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Warmup

Warmup. Pu-245 is bombarded with neutrons to instigate a fission reaction. Upon absorbing 1 neutron, the nucleus releases gamma radiation; 2 protons and zinc-65 remain, as well as one other isotope. Write an equation for this nuclear decay process. Perform the following mathematical operations:

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Warmup

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  1. Warmup • Pu-245 is bombarded with neutrons to instigate a fission reaction. Upon absorbing 1 neutron, the nucleus releases gamma radiation; 2 protons and zinc-65 remain, as well as one other isotope. Write an equation for this nuclear decay process. • Perform the following mathematical operations: a. ln(3.456) = x b. ln(x )= -2.57 e e x = 1.240 x = e-2.57 x = 7.65 x 10-2

  2. Half Life Kinetics of Radioactive Decay:

  3. HALF-LIFE is the time that it takes for 1/2 a sample to decompose. After the duration of one half-life, one half of the substance decomposes. 3. According to the decay pattern of 20.0 mg of 15O, what amount remains after 3 half-lives? After 5 half-lives?

  4. Different radioactive elements have different half-lives!

  5. 4. Ra-234 has a half-life of 3.82 days. If you start with 50.0 grams of Ra-234, how much of it is left after: 3.82 days? 7.64 days ? 11.46 days ? 15.28 days ? 25.0 grams 12.5 grams 6.25 grams 3.125 grams

  6. 238U 206Pb + 8 4 + 6 0 92 82 2 -1 t½ = 4.51 x 109 years 5. How long will it take for 100 atoms U-238 to become 25 atoms U-238 and 75 atoms other stuff? (ignore sf) atoms (number) 100 50 25 Time (years) 0 4.51 x 109 9.02 x 109 But what if I asked for something inexact, like 10.2 days? Or the amount of time for 30.8 grams to decay into Polonium?

  7. 6. If I have a sample of 2259 atoms U-238 left,how old is the sample if there were originally 2560 atoms U-238? Nt = # of atoms (or mass) at time t N0 = # atoms (or mass) at time t = 0 t = length of time indicated (not half-life) k = decay constant lnNt = lnN0 - kt t1/2 = half life of substance ln2259 = ln2560 – kt k = 1.53659 x 10-10 Problem: I need k t1/2 = 0.693 k ln2259 = ln2560 – (1.54 x 10-10)t -0.1250850 = – (1.54 x 10-10)t 4.51 x 109 years= 0.693 k t = 8.122 x 108 years

  8. 7. A watch made in 1521 AD contained 24.5 mg radium-226. In 1967, the amount of radium-226 is 20.2 mg. What is the half-life of radium-226? t1/2 = 0.693 4.327 x 10-4 lnNt = lnN0 - kt t1/2 = 1600 years ln20.2 = ln24.5 – k(446) k = 4.327 x 10-4 t1/2 = 0.693 k

  9. 14C 14N + 0 +  6 7 -1 t½ = 5730 years 8. If a sample of wood has only 32% of the original amount of carbon-14 left, how old is the sample? t1/2 = 0.693 k lnNt = lnN0 - kt 5730 years= 0.693 k ln32 = ln100 – kt k = 1.21 x 10-4 ln32 = ln100 – (1.21 x 10-4)t -1.13943 = – (1.21 x 10-4)t t = 9400 years

  10. 9. The half life of I-123 is 13 hr. How much of a 64.0 g sample of I-123 is left after 31 hours? t1/2 = 0.693 k lnNt = lnN0 - kt lnNt = ln64.0 – (5.33076 x 10-2)(31) 13 = 0.693 k lnNt = 4.158883 – 1.652536 k = 5.33076 x 10-2 lnNt = 2.506347 e e Nt = e2.506347 Nt = 12.3 grams

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