This exercise is the same as the Interactive exercise #2 that is located in Module 2 Lecture D.

• Launch the Periodic Table
  1. Click on an element to bring up its spectra in the two vertical windows.
  2. Mouse over the features to read off the wavelengths of those features
  3. Note that may more features are visible in Terrestrial Lab spectroscopy than in an actual stellar atmosphere. However, the wavelengths of the features are exactly the same.
  
  
  

• Launch the Absorption Line Simulator. (JAVA JNLP file - hopefully it launches)

  Set the temperature to 10,000 degrees.

  To the right is an example screen shot for element AX showing the 4 spectral lines (wavelengths omitted) that you would need to match up with the periodic table of elements. The white line at the top labelled 4105/0 is what you slide up and down to measure the wavelengths of the 4 dark lines. Your response to this question should include

  • the wavelengths of the identified lines in AX and BX.
  • Which element in the periodic table that you think corresponds to AX and BX (remember, AX and BX both are elements with atomic numbers less than 20)

  Enter the four wavelengths for AX and BX into the RTF template in the appropriate column as well as your choice for elements, from the Periodic Table, that best correspond to AX and BX.

  
  
  
  
  
  
  
  
  

  Question 2:

  Refer to the right diagram. The electron is pictured as residing in the ground state. Answer this series of questions for the indicated scenarios.

  a) Suppose the electron is excited to the highest state (energy level = 12). It can only stay in that state for a very small amount of time before it wants to go back to the ground state. List all the possible values of photon energies that this atom "emit" on its return to the ground state.
  
  
  

  b) If an incoming photon has energy = 9 units and the electron is in the ground state (as pictured), what will happen to the incoming photon and the electron?

  
  
  c) if the electron is in the first excited state (e.g. energy level =5) and an incoming photon of energy = 5 units hits the atom, what will happen to that photon and the electron?

  
  
  
  
  
  
  
  
  
  Question 3. This refers to the material in Module 3 Lecture A as related to the determination of stellar parallax by Tycho.

  Open the simulation. (FLASH based)

  At the bottom is your detector, in this case 3 independent pixels. The eye above reflects the orbit of the Earth around the Sun. The angle is the parallax angle. In order for a parallax to be detected, the Star has to move at least one independent pixel. In this default case, there is no detection (the star is too far away and/or the resolution of the detector is too imprecise).

  The course grid simulates measurements from the ground through our atmosphere.

  The Fine Grid refers to measurements made from space.

  Separation refers to distance from the Earth to the star; smaller values are larger distances.

  a) With the course grid checked (i.e. 3 pixels), what is the required minimum separation (i.e. the distance to the star) to produce a detection. Increment the seperation by clicking on the arrows?

  b) Leaving the separation at that minimum value, click on Fine Grid. How many pixels (e.g. resolution elements) of movement is there in this case?

  c) With the fine grid, explain whether or not you can detect stellar parallax at the largest seperation (e.g. seperation = 1).

  d) Now explain why space based observations offer a much better way of detecting stellar parallax than can be done from the ground.

  Question 4

  We have a calibrating star - let's call this star Janelle.

  Janelle has the following properties:

  • distance from observer = 20 light years
  • flux on our digital detector = 4 Energy Units (energy units are arbitrary)
  • Intrinsic Energy Output (Luminosity) = 10 solar luminosities
  As an example to how to solve these problems, using scaling from a calibrating source, consider this case. We observe Star Example - it has a flux on my detector of 8 units. Independent evidence shows that star Example has an intrinsic energy output of 2 solar luminosites. What is the distance to star Example?

  Well what do we know about star Example compared with our calibrating star Janelle:

  1. First of all, we know that if star Example was at a distance of 20 light years ( the same distance as Janelle), then the observed flux would be 5 times lower. Why, because star Example is intrincially 5 times fainter than star Janelle. So if a 10 solar luminosities at a distance of 20 light years produces a flux of 4 energy units, then a 2 solar luminosity star at the same distance will result in an energy flux of 0.8 units (4/5).

  2. But my observed flux is 8 units, not 0.8 units. Therefore star Example must be at at distance thats closer than 20 light year so that the received flux is higher.

  3. Now I notice that the observed flux (8 energy units) is actually 10 times more than it would be if star Example were at 20 light years (8/.8) = 10.

  4. Now I apply the inverse square law - to increase the flux by a factor of 10, I must move to star closer to me by a factor of the square root of 10. Thus the distance to star Example is 20/ √ 10  or about 6 light years.

  There are four other stars in the sky whose luminosity or distance or energy flux we want to obtain using Janelle as the reference point via the same scaling argument I just went through, You really do have all the information you need to answers these questions.

  Show all work/reasoning in the last column of the table for question 4 in the RTF template in answering these questions:

  Star Zeta is known to have the same Luminosity as Janelle but its observed flux on our detector is 40 Energy Units. What is the distance to the star Zeta?

  Star PoodleMania has a known distance of 50 light years and has a flux on our detector which is the same as Janelle (e.g. 4 energy units). What is the luminosity (in units of solar luminosities) of the star PoodleMania?

  Star WhopperNoodle has a luminosity of 20 solar luminosities and a distance of 20 light years. What is the received energy flux on the detector?

  Star PanCow has a luminosity of 1 solar luminosity and a distance of 1 lightyear. What is the received energy flux on the detector?