Name__________________________________ Blackbody Radiation Temperature Dependence of the Light Output vs. Wavelength Graph Go to the website – http://www.mi.infm.it/manini/dida/BlackBody.html This is a Java applet which shows a graph of light output vs. wavelength for an object. The slider at the bottom of the applet allows you to control the object’s temperature. The number to the right of the slider is the temperature in Kelvin. Move the slider back and forth and observe what happens to the graph of light output vs. wavelength. Bands of colors show where the wavelengths of visible light are. The smallest wavelength shown on the graph is 0 m and the largest wavelength displayed is 1.00×10−6 m which is in the infrared portion of the electromagnetic spectrum. To the left of the graph is a frame with four colored circles. The top three circles give an indication of how much red(R), green(G), and blue(B) light is being emitted by the object. The fourth circle (Appearance) shows what color the object would actually appear given the fact that all of the emitted colors would be mixed together. Play with this a little bit to see how it works. 1) Set the slider to the temperature of the human body (about 300 Kelvin). What wavelengths of light does the object emit? Would you be able to see any of the light this 300 K object emits? Would you be able to see the emitted light with an infrared camera? 2) Now increase the object’s temperature to 1500 Kelvin. What wavelengths of light are emitted by the object now? How does the amount of infrared light emitted compare to the amount of visible red light emitted? Explain why the object appears red in color. 3) Now increase the object’s temperature to 5000 Kelvin. This is about the temperature of a light bulb filament. What wavelengths of light are emitted by the object now? Explain why the object appears white in color. 4) Now increase the object’s temperature to 10,000 Kelvin. Explain why the object appears blue in color. Notice that as the temperature increases, the appearance of the object goes from red to orange, then to yellow, then to white, and finally to blue. Even though the object emits green light, we never see it as being green. Explain why this is. 5) As you increase the temperature with the slider, explain how the peak wavelength changes? 6) As you decrease the temperature with the slider, explain how the peak wavelength changes? Do not close the simulation you have been using. Simply minimize it so that you can come back to it a little later in the lab. Relationship between Peak Wavelength and Temperature 1) Go to the following website: http://astro.unl.edu/classaction/light.html 2) At the bottom left, click on the “Animations” tab, then select the “Blackbody Curves (NAAP)” simulation. 3) Take a few minutes to learn how the features of this simulation work. Learn how to add and remove curves and change their temperatures. a) Click the “add curve” button one or more times. b) Change the temperature slider. c) Select another curve (click on the curve’s information in the table at right) and change the temperature of this curve. d) Remove all but two curves. 4) Learn the “vertical scale” options. Have two curves in the window. a) Check the “auto scale all curves” option and change the temperature of one curve. b) Check the “auto scale to selected curve” option and change the temperature of one curve. c) Check the “lock scales” option and change the temperature of one curve. 5) Learn the “horizontal scale” options. a) Select the “Horizontal Scale” tab. Note how changing the rightmost limit change the view. Note also that each tick mark represents 100 nm. The other unit you see on the scale is micrometers (m). 1000 nm = 1 m 6) Now create four curves that all show at the same time. Adjust their temperatures to the following values: 3000 K, 3500 K, 4000 K, 4500 K. a) Click the “Indicate Peak Wavelength” option at the right of the simulation. Select the 3000 K curve. At what wavelength does the peak of this spectrum occur? Note that this wavelength is recorded in the table below. b) Repeat for the other curves and fill in the peak wavelength values in the table. Formulate a general rule (one or two sentences) that explains how the peak wavelength changes as the temperatures changes. c) Now, multiply the temperature by the peak wavelength and write this number (in scientific notation to three decimal places) in the third column of the table. The first one has been done for you. What do you notice about these numbers? Temperature (K) 3000 Peak Wavelength (nm) 965.9 Temp.× Peak Wavelength (nm-K) 2.898×106 3500 4000 4500 d) Note that the temperature times the peak wavelength always gives the same number. How could you use this fact to predict the peak wavelength of a blackbody spectrum for any temperature? e) Use your method to predict the peak wavelength for a blackbody at a temperature of 10,000 K. Show your calculation below. f) Test your prediction with the simulator. Was it close? What you have discovered is known as Wien’s Law. It says that the product of the temperature of a blackbody and the peak wavelength of the spectrum is always the same number. How could this possibly be useful? Read on! 7) When we look at the spectrum of light coming from a star, we can easily identify the peak wavelength. The peak wavelengths for the spectra of a few stars are listed in the table below. a) Rank these stars from hottest to coldest. You do not have to calculate anything to do this. If you need a hint, look back at the rule you wrote in part 6(b) of this activity. b) Now, Use what you have learned so far to calculate the surface temperatures of these stars. Record this in the table below. c) Reopen the first simulation you used and figure out what color each of these stars would appear by moving the slider to the right temperature. Put this in the table as well. Star Name Peak Wavelength (nm) Betelgeuse 828.0 Rigel 263.5 Sirius B 118.6 Surface Temp. (K) Color Luminosity and the Light Output vs. Wavelength Graph The total amount of light energy emitted by any object per unit time is called the object’s luminosity. We can determine something about the luminosity of an object by looking at its light output vs. wavelength graph. Consider the graphs shown below for the objects D, E, and F. Radio Microwave Red Infrared Orange Green Yellow Wavelength Violet Blue X-ray Ultraviolet Radio Energy Output Gamma Ray Wavelength Microwave Radio Microwave Wavelength Red Orange Green Yellow Violet Blue X-ray Gamma Ray F Ultraviolet Red Infrared Energy Output Orange Green Yellow Violet Blue X-ray Ultraviolet Gamma Ray D Infrared Energy Output E 1) Which of these objects (D,E, or F) is putting out the greatest total amount of light (i.e. which object has the greatest luminosity)? Explain how you reach your conclusion. 2) Rank the three objects (D,E,F) from lowest luminosity to highest luminosity. Explain your reasoning. 3) A good way to think of the above activity is that the luminosity is related to the total area under the curve on the graph of light output vs. wavelength. With your pen or pencil, shade in the area under the curves for objects D, E, and F. The greater the area under the curve, the greater the overall light output. 4) Bring up the “Blackbody Curves (NAAP)” simulation again and remove all but one curve. Set the temperature of the curve to 5000 K. In the small table at the right of the simulation you can read off the “area under curve.” Record the area under the 5000 K curve in the table below. Change the temperature to 10,000 K and record the area under the curve. Change the temperature to 15,000 K and record the area under the curve. Temperature (K) 5000 10,000 15,000 Area Under Curve (W/m2) 5) Notice that 10,000 K is double 5000 K. When the temperature is doubled, by what factor does the area under the curve increase? To answer this question, take the area under the 10,000 K curve and divide it by the area under the 5000 K curve. 6) Notice that 15,000 K is triple 5000 K. When the temperature is tripled, by what factor does the area under the curve increase? It is well known that the luminosity of an object, and therefore the area under its blackbody curve, is proportional to the temperature of the object raised to the fourth power. More specifically L = ×A×T4 where L is the luminosity of the object, is a constant, A is the surface area of the object, and T is the object’s temperature. 7) According to the above formula, if you double the temperature, by what factor should the luminosity increase? Is this what you observed when the temperature doubled from 5000 K to 10,000 K? 8) According to the above formula, if you triple the temperature, by what factor should the luminosity increase? Is this what you observed when the temperature tripled from 5000 K to 15,000 K? Exercises 1) Below are light output vs. wavelength graphs for two objects, G and H. Energy Output G Radio Microwave Red Infrared Orange Green Yellow Violet Blue X-ray Ultraviolet Gamma Ray H Wavelength a) Compare temperatures of objects G & H. Explain your reasoning. b) Compare the sizes of objects G & H. Explain your reasoning. 2) Below are light output vs. wavelength graphs for two stars, J and K. Radio Microwave Red Infrared Yellow Orange Green Violet Blue X-ray Ultraviolet J Gamma Ray Energy Output K Wavelength a) Compare temperatures of stars J & K. Explain your reasoning. b) Compare the sizes of stars J & K. Explain your reasoning.