Understanding Nuclear Decay Series & Half-life Concepts

1. Half Life and Radioactive Decay

2. Nuclear Decay Series All elements above Atomic Number 83 have Unstable nuclei and are therefore radioactive. Alpha Particle Most abundant isotope

3. 234Pa + 0e -1 91 Thorium Decay Of course Thorium’s atomic number is also greater than 83. So it to is Radioactive and Goes through beta decay. Protactinium

4. U-238 Decay Series Protactinium decays Next and so on until we reach a stable Non-radioactive Isotope of lead Pb-206 Atomic No. 82

5. U-238 Decay Series

6. Decay Series U-238 IS NOT the only radioactive isotope that Has a specific decay series. All radioisotopes have specific decay paths they follow to ultimately reach stability

7. Decay Series Time Span The next Question you might consider asking is how long does this decay process take? The half life of U-238 is about 4.5 billion years which is around the age of the earth so only about half of the uranium Initially present when the earth formed has Decayed to date. Which leads us into a discussion of Nuclear Half life

8. Nuclear Half-life Unstable nuclei emit either an alpha, beta or positron particles to try to shed mass or improve their stability. But can we predict when a nucleus will Disintegrate? The answer is NO for individual nuclei But YES if we look at large #’s of atoms.

9. Nuclear Half-life Every statistically large group of radioactive nuclei decays at a predictable rate. This is called the half-life of the nuclide Half life is the time it takes for half (50%) of the Radioactive nuclei to decay to the daughter Nuclide

10. Nuclear Half-life The Half life of any nuclide is independent of: Temperature, Pressure or Amount of material left

11. 64 beans Successive half cycles 1 32 beans 50% 2 16 beans 3 8 beans 4 4 beans Beanium decay What does the graph of radioactive decay look like? This is an EXPONENTIAL DECAY CURVE

12. Loss of mass due to Decay Amount of beanium 64 32 16 8 4 Fraction left 1 ½ ¼ 1/8 1/16 Half life’s 1 2 3 4 If each half life took 2 minutes then 4 half lives would take 8 min. The equation for the Number of half Lives is equal to: Time (elapsed) / Time (half Life) 32 minutes / 4 minutes = 8 half life’s

13. 22,920/5730 = 4 Half-life’s t0 Carbon 14 is a radionuclide used to date Once living archeological finds Carbon–14 Half-life = 5730 years

14. Half-Lives • In order to solve these half problems a table like the one below is useful. • For instance, If we have 40 grams of an original sample of Ra-226 how much is left after 8100 years? 10 grams 5 grams 2.5 grams 1.25 grams

15. Problem: A sample of Iodine-131 had an original mass of 16g. How much will remain in 24 days if the half life is 8 days? Step 1: Half lives = T (elapsed) / T half life = 24/8 = 3 Step 2: 16g (starting amount) 8 4 2g Half lives 0 1 2 3

16. Problem: • What is the original amount of a sample of H–3 if after 36.8years 2.0g are left ? Table N tells us that the half life of H-3 is 12.26 yrs. 36.8 yrs / 12.26 yrs = 3 half lives. Now lets work backward Half life 3 2 grams Half life 2 4 grams Half life 1 8 grams Time zero 16 grams

17. Problem: • How many ½ life periods have passed if a sample has decayed to 1/16 of its original amount? Time zero 1x original amount First half life ½ original amount Second half life ¼ original amount Third half life 1/8 Fourth half life 1/16

18. Problem: • What is the ½ life of a sample if after 40 years 25 grams of an original 400 gram sample is left ? Step 2: Elapsed time = # HL Half-life 40 years = 4 HL Half-life Half life = 10 years Step 1: 25 grams 4 half lives 50 3 half lives 100 g 2 half lives 200 g 1 half life 400 g time zero