1. OB: nuclear chem class #2 practice decay reactions, the half life of radioisotopes A half life is the amount of time it takes for one half of a given radioisotope to transmute. Which half, even which atoms will actually decay is a mystery. But, statistically, half will transmute in a given half life.

2. First, let’s practice the decay reactions for these isotopes… 14 6 C 198 79 Au 131 53 I 239 94 238 92 37 20 Pu U Ca

3. First, let’s practice the decay reactions for these isotopes… 14 7 N 198 79 Au 131 53 I 239 94 238 92 37 20 Pu U Ca 198 80 Hg 14 6 C 131 54 Xe 235 92 U 234 90 Th 37 19 K + + + + + + 0 -1 e e e 4242 He 4242 0 +1 e Gold-198 undergoes beta decay and transmutes to mercury-198 Carbon-14 transmutes to N-14 by beta decay. Iodine-131 becomes Xe-131 by beta decay. Pu-239 transmutes into U-235 by alpha decay. Alpha decay occurs and uranium-238 becomes thorium-234. Calcium-37 undergoes positron decay and forms into potassium-37.

4. HALF LIFE: the amount of time it takes for one half of a radioisotope to decay into a daughter isotope. The details of why this occurs or how this occurs, or even when any particular isotope will decay is unknown. What is known very well is the amount of time it takes for these isotopes to decay. Statistics are easy compared to looking at individual atoms. Some half lives of isotopes are very, very long, in the millions of years. Some isotopes have half lives measured in milliseconds (thousandths of a second). Many half lives are listed in table N, let’s look now…

5. The half life of radioactive gold-198 is 2.69 days. This means that if you have 150.0 grams of Au-198, in 2.69 days you will have just 75.00 grams of this isotope, and 75.00 grams of what ever it is that it transmuted into (Hg-198) In 2.69 more days, you will have just 37.50 grams of the radioactive gold, and 37.50 more grams of the mercury. After yet another 2.69 days, you’ll have only 18.75 grams of your gold. Each half life passes and another half of the radioactive isotope decays away.

6. The beta decay of gold-198 Mass Half Lives 150.0 g 0 75.00 g 1 37.50 g 2 18.75 g 3 In our class the half lives will always be whole numbers, we will not measure these in partial half lives. The math is easy in high school. Total time passed: 2.695 days 5.390 days 8.085 days

7. What’s the half life in time? What’s the decay mode? K-37 I-131 Ra-226 Uranium 238

8. What are the half lives of these radioisotopes? What is their decay mode? K-371.23 secondspositron I-1318.021 daysbeta Ra-2261599 yearsalpha Uranium 238 4,470,000,000 years alpha

9. You accumulate 22.0 grams of the radioisotope carbon-14. How long before you have only 2.75 grams? Every single half life problem demands that you draw a timeline. Every single one, even this one. 22.0 g 0 half lives

10. 22.0 g 0 half lives You accumulate 22.0 grams of the radioisotope carbon-14. How long before you have only 2.75 grams? 1 half life 11.0 g 2 half lives 5.50 g 3 half lives 2.75 g It takes the length of time of three half lives for 22.0 g of Carbon-14 to transmute into just 2.75 grams. Since each half life of this radioisotope is 5715 years, 5715 years X 3 = 17,145 years It will take 17,145 years for this to happen.

11. The doctor wants to inject you with some radioactive Iodine-131 to measure your thyroid uptake. She injects you with 2.00 grams. How long until you have just 0.03125 g left in you? (disregard the significant figures here) 2.00 g 0 half lives Start your timeline, and watch the calculator buttons. Go slowly.

12. The doctor wants to inject you with some radioactive Iodine-131 to measure your thyroid uptake. She injects you with 2.00 grams. How long until you have just 0.03125 g left in you? (disregard the significant figures here) 2.00 g 0 half lives 1.00 g0.500 g0.250 g 0.125 g0.0625 g0.03125 g 123456 It will take 6 half lives for this 2.00 g radioactive iodine to transmute away so that only 0.03125 g remains. Each half life is 8.07 days, so… 6 X 8.021 days = about 48.126 days, about 1 ½ months.

13. You put 400.0 grams of Fe-53 in your pocket at noon. At what time you have 12.5 grams of this iron left? What has the other 387.5 grams become? What decay mode did this undergo? 400.0 g 0 half lives The easy stuff first, then the math… Iron-53 undergoes positron decay this way:

14. You put 400.0 grams of Fe-53 in your pocket at noon. At what time you have 12.5 grams of this iron left? What has the other 387.5 grams become? What decay mode did this undergo? 400.0 g 0 half lives The easy stuff first, then the math… Iron-53 undergoes positron decay this way: 53 26 Fe 0 +1 e+ 53 25 Mn This is positron decay.

15. You put 400.0 grams of Fe-53 in your pocket at noon. At what time you have 12.5 grams of this iron left? What has the other 387.5 grams become? What decay mode did this undergo? 400.0 g 0 half lives 200.0 g100.0 g50.0 g25.0 g12.5 g 1 2 3 4 5 5 half lives must pass for this to happen. Each half life of Iron-53 is 8.51 minutes. 8.51 minutes X 5 = 42.55 minutes (let’s round that to 43 minutes) So… it will be about 12:43 PM