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Understanding Decay Rate and Radiometric Dating in Nuclear Chemistry

Explore concepts of decay rate, half-life, and radiometric dating in nuclear chemistry, including examples and calculations. Learn about probability of decay, activity, and exponential decay in this informative guide.

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Understanding Decay Rate and Radiometric Dating in Nuclear Chemistry

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  1. Decay Rate • Contents: • Probability of decay and Activity • Whiteboard • Half life and exponential decay • Whiteboard • Radiometric dating

  2. Probability and activity  - Per second probability of a nuclei decaying (s-1) N - Number of un-decayed nuclei (number) N/t - Activity - decays/sec (s-1) N/t = N TOC

  3. Whiteboards: Activity and decay probability 1 | 2 | 3 TOC

  4. What is the activity if you have a  of 3.19 x 10-10 s-1, and you have 5.12 x 1023 un-decayed nuclei? N/t = N = (3.19 x 10-10 s-1)(5.12 x 1023) = 1.63 x 1014 decays/s (or s-1) W 1.63 x 1014 decays/sec

  5. What is the  if 1.27 x 1020 un-decayed nuclei generate 1420 decays per second? N/t = N 1420 s-1 = (1.27 x 1020)  = 1.12 x 10-17 s-1 W 1.12 x 10-17 s-1

  6. Radon 222 has an atomic mass of 222.02. How many grams of it do you have if your activity is 8.249 x 1016 decays/sec, and your decay probability is 2.098 x 10-6 s-1? (4) NA = 6.02 x 1023 atoms/mol n = N/NA n = (grams you have)/(molar mass) N/t = N 8.249 x 1016 s-1 = (2.098 x 10-6 s-1)N N = 3.93184 x 1022 nuclei n = (3.93184 x 1022)/(6.02 x 1023 mol-1) = 0.065312954 grams = n(molar mass) = (0.065312954)(222.02) = 14.5 g W 14.5 g

  7. Half life and exponential decay •  - Per second probability of a nuclei decaying (s-1) • N - Number of un-decayed nuclei (number) • N/t - Activity - decays/sec (s-1) • N/t = N (not in data packet) • N = Noe-t - Exponential decay • No - Original value • N - Value at time t • t - Elapsed time • Diff EQ… TOC

  8. Half life and exponential decay • N/t = N (not in data packet) • N = Noe-t - Exponential decay • No - Original value • N - Value at time t • t - Elapsed time • T1/2 - Half life - time for half nuclei to decay • 1/2No= Noe-T1/2 • 1/2= e-T1/2 • 2 = eT1/2 • ln(2) = T1/2 • T1/2= ln(2)/ TOC

  9. Half life and exponential decay N/t = N (not in data packet) N = Noe-t - (in data packet) T1/2= ln(2)/- (in data packet) Half lives occur over and over Half life here is 20 s TOC

  10. Half life and exponential decay N/t = N (not in data packet) N = Noe-t - (in data packet) T1/2= ln(2)/- (in data packet) Example: Bi 211 has a half life of 2.14 min. What is the per second probability of a nuclei decaying? If you start out with 32 grams of Bi 211, how much is left after 385.2 s? After what time is there 23 grams left? Use formulas Cheat (385.2 s = 3 half lives) TOC

  11. Whiteboards: Half life and decay probability 1 | 2 | 3 | 4 | 5 | 6 TOC

  12. Oregonium has a decay probability of 8.91 x 10-8 s-1. What is its half life in days? T1/2= ln(2)/= ln(2)/(8.91 x 10-8 s-1) = 7779429.636 s = 90.0 days W 90.0 days

  13. What is the nuclear decay probability of a substance that has a half life of 96.23 minutes? T1/2= ln(2)/- (in data packet) T1/2= (96.23 min)(60 sec/min) = 5773.8 s = ln(2)/  = ln(2)/(5773.8 s) = 0.0001201 s-1 W 0.0001201 s-1

  14. Oregonium has a decay probability of 8.91 x 10-8 s-1. If you have 1250 grams of Oregonium initially, how many grams do you have after 30.00 days? (x24x3600) N = Noe-t - (in data packet) N = (1250) e-(8.91x 10-8)(30*24*3600) N = 992 g W 992 g

  15. Tualatonium has a half life of 12 seconds. If you start with 64 grams of it, how much remains after a minute? (Cheat) 60 seconds is exactly 5 half lives, so divide in half five times 64/25 = 2.0 grams W 2.0 grams

  16. Tigardium has a half life of 8.34 seconds. The initial activity is 1350 counts/second, after what time is the activity 125 counts/sec? = ln(2)/T1/2 = 0.083111173 s-1 N = Noe-t - (in data packet) N/No = e-t ln(N/No) = -t ln(No/N) = t ln(No/N)/ = t = ln(1350/125)/(0.083111173 s-1) t = 28.6 s W 28.6 s

  17. A certain substance has an activity of 1245 counts/sec initially, and an activity of 938 counts/second after exactly 3.00 minutes. What is the half life of the substance? N = Noe-t - (in data packet) N/No = e-t ln(N/No) = -t ln(No/N) = t ln(No/N)/t =  = ln(1245/938)/(180. s) = .001573 s-1 T1/2= ln(2)/(.001573 s-1)= 441 s W 441 s

  18. Radiometric dating • Know original proportion of unstable nuclei • Measure current proportion • Use N = Noe-t to calculate elapsed time • Carbon 14 dating: • C14 created in atmosphere (T1/2 = 5730 Y) • Living things absorb C14 in known amounts • They die, and quit absorbing C14 • Rocks can be dated • Hardening forms nearly pure crystals • Magma is product of fission within the earth • Lead - Earth’s age - Uranium/Lead - Clean room - lead in fuel. TOC

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