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Name Practice Worksheet Independent Study on Nuclear Chemistry Half-life Problems Reference Table “O” for Physical Setting/CHEMISTRY summarizes the types of radioactive particles (emanations) that can be released or absorbed by a nucleus during the transmutation of a nuclide and half-lives for selected radioisotopes. OBJECTIVES: Define half-life and give examples. Solve half-life problems REGENTS’ Major Understanding: Spontaneous decay can involve the release of alpha particles, beta particles, positrons and/or gamma radiation from the nucleus of an unstable isotope. These emissions differ in mass, charge, and ionizing power, and penetrating power. (3.1p) Nuclear reactions can be represented by equations that include symbols which represent atomic nuclei (with the mass number and atomic number), subatomic particles (with mass number and charge), and/or emissions such as gamma radiation. (4.4c). Each radioactive isotope has a specific mode and rate of decay (half-life). (4.4a) The following equation CAN be used to determine the amount of radioisotope remaining. However, there are multiple methods for solving half-life problems t 1 m final m initial ( ) T 2 m final final mass minitial initial mass t total time elapsed T half-life (Table N) t 1 Fraction remaining ( ) T 2 SAMPLE QUESTION: Most chromium atoms are stable, but chromium-51 is an unstable isotope with a half-life of 28 days. What fraction of a sample of Cr-51 will remain after 168 days? 168 1 1 Solve: Fraction remaining ( ) 28 = 0.015625 = 2 64 SAMPLE QUESTION: How much was present originally in a sample of chromium-51 if 0.75 g remains after 168 days? 168 1 Solve: 0.75 minitial ( ) 28 48 g minitial 2 Problem Set #1: Solve the following half-life problems using a method of your choice 1) Fluorine-21 has a half-life of 5.0 seconds. If you start with 25 g of fluorine-21, how many grams would remain after 60.0 s? 2) If 10.0 mg of cesium-137 disintegrates over a period of 90.69 years, how many mg of cesium-137 would remain? 3) A sample of gold-198 has a mass of 30.0-g. How many days are required for the gold-198 to decay to 7.5-g? 4) After 21.04 years, 25.0-g of cobalt-60 remains unchanged. How much cobalt-60 was in the original sample? Problem Set #2: Solve the following half-life problems using a method of your choice 1) After 62.0 hours, 1.0 g remains unchanged from a sample of 42 K . How much 42 K was in the original sample? 2) If 80.0 mg of a radioactive element decays to 10.0 mg in 30.0 minutes, what is the elements half-life, in minutes? 3) In 6.20 hours, a 100.0 gram sample of Ag-112 decays to 25.0 g What is the half-life of Ag-112 in hours? 4) What is the mass of K-42 remaining in a 16.0-g sample of K-42 after 37.2 hours? 5) If 3.0 g of Sr-90 in a rock remained unchanged in 1999, approximately how many grams of Sr-90 were present in the original sample in 1943? 6) A sample of I-131 decays to 1.0 g in 40.35 days. What was the mass of the original sample? 7) What is the total mass of Rn-222 remaining in an original 160.0-mg sample of Rn-222 after 19.1 days? 8) A radioactive element has a half-life of 2 days. What is the fraction remaining after 6 days? Problem Set #3 1. As the temperature of a sample of a radioactive element decreases, the half-life of the element (A) decreases (B) increases (C) remains the same (D) varies with pressure 2. If one-eighth of the mass of the original sample of a radioisotope remains unchanged after 4800 years, the isotope could be (A) H-3 (B) K-42 (C) Sr-90 (D) Ra-226 3. Which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10 years? (A) 2.0 grams of Au-198 (C) 2.0 grams of K-42 (B) 2.0 grams of P-32 (D) 2.0 grams of Co-60 4. Which of the following 10-g samples of radioisotope will decay to the greatest extent in 28 days? (A) P-32 (B) Fr-220 (C) Kr-85 (D) I-131 5. As the pressure of a sample of a radioactive element decreases, the half-life will (A) decrease (B) increase (C) remain the same 6. Which sample will decay least over a period of 30 days? (A) 10 g of P-32 -198 (B) 10 g of I-131 (C) 10 g of Au (D) 10 g of Rn-222 Answers: Problem Set #1: (1) 6.1 x 10-3 g (2) 1.25 g (3) 5.38 days (4) 400. g Problem Set #2: (1) 32.0 g (2) 10 min (3) 3.10 hours (4) 2.0 g (5) Approximately 12.0 g (6) 32.0 g (7) 5.0 mg (8) 1/8 remains Problem Set #3: (1) C (2) D (3) D (4) B (5) C (6) A