustration indicating the regions of spectrum to which the atmosphere is mostly transparent but also to which it’s opaque (at the bottom). [See next page.] 4

Blackbody radiation and greenhouse effect Electromagnetic Spectrum: The entire electromagnetic spectrum, running from long- wavelength, low-frequency radio waves to short-wavelength, high-frequency gamma rays. (Chaisson, 20130909, p. 66) 5