Activity 3: How Does the Conservation of Energy Apply to Detecting X-Rays?

Time required: 30 min – 2 hours. Little or no prep time.

• Apply the law of conservation of energy to explain common, practical phenomena.
• Relate the energy of an x-ray photon to the temperature change when the x-ray is absorbed.

Standards:
National Science Education Standards:
Standard B: Interactions between matter and energy

1. Waves, including sound and seismic waves, waves on water, and light waves, have energy and can transfer energy when they interact with matter.
2. Electromagnetic waves result when a charged object is accelerated or decelerated. Electromagnetic waves include radio waves (the longest wavelength), microwaves, infrared radiation (radiant heat), visible light, ultraviolet radiation, x-rays, and gamma rays. The energy of electromagnetic waves is carried in packets whose magnitude is inversely proportional to the wavelength.
   • Compare regions of the electromagnetic spectrum.

Overview:

For a description of how the XRS works and how the absorber and thermistor work together, go to http://heasarc.gsfc.nasa.gov/docs/suzaku-epo/science/instruments/how_xrs.html - "How does the XRS work?"

Some facts that deal with the properties of the material absorbing the x-rays:

Material	HgTe
Density of HgTe	8.0 x 107 g/m3 or 0.008 g/mm3
Dimensions of absorber	0.624 mm x 0.624 mm x 0.008 mm
Heat Capacity of absorber (C)	0.11 pJ / K
Power transfer between absorber and thermistor (temperature sensing device)	61 pW/ K

1. Calculate the total mass of the absorber.
   Answer: 25 µg or 2.5 x 10^-5 g
2. Calculate the amount of energy for a 1.0 keV photon.
   Answer: Recall that 1 eV = 1.6 x 10^-19 J. So for 1 keV, the energy is 1.6 x 10^-16 J
3. Calculate the temperature change caused by the detection of this 1.0 keV photon. [Hint: The equation ΔQ = CΔT will allow us to calculate the change in temperature.]
   Answer: 1.45 x 10^-3 K or 1.45 mK
4. Why is it a key concept in the functioning of this detector that it be EXTREMELY cold? Consider the ratio of the change in temperature that you just found to the surrounding temperature. Use mathematical reasoning in your answer.
   Answer: The temperature difference is so small that it is insignificant compared to temperatures that are many orders of magnitude greater. Thus, the XRS must operate at the lowest possible temperature to maximize the possibility of detecting x-rays and differentiating their energies. Note: the operating temperature for the unit is 0.06 K or 60 mK, which is still about 40 times greater than the temperature increase from the 1.0 keV photon.
5. How many x-rays would have to hit the detector to raise the temperature 1.0 K, if we assume that no heat is flowing out of the detector? Hint: Divide 1.0 K by your answer to #3.
   Answer: approximately 690 photons
6. If the absorber absorbed a 1.0 keV X-ray photon every second, how much energy would have to be dissipated to keep the detector at constant temperature?
   Answer: 1.6 x 10^-16 J/s
7. If the energy was transferred from the absorber to the thermistor, what would the energy transfer rate need to be (of course rate of energy transfer is the same as powerJ)?
   Answer: 1.6 x 10^-16 J/s
8. Suppose the absorber collected 100 x-ray photons per second, with each x-ray being of energy of 1.5 keV. What would be the answers for #6 and #7 above?
   Answer: 2.4 x 10^-14 J/s
9. Recovery time is the time needed for the absorbed energy to be removed from the absorbers. What is the recovery time if the instrument detects 100 x-ray photons with an average energy of 1.5 keV each ? Hint: Note that the "Power Transfer Rate" provides how much energy may be dissipated in a given time period.
   Answer: The characteristic time is given by the ratio of the Heat Capacity to the Power Transfer: 0.11 x 10^-12 (J/K) / 61 x 10^-12 (J/K-s) = 1.8 x 10^-3 s or 1.8 ms
10. Iron (Fe) tends to produce photons of 6.701 keV and 6.973 keV. Answer questions 2, 3, and 5-7 for these two values. You may wish to have students use a spreadsheet where each calculation is done in a new column.
    Answer: For the 6.701 keV photon
    2. 1.07 x 10^-15 J
    3. 1.01 x 10^-2 K
    5. 103 photons
    6. 1.07 x 10^-15 J/s
    7. 1.07 x 10^-15 J/s
    
    For the 6.973 keV photon
    2. 1.12 x 10^-15 J
    3. 1.05 x 10^-2 K
    5. 98 photons
    6. 1.12 x 10^-15 J/s
    7. 1.12 x 10^-15 J/s
    

11. Other common elements have "signature" spectroscopic lines that are within the range of the XRS. The table below summarizes these lines:

    Energies of Elemental Spectral Line Features
    

    Element	Energy (keV)
    O	0.547
    Ne	0.922
    Mg	1.352
    Si	1.865
    S	2.461
    Ar	3.140
    Ca	3.903
    Fe	6.701

    Complete the above calculations for each of the spectral peaks indicated to the left. You may want to divide the work among individuals or groups and share results later. (Solutions.)

Extension:

1. Gamma rays are even more highly energetic than x-rays. Suppose 50 photons of 100 keV are absorbed. Calculate #1-7 except #4. What possible effects might such a bombardment have on the absorbers and their response times?
2. Observe the graph below. This was the first image taken from another Suzaku instrument, one of four x-ray imaging spectrometers (XIS). Print out the image. List the peaks that you can identify from the image that correspond to the peaks that we would expect to find from elements in the table. Which element(s) are indicated by the graph in the image?
3. Refer to question #9 from the activity. Make a scientific judgment based on what you know: Does the answer seem like a reasonable response time to be able to dissipate bombardment of x-rays as described in #8 above? What is or would be the basis for your judgment?

This is the first image taken by the XIS-1 aboard Suzaku. The image selected was that of a supernova remnant known as E0102-72.3, and was taken on Aug. 12 and 13, 2005. What elements do we see evidence for in this image? The circled area highlights increased intensity in a region of the spectrum providing evidence for the presence of oxygen in the remnant.

Student Worksheet

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