WA 10 Dearing

4. Complete the following nuclear equations, and identify X in each case. (15 points) a. 222 Rn → 218 Po + X = 4 2 α b. 231 Th → 231 Pa + X = 0 -1 β c. 226 Ra → 4 He + X = 222 86 Rn d. 14 C → 14 N + X = 0 -1 β e. 20 F → –1 β + X = 20 F 5. Which of the reactions in exercise 4 show alpha decay? Which show beta decay? (5 points) Alpha decay = a, c Beta decay =b, d, e 6. Define half-life. Write the equation relating the half-life of a first-order reaction to the rate constant. (3 points) (Reference: Chang 13.22) Half-life is the time for the radioactivity of a specified isotope to fall to half its original value. t ½ = 0.693 / k 7. If uranium-238 has a half-life of 45 billion years, how many years would it take for a 10-gram sample of U-238 to decrease to 2.5 grams? (3 points) 10g/2 = 5g/2 = 2.5g = 2 half lives required. 45 x 2 = 90 billion years 8. The radioactive decay of Tl-206 to Pb-206 has a half-life of 4.20 min. Starting with 5.00 × 10 22 atoms of Tl-206, calculate the number of such atoms left after 42.0 min. (10 points) (Reference: Chang 19.27) 42.0min / 4.20min = 10 half lives, 5.00×10 22 / 2 = 2.55×10 22 / 2, continue to divide by 2 for 10 times = 4.88 × 10 19 atoms remain after 42min 9. Strontium-90 is one of the products of the fission of uranium-235. This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long (in yr) it will take for 1.00 g of the isotope to be reduced to 0.200 g by decay. (10 points) (Reference: Chang 19.31) k = 0.693/28.1 = 0.02466 t = (1/0.02466) = 40.55 x ln( 1.0/0.2) = 1.609 t = 40.55 x 1.609 = 65.244 years to reduce to 0.200g 2