Hofstra 2019 Fall MPHY 214
Rules of the exam
A. There are six questions in this exam.
B. The full marks of this exam are 100 points. It is worth 20% of your final grade.
C. The exam begins on 8:00 am, 11/3/2019 and ends on 12:00 noon, 11/6/2018.
D. You are NOT allowed to discuss your work with other people.
E. Please type your answers in a MS Word document and email me the final document by
F. You need to show all steps to earn full credit. Just putting the answer on the paper is not
G. If you don’t want to type, please write your anwers neatly. You might lose points if I can
not read your writings.
1. Two x-rays detectors were used to measure the intensity of an x-ray souce at the same
location. Each dectior was used to measure the intensity 100 times and the averaged
intensity was the same (1000) for both detectors. However, the standard deviation was 50
for the first dector and 35 for the second detector. Can you explanation what might cause
such discrepancy? (10 points)
2. A -ray h1, is emitted by a radioactive atom in V. The photon undergoes triplet
production, giving kinetic energy T1 and T2 to the electrons and T3 to the positron.
Illustrate the events in the following questions using a circle diagram similar to that
used in the text book, and calculate 𝜖𝑡𝑟 , 𝜀𝑡𝑟
, 𝜀, K, Kc, and D. (10 points)
a. Both electrons leave V with kinetic energy T’1 and T’2. The positron runs its
course in V and still has kinetic energy T’3 when it is annihilated inside V. The
resulting two photons escaped from V
b. Electron 1 stops within the volume and electron2 leaves V with kinetic energy T’2.
The positron also leaves V with kinetic energy T’3 and still has kinetic energy T’’3
when it is annihilated outside V.
3. In radioactive decay from an initially pure parent, the parent’s and daughter’s half-lives
are respectively 𝜏1⁄2,𝑃 and 𝜏1⁄2,𝐷 . Let 𝑡𝑁,𝑒𝑞 be the time when the daughter’s population is
equel to the parent’s population: (20 points)
a. What is the general form for 𝑡𝑁,𝑒𝑞 ? What are the assumptions for your answers?
b. What is 𝑡𝑁,𝑒𝑞 if 𝜏1⁄2,𝑃 = 𝜏1⁄2,𝐷 ?
c. Plot the populations of parent and daughter as a function of time for 𝜏1⁄2,𝑃 and 𝜏1⁄2,𝐷
of you choice when the assumptions in (a) hold true.
d. Plot the populations of parent and daughter as a function of time for 𝜏1⁄2,𝑃 and 𝜏1⁄2,𝐷
of you choice when the assumptions in (a) are violated.
4. What is the average dose (Gy) in an tin foil of thickness 1.2 g/cm2, from being irradiated
perpendicularly by 1012 e/cm2 of energy T0 = 10 MeV. (20 points)
5. Appendix A is the TMR table of the 15X beam of a linear accelerator measures with
𝑆𝐷𝐷 = 100 cm from the source. Solve the following questions for the 10×10 cm2
field size using the Greening’s approximation. Note: there are some typos on the slide
for “Relation between TPR or PDD” for “Andreo CHAPTER 7. X-ray Production and
Quality.” Please check the textbook for the correct formulas. (20 points)
a. What are 𝜇𝑒𝑓𝑓,𝑝
and 𝑧max ?
b. Plot the PDD curve and compare it with the measured PDD in Appendix B.
6. Design an experiment for measuring 𝜇𝑡𝑟 . (20 points)
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