1. In an undisturbed natural uranium ore, all the decay chainproducts of uranium-238 have accumulated to their equilibrium concentrations over geological time periods, such that they are all being produced and are decaying away at the same rate. Natural Uranium Contains 99.284 wE\% of u238,0.711 wt \% of u235, and 0.0053 wt % of u254. a. Fill in the missing information in the decay product table befon b. Using the information provided in the decay product table above, What type of equitibrium is estabhshed in the U-238 decay Chain? How do yoy know this will happen? c. Which isotope in this Chain dictates the rate of decay? Why? d. How long would it take for these speyes to establish equilibrium? Hint: Use your understanding of secular equilibrium to estimate this. e. Once this equilibriam is established, what is the rate of decay of each radiaachive species in the U-238 chain (in Kilobecquerel per gram of natural uranium)? The abundance of U238 in natural uranium is 99.284%. Hint: Bq is the number of atoms disintegrating per second or the rate of decay. f. Use a method of your choice to venify your solution in parts (d) and (e) above by checking the activity of 4238 and 4234 after the time estimated above. Hint: To achiere this, you may find the analytical solutions (solve ODEs by hand or use Bateman equation) or find the numerical Solations (using a solver Such as polymath or by writing a script in MATLAB, python etc). Show working. g. What is the total a ctivity of the undisturbed natural uranium ore (in kubbecquerel per gram of natural uranium) once equilibrium has been estabhished? You may neglect Contribution from the achuity of the U-235 decay chain. 1. In an undisturbed natural uranium ore, all the decay chainproducts of uranium-238 have accumulated to their equilibrium concentrations over geological time periods, such that they are all being produced and are decaying away at the same rate. Natural Uranium Contains 99.284 wE\% of u238,0.711 wt \% of u235, and 0.0053 wt % of u254. a. Fill in the missing information in the decay product table befon b. Using the information provided in the decay product table above, What type of equitibrium is estabhshed in the U-238 decay Chain? How do yoy know this will happen? c. Which isotope in this Chain dictates the rate of decay? Why? d. How long would it take for these speyes to establish equilibrium? Hint: Use your understanding of secular equilibrium to estimate this. e. Once this equilibriam is established, what is the rate of decay of each radiaachive species in the U-238 chain (in Kilobecquerel per gram of natural uranium)? The abundance of U238 in natural uranium is 99.284%. Hint: Bq is the number of atoms disintegrating per second or the rate of decay. f. Use a method of your choice to venify your solution in parts (d) and (e) above by checking the activity of 4238 and 4234 after the time estimated above. Hint: To achiere this, you may find the analytical solutions (solve ODEs by hand or use Bateman equation) or find the numerical Solations (using a solver Such as polymath or by writing a script in MATLAB, python etc). Show working. g. What is the total a ctivity of the undisturbed natural uranium ore (in kubbecquerel per gram of natural uranium) once equilibrium has been estabhished? You may neglect Contribution from the achuity of the U-235 decay chain