CHM212 Chapter 21 Learning Curve

242 s -how many half lives does it take to go from 16.00 g to 1.00 g? (1/16)*100% = 6.25% % activity = (1/2)^n x 100% -where n is the number of half-lives 6.25% = (1/2)^n x 100% 0.0625 = (1/2)^n log(0.0625) = nlog(1/2) n = 4 -if it takes 4 half lives to reach 1.00 g, and 1 half life = 60.5 s, then.... 4(60.5 s) = 242 s

(212 = 𝐴)Bi is a radioactive isotope with a half-life of 60.5 s. How many seconds will it take for a 16.00 g sample of (212 = 𝐴)Bi to decay to 1.00 g?

4.39 × 10^9 years . The half-life, (t(1/2)), is related to the decay constant, k, through the following equation: t(1/2) = (ln(2))/k

(238 = 𝐴)U has a decay constant of 1.58 × 10^−10 years^-1. What is its half-life?

138.9 hours % activity = (1/2)^n x 100% -where n is the number of half-lives 12.5% = (1/2)^n x 100% 0.125 = (1/2)^n log(0.125) = nlog(1/2) n = 3 -if it takes 3 half lives to decay to 12.5%, and 1 hlf life = 46.3 h, then... 3(46.3 h) = 139 hours (138.9)

(153 = 𝐴)Sm is a therapeutic radioisotope with a half-life of 46.3 h. How many hours will it take for a sample of (153 = 𝐴)Sm to decay to 12.5% of its original mass?

(177/72)Hf -the problem gives us: (177/71)Lu ⟶ ??? (0/-1)e 177 = ? + 0 ? = 177 71 = ? + (-1) 72 = ?

(177/71)Lu is a beta particle emitting therapeutic radionuclide. Identify the daughter isotope of its decay.

(173/70)Yb -the problem gives us: (173/71)Lu + (0/-1)e ⟶ ??? 173 + 0 = ? ? = 173 71 + (-1) = ? ? = 70 #70 on the periodic table Ytterbium(Yb)

(173/71)Lu, one of the more stable lutetium radioisotopes with a half-life of 1.37 years, undergoes an electron capture reaction. What is the daughter isotope of this reaction?

(174/70)Yb -the problem gives us: (174/71)Lu ⟶ ??? + (0/1)e 174 = ? + 0 ? = 174 71 = ? + 1 ? = 70

(174/71)Lu is a long-lived radioisotope of lutetium with a half-life of 3.31 years. Given that it decays by positron emission, what is its daughter isotope?

Answer (221/87)Fr Explanation: -the problem gives us... (225/89)Ac ⟶ ??? + (4/2)He 225 = ? + 4 ? = 225 -4 = 221 89 = ? +2 ? = 89 - 2 = 87 -what element is on the periodic table is #87? Francium(Fr) -the answer is (221/87)Fr

(225/89)Ac is an alpha particle emitting therapeutic radionuclides used for targeted cancer therapies. Its decay cascade produces 4 net alpha particles. Identify the daughter isotope produced after its first alpha decay.

Use the integrated rate law to calculate the initial amount of a radioisotope: N0 = Nt × e^(kt) N0 = 2.65 g x e^(0.1315*2.00) N0 = 2.65 g x 1.30 N0 = 3.45 g

(60 = 𝐴)Co is a radioisotope of cobalt with a decay constant, k, of 0.1315 years−1. Given that 2.65 g of (60 = 𝐴)Co remain after 2.00 years, how many grams of (60 = 𝐴)Co were initially present in the sample?

(4/2)He (alpha particle) 212 = 208 + ? ? = 212 - 208 = 4 84 = 82 + ? ? = 84 - 82 ? = 2

Identify the missing particle in the following nuclear decay reaction: (212/84)Po → (208/82)Pb + ?

109.7 min % activity = (1/2)^n x 100% -where n is the number of half-lives 25% = (1/2)^n x 100% 0.25 = (1/2)^n log(0.25) = nlog(1/2) n = 2 so if 219.4 is 2 half-lives (n), then... 219.4 min/2 = 1 half life the answer is 109.7 min

It takes 219.4 min for a sample of (18 = 𝐴)F to decay to 25% of its initial mass. What is the half-life of (18 = 𝐴)F?

above the belt of stability For the lighter elements (Z < 20), the N/Z ratio of stable isotopes is approximately 1. (45/20)Ca has 20 protons and 25 neutrons. Therefore, the N/Z ratio is greater than 1, placing this isotope above the belt of stability.

Where does (45/20)Ca lie relative to the belt of stability?

(16/8)O For the lighter elements (Z < 20), the N/Z ratio of stable isotopes is approximately 1. This oxygen isotope has 8 protons and 8 neutrons in its nucleus, and a N/Z = 1. Therefore, (16/8)O is predicted to be stable.

Which of the following isotopes is predicted to be stable? (14/6)C (238/92)U (16/8)O (127/50)Sn

(210/85)At Isotopes with Z > 83 are not shown on the graph because above Z = 83, stable nuclei do not exist. Therefore, (210/85)At is unstable.

Which of the following isotopes is predicted to be unstable? (210/85)At (50/24)Cr (12/6)C (14/7)N

(213/83)Bi -the problem gives us: ??? → (209/81)Tl + (4/2)He ? = 209 + 4 ? = 213 ? = 81 + 2 ? = 83 (213/83)Bi

Which radioisotope produces (209/81)Tl via alpha decay?

(c) The half-life of a radioactive isotope is the time required for half of the original sample to undergo radioactive decay. The half-life of a radioactive isotope is the time required for half of the original sample to undergo radioactive decay.

Select the true statement about the half-life of a radioisotope. (a) The half-life of a radioisotope is the amount of time it takes for the radioisotope to completely decay. (b) The half-life is the same for all radioisotopes. (c) The half-life of a radioactive isotope is the time required for half of the original sample to undergo radioactive decay. (d) The half-life of a radioisotope is the amount of time it takes for the radioisotope to double in quantity.

alpha decay All known stable isotopes are shown on the graph. Above Z = 83, stable nuclei do not exist. Po-210 has an atomic number greater than 83. Isotopes above Z > 83 tend to undergo alpha decay to decrease Z. Therefore, (210/84)Po is most likely to undergo alpha decay.

Which type of nuclear decay is the radioisotope (210/84)Po likely to undergo?

an alpha particle An alpha particle is a helium nucleus containing 2 protons and 2 neutrons and is represented as either (4/2)α or (4/2)He.

What does the nuclear symbol (4/2)He represent?

25% The half-life of a radioactive isotope is the time required for half of the original sample to undergo radioactive decay. After one half-life, 50% of the radioisotope remains. After two half-lives, 25% of the radioisotope remains.

What percentage of a sample of a radioisotope remains after two half-lives have passed?