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HARTNELL AST 1 - Blackbody Spectrum and Wein's Law Laboratory-2

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Blackbody Spectrum and Wein’s Law Laboratory ModuleIntroduction In this lab, you'll play around with a simulator that lets you see what the blackbody spectrum of differentobjects look like. You will also use Wein’s law to calculate the temperature of the objects and learn the relationship between the temperature and the peak wavelength that the object produces.Open up the blackbody simulator located here: this simulation, the y- axis of the graph represents the Spectral Power Density (or brightness) and the x-axis represents the wavelength in units of µm (microns). You can adjust the scale of the graph by usingthe + or - symbol near each of the axes. Use these to scale the graph so that you can see the entire blackbody curve (red curve). To the right are some objects with different temperatures. Move the arrowupwards to increase the temperature. The corresponding temperature in Kelvins is listed above. Superposed on the black body curve is the rainbow with the seven major colors (violet, indigo, blue, green, yellow, orange, and red). Keep in mind that each color of the rainbow corresponds to different wavelengths. The values of the wavelength of the colors can be found beneath on the x-axis. Equation 1: Wein’s Law The mathematical relationship between the peak wavelength that a black body emits and its temperature is called Wein's Law.ʎpeak=2898 µmKTIn this equation, ʎpeak represents the peak wavelength (wavelength with maximum brightness) of the blackbody spectrum, T represents the temperature in units of Kelvins. Kelvin is a unit of temperature that scientists use. Note: the µmK in the equation are just units in the equation, where if you plug in thetemperature, T, in Kelvins (K), then you are left with the unit of peak wavelength µm.If you can measure the peak wavelength emitted by the black body, you can calculate the temperature ofthe object directly.Exercises and QuestionsExercise: Use the arrow to increase the temperature to different values. Question 1:a) What happens to the peak wavelength of the blackbody as you increase the temperature? Does it shift to shorter or longer wavelengths? b) What happens to the spectral power density (brightness) of the blackbody as you increase the temperature? Does it increase or decrease?Exercise: Use Wein’s Law (Equation 1) to calculate the temperature for each of the peak wavelengths (ʎpeak). Put your temperature values corresponding to each peak wavelength in the Table 1. Important note, to solve for temperature, T, you need to switch the position of T and ʎpeak in the equation. Don’t forget to put the units.Make sure to show your work for one of the calculations as a sample calculation in your lab write up. This includes writing Wein’s equation and solving for T. Once you determine the temperature, use the arrow to slide to the temperature that matches with your answer. Look at the graph to see which color of the rainbow the curve peaks at. Please refer to the lecture if you forget what the seven colors of the rainbow are. Write down what the peak color is in Table 1.Table 1.ʎpeak (µm) Temperature (K) Peak Color0.40 µm0.45 µm0.50 µm0.60 µm0.70 µmYou should now check your work by selecting Graph Values (located in the square at the top above the camera icon) in the simulation. Move the arrow to match the temperatures on your table and compare the value of the peak wavelength (ʎpeak ) on the x-axis (should be highlighted in yellow) to the value of the ʎpeak in Table 1 for each temperature. If they are very close or they match, then you are correct! If they are off, then you made a mistake in your calculations. If this is the case, try to figure out what mistake you made. If you cannot figure it out on your own, you should contact me for help, but make sure that you take a picture of your calculations and send it to me before asking me. Question 2: a) What peak color is associated with the coolest temperature? _____________b) What peak color is associated with the hottest temperature? ______________Question 3: What is the temperature of our Sun? ______________Question 4: a) What is the peak wavelength of our Sun? _____________b) What color is associated with this peak wavelength? ______________c) Why doesn’t the Sun appear to be that color? Hint, if you forgot the answer, make sure to review the lecture. Question 4 (#2): Five billion years from now, when our Sun runs out of fuel for nuclear reactions, it will expand in size to engulf the Earth. As it swells up, it will turn red. What will happen to the temperature of our Sun when it turns red? Question 5: Compare the properties of Sirius A (a star that is twice as massive than our Sun). Discuss the differences that you see between the temperature, brightness, and peak color of Sirius A as compared toour Sun. Use the blackbody curve to help you answer the question.Question 6: Describe specifically how Astronomers are able to determine the temperatures of stars in the sky. Extra Credit Question (+1pt E.C.): You can convert the temperature from Kelvins to Fahrenheit using this equation: Equation 2: Tf=(Tk−273)95+32 Here Tf is the Fahrenheit temperature and Tk is the Kelvin temperature.Use this equation to calculate the temperature of a) the light bulb, b) the Sun, and c) Sirius A in Fahrenheit. Please show your work for

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