NUC-490 Written Assignment 4 (Module 5) Page 1 of 9 Student Name: Module 5 - Assignment Exercises The following 10 exercises build upon your previous education and training, and the Summary Examples you studied from this Module. These exercises will challenge you to put all those elements together. Instructions: Attempt all 10 exercises. Make sure you answer all parts of each question. These exercises are \"open reference\". You may use text book(s), the internet, and the example materials you studied at the beginning of this module. Do your own work. While you may use other referenced resources, this module is an assessment of your knowledge and ability. Show all your work. Do not leave your mentor wondering how you got from one step to the next. Submit your solutions electronically using scanned images, preferably pdf, of your work. Or you can use equation editor such as MathType to enter your solutions directly below. Exercise 1 - Given that Beryllium-11 ( (a) what percentage of a sample of 11 4 Be ) has a half-life = 13.81 sec, 11 4 Be will remain after 25 seconds? (b) what percentage will have decayed? Exercise 2 - A certain radioactive material decays at a rate proportional to the amount present. Initially there is 50 milligrams of the material present. After two hours, the amount of radioactive material has lost 10% of its original mass. a) Calculate the value of the decay constant, . b) Find the half-life of the material. NUC-490 Written Assignment 4 (Module 5) Page 2 of 9 NUC-490 Written Assignment 4 (Module 5) Page 3 of 9 Semi-Log plot of radioactive decay 10 9 8 7 6 5 4 Number of radioactive atoms N X 1020 3 2 1 0 1 2 3 4 5 6 Time (hours) Exercise 3 Use the Semi-Log Plot of Radioactive Decay above to determine the half-life and the decay constant of the sample. (a) Choose two points and calculate the decay constant and half-life from the exponential decay equation. (b) Check your answer by estimating the half-life directly from the graph. NUC-490 Written Assignment 4 (Module 5) Page 4 of 9 Exercise 4 The attenuated intensity I of a neutron beam normally incident on a certain shielding material is proportional to the intensity of the beam as it passes (the distance x) through the shield, i.e. dI =mI dx Where m is the constant of proportionality. If a 25 cm thick shield of this material attenuates the beam by a factor of 1,000, what thickness of the material is required to attenuate the beam by a factor of 5,000? Assume the incident beam has an intensity of I o when it enters the shield. Exercise 5 Given a radioactive particle that encounters a shielding barrier, it is known to decelerate and come to rest within the shielding in 6 microseconds (6 s). In this example, presume the distance (d in microns (m)) the particle will travel in the time period after hitting the shielding is given by the following equation. Given the bounds t0 = 0 s and tmax = 6 s 3 2 d=t 18 t +108 t (a) What is the maximum distance the particle will travel into the shielding? (b) What is the velocity of the particle at t = 4 s? (c) What is the acceleration of the particle at t = 3 s? Exercise 6 Given the velocity function of a particle to be v ( t )=4 e2 t2 NUC-490 Written Assignment 4 (Module 5) Page 5 of 9 (a) Find the position function, s(t), that describes where the particle will be at time t in microseconds (s). (b) Given that s(0) = 0 microns (m), find s(6 s). Exercise 7 Using the log-log graph below, determine the maximum range of: a. b. c. d. 1.0 MeV beta particles passing through air 3.0 MeV beta particles passing through water 0.8 MeV beta particles passing through plastic 2.0 MeV beta particles passing through lead 1000 Penetration Ability of Beta Radiation Ans: Ans: Ans: Ans: Air NUC-490 Written Assignment 4 (Module 5) Page 6 of 9 Maximum Range of Beta Particles (inches) 100 10 Water Plastic or Lucite Concrete Glass Aluminum 1 Iron Copper Lead 0.1 0.01 0.001 0.1 0.2 0.3 0.5 1.0 Energy (MeV) 2 3 5 10 NUC-490 Written Assignment 4 (Module 5) Page 7 of 9 Exercise 8 - Using the graph below: a. Determine the percentage of Cobalt-60 gamma ray transmitted through a 50 cm thick concrete shield. b. Estimate the thickness of concrete required to attenuate Radium-226 photons to 0.02% of the source strength. 100% Ans: Ans: Transmission of Gamma Radiation through Concrete 10% 1% 0.1% 0.01% Legend 0.001% 1. 2. 3. 4. 5. 0.0001% 1 0 50 cm (19.7\") 2 3 100 cm (39.4\") 4 5 150 cm (59\") 198 Au Ir 137 Cs 60 Co 226 Ra 192 NUC-490 Written Assignment 4 (Module 5) Page 8 of 9 Exercise 9 - The activity of a certain radioactive nuclide is plotted on a semilog graph as a function of time. Use this graphic data to determine: a. The half-life of this radionuclide b. How long it will take for the activity to decrease from 100,000 disintegrations per minute (dpm) to 1000 dpm? c. The activity (dpm) after 88 hours 1 10 Ans: Ans: Ans: Activity vs. Time Activity (dpm) 1 10 1 10 1 10 0 20 40 60 Time (Hours) 80 100 NUC-490 Written Assignment 4 (Module 5) Page 9 of 9 Exercise 10 - A pipe 10 cm in diameter contains steam at 200 . It is covered with an insulating material that is 5 cm thick. This insulating material has a constant of thermal conductivity K = 0.00060 cal/cm 2 sec. The outside surface of the system is 35 . Find the heat loss per hour from a 2 meter length of the pipe. y 35 5 cm 200 x x2 - x1 5 cm