Kayla's+Lab

=Kayla's Labs = toc

Tuesday, September 14, 2010 - Blackbody Radiation
**Blackbody Radiation - Lab. 1 ** Light, Waves, Wavelengths, and Frequency
 * Part I: **

 This part of the lab is designed to demonstrate the relationship between period and frequency for a light wave. Period is the time needed to complete one full cycle and frequency is the number of cycles per second (also called Hertz or abbreviated to Hz). This means that period (T) and frequency (n) are each the reciprocal of the other.

Cycle Duration ||= T = 1/v ||= s ||= T = **λ** / c ||
 * = SUMMARY OF SYMBOLS, PARAMETERS and VALUES ||
 * = Physical Value ||= Symbol ||= Unit ||= Formula ||
 * = Frequency ||= ν = 1/T ||= Hz = 1/s ||= v = c /**λ** ||
 * = Wavelength ||= **λ** ||= m ||= **λ** = c / f ||
 * = Time Period or
 * = Wave Speed ||= c ||= m/s ||= c = **λ** * n ||

 Now look at the simulation below. Notice that the x-axis in this simulation is time (t) whereas, your textbook Climate Change uses the same information but displays it with a x-axis showing distance. A set of waves is shown in the model below, each one having a frequency that doubles the previous one (or a period that is half the previous one). You can make the waves overlap by clicking in the square beside the word "overlap" and undo the overlap by clicking in the box to remove the check mark. You can also vary period and frequency using the slider bar. If you let your cursor rest over one of the lines it will give you the frequency of that line at that setting, which, because they are reciprocals also give you the period. The questions below should be easily answered from Chapter 2 of Climate Change and the simulation. However, feel free to use reliable Internet sources if you would prefer.


 * Questions: **

1. What is wavenumber?  Wavenumber, which is similar to frequency, refers to the amount (number) of cycles per centimeter of legnth. The difference bewteen frequecny and  time is that it is measure with space and not time.

 2. Why is wavenumber preferred by scientists who discuss IR light?  Using wavenumber is preferred by scientist who discuss IR light because it is a central unit of measure that can be used by everyone, rather than having  to use both frequency and wave legnth.

 3. What is the period (T) of IR radiation (wavelength around 10 micrometers)? <span style="font-family: 'Comic Sans MS',cursive;"> t = 1/v where t = wavelenght/c <span style="font-family: 'Comic Sans MS',cursive;"> t = 10 micrometers / 3*10^8 meters = 10/300,000,000*1,000,000,000 = 0.00000000000003

<span style="font-family: 'Comic Sans MS',cursive;"> 4. Infrared light has a wavelength of about 10 microns. What is its wavenumber in cm-1? <span style="font-family: 'Comic Sans MS',cursive;"> 100,000 cm^-1

<span style="font-family: 'Comic Sans MS',cursive;"> 5. Visible light has a wavelength of about 0.5 microns. Whas is its frequency in Hz (cycles per second)? <span style="font-family: 'Comic Sans MS',cursive;"> 3*10^8?0.5*1,000,000,000 microns/ meter= 600,000,000,000,000 Hz

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;"> Blackbody Spectrum - a link between wavelength and heat
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">Part II: **

<span style="font-family: 'Comic Sans MS',cursive;">Matter that is able to absorb or emit all frequencies of light is called a blackbody. All blackbodies (I know they don't come to mind as an examples of a blackbodies right away, but think "The Sun" and 'The Earth" here. We will treat them both as blackbodies in this exercise) heated to the same temperature emit thermal radiation with the same em-spectrum. If the Earth were heated to the same temperature as the Sun they would both emit a spectrum of light with a peak in intensity in the visible range. However, they are not heated to the same temperature and they have clearly different peak emission ranges.

<span style="font-family: 'Comic Sans MS',cursive;"> Planck's law gives the intensity of the energy radiated by a blackbody as a function of wavelength and temperature. As the temperature of a blackbody increases, the peak wavelength shifts from red to blue. Extremely hot blackbodies emit most of their energy in the ultraviolet range, while cool blackbodies emit primarily in the infrared. Stars behave like blackbodies, so their color follows their temperature, too. Stars similar to theSun (with a temperature of about 5800 Kelvin) appear nearly white because the visible part of the intensity curve is nearly flat.

<span style="font-family: 'Comic Sans MS',cursive;"> Below is an interactive figure that will let you experiment a bit with the idea that the temperature of the body determines the wavelength of light that will be emitted from that body.

<span style="font-family: 'Comic Sans MS',cursive;"> Notice that in the model below, the y-axis is in units of "normalized intensity". That just means that in each case the maximum intensity of the radiation is set as equal to "1", no matter what the true intensity is. This allows you to compare the spectra of blackbodies over a very large range of irradiance intensities.


 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Questions: **

<span style="font-family: 'Comic Sans MS',cursive;"> 1) Notice the units that wavelength are shown in -- nanometers. Sometimes wavelengths are reported in micrometers, sometimes in centimeters and sometimes even in meters. Explain when and why it might be more convenient to use units of nanometers and when it might be convenient to use units of meters. <span style="font-family: 'Comic Sans MS',cursive;">If in a situation in which the wavelegnth needs to be measured, it would make more sense to measure using the closest unit. For exampleif you were to measure the wavelegnth as 78,000,000,000 nanometers, then it would make more sense to just convert that to 78 meters.

<span style="font-family: 'Comic Sans MS',cursive;"> 2) As temperture is decreased from the highest possible temperature on this simulation, describe what happens to the peak wavelength of light emitted by a blackbody? <span style="font-family: 'Comic Sans MS',cursive;">As the temperature decreases from the highest possible temperature on this simulation, the wavelegnth increases in nanometers (up to 1000) as it moves from ultrviolet radiation all the way to visible light.

<span style="font-family: 'Comic Sans MS',cursive;"> 3) Which is hotter, a blackbody emitting radiation in the visible light range of wavelengths or a blackbody emitting in the infrared range of wavelengths? Explain your answer based on the information you gathered in Parts I & II. <span style="font-family: 'Comic Sans MS',cursive;">Visible light would be hotter. This is because IR has a longer wavelength and shorter frequency than that of visible light.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">Comparing Sun and the Earth Shine
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">Part III.A. **

<span style="font-family: 'Comic Sans MS',cursive;">As the temperature of a blackbody increases, the maximum wavelength decreases since the blackbody emits higher frequency/energy photons. The distribution also becomes less spread out at higher temperatures as the radiated energy becomes more focused around the maximum intensity wavelength.

<span style="font-family: 'Comic Sans MS',cursive;"> Definitions helpful to understand subsequent graphs:

<span style="font-family: 'Comic Sans MS',cursive;"> There are a confusing array of standard ways to show the amount of energy incident on or emitted from a blackbody. Here are a few that should help with the following figures.

<span style="font-family: 'Comic Sans MS',cursive;"> Irradiance is the amount of light energy incident on a given area of surface in a given amount of time, measured in Watts/m^2.

<span style="font-family: 'Comic Sans MS',cursive;"> "Irradiance" is used when the electromagnetic radiation is incident on the surface or when the radiation is emerging from the surface. The SI units for all of these are watts per square meter (W/m^2). All of these quantities characterize the total amount of radiation present, at all frequencies.

<span style="font-family: 'Comic Sans MS',cursive;"> It is also common to consider each frequency in the spectrum separately. When this is done for radiation incident on a surface, it is called spectral irradiance, and has SI units W/m^3 for the wavelength (that is in the denominator, m^2 multiplied by m of wavelength --> m^3.

<span style="font-family: 'Comic Sans MS',cursive;"> Radiative flux, or radiative flux density, is the amount of energy moving in the form of photons or other elementary particles at a certain distance from the source per unit of area per second and can be considered for each wavelength.

<span style="font-family: 'Comic Sans MS',cursive;"> The Sun's radiative flux in the non-interactive figure below ( in units of W/m^2/ wavelength in micrometers) are scaled down by a factor of 10^6 so that both spectra can be seen on the graph together.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">Comparing Sun and Earth Shine
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">Part III. B. **

<span style="font-family: 'Comic Sans MS',cursive;">Now take a look at the figure below.

<span style="font-family: 'Comic Sans MS',cursive;"> 1) It is very similar to the non-interactive figure above but there are some key differences. Leave out the line labeled " lSubscript[, max]" and the interactivity of this figure as compared to the one above. What are the main differences between the two figures? <span style="font-family: 'Comic Sans MS',cursive;"> The main differences are the scales and overall shape of graphs. The differences in scale is that on the Wavelegnth axis, on the Interactive model the scale is regular (the numbers increase steadily at the same pace) while the still model's scale is logarithmic (as in it steadily increases more and more each increment it goes up). This leads to the second difference. The difference in shape is a product of the different scalings used on the "Y" axis.

<span style="font-family: 'Comic Sans MS',cursive;"> 2) Set the slider bar on the figure below to a temperature of 3500 K. What type of electromagnetic radiation would you expect to find in the range of the emissions of this spectrum (length units on the y-axis may need some conversion and thought)? What is the peak irradiance? <span style="font-family: 'Comic Sans MS',cursive;"> I would expect to find visible and IR. This is because the peak irradiance is approximately 750, which means that is right in between both the IR and visible light ranges.

<span style="font-family: 'Comic Sans MS',cursive;"> 3) Now set the temperature to 5100 K. What type of electromagnetic radiation would you expect find in the range of the peak emission of this spectrum? What is the peak irradiance? <span style="font-family: 'Comic Sans MS',cursive;"> I would expect to find mostly visible light. The is because the peak radiance is apporixmatley around 550.

<span style="font-family: 'Comic Sans MS',cursive;"> 4) Explain the differences in the shapes of the spectra at these two temperatues. <span style="font-family: 'Comic Sans MS',cursive;"> The shape of the spectra at 5,100K is a whole lot steeper and taller than that of the spectra at 3,500K.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;"> Greenhouse Gas and Earth Shine
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">Part IV: **

<span style="font-family: 'Comic Sans MS',cursive;">How does all of this related to climate change science again?

<span style="font-family: 'Comic Sans MS',cursive;"> The Earth is warmed by electromagnetic light that travels 93 million miles from the sun at the speed of light ( 3 x 10^10 cm/second or, for Gray and Allen, 3 x 10^8 m/s) with a peak irradiance in the visible light range.

<span style="font-family: 'Comic Sans MS',cursive;"> The part of the Earth to recieve that radiation is the atmosphere. Most of the gases in the atmosphere are "invisible" to light in this frequency range and so the radiation pass through the atmosphere and gets to the solid and liquid surfaces of the Earth where energy from the sun is absorbed and reflected depending upon the specific materials. The surfaces heat up and re-emit that energy but the temperature of the Earth, as a result of these processes, is much lower than that of the Sun, so the re-emitted radiation peaks in the IR portion of the spectrum (Planck's Law). As this re-emitted, longer wavelength, IR-radiation passes into the atmosphere, it is no longer "invisible" to several of the gases that form the atmosphere, including carbon dioxide, water vapor, methane, chlorofluorocarbons and nitrous oxide. These gases absorb the IR energy and store it in their bonds (remember? like a battery...) and it is re-re-emitted back into the atmosphere further heating the surface layers of the Earth.

<span style="font-family: 'Comic Sans MS',cursive;"> Watch an animation of this process by clicking here. (Sorry, I couldn't the animation to post on Mathematica).

<span style="font-family: 'Comic Sans MS',cursive;">1) Use the image below to describe how this would work with a closed up car parked in a sunny spot on cool day. Put in labels where they are need to show the different types of radiation and what happens to it. How good an analogy do think this is for the Greenhouse Effect on Earth? Explain.

//<span style="font-family: 'Comic Sans MS',cursive;"> **If you are having trouble labeling the image in Mathematica, just use words and the colors of the various lines and arrows to describe the labeling** //

<span style="font-family: 'Comic Sans MS',cursive;">When the visible light (depicted as a yellow arrow) hits the windsheild of a car (depicted as the light blue arrow) some of the light is absorbed and some is reflected. The IR, that was mixed in along with ultrviolet light and visible light, is reflected off the windshied. The visible light is then absorbed by the car's interior, such as the seats, dashboard, etc. (depicted as the balck-grey). These items then give off IR (along with othe forms of radiations). Becuase the IR can't escape throguh the glass, the car essentally becomes a small scale model of the Greenhouse Effect.