Review: Alpha Decay

1. Review: Alpha Decay • A nucleus emits an alpha particle • Ionizing to particles around it – extremely hazardous if ingested – passes easily into cells

2. Decay chain for Uranium • 14 decays lead (stable)

3. 2. Beta Decay • Beta negative decay A neutron within a nucleus transforms into a proton, an electron and an antinutrino Beta decay occurs in the nuclei where there is an imbalance of neutrons to protons. Typically, if a light nucleus has too many neutrons to be stable, a neutron will spontaneously change into a proton, and an electron and an uncharged massless particle called an antineutrino u are ejected to restore the nucleus to a more stable state.

4. Antineutrino • Particle was named a neutrino (little neutral one). • In 1956 the existence of neutrinos was finally verified experimentally. • Two types: neutrino and antineutrino. • Both types are identical except for opposite spins.

5. B. Beta positive decay

6. Gamma Decay (γ-decay) • Nuclei energy levels change, which correspond to different configurations of nucleons within a nucleus • Excited states of a nucleus - nucleons are farther apart, binding energy is less, but the total energy of the nucleus is more than the ground state • When the nucleus makes a transition to a lower energy level, it emits a gamma ray photon

7. Generally, after a radioisotope has emitted an alpha or beta particle, the daughter nucleus holds an excess of energy. The protons and neutrons in the daughter nucleus then rearrange slightly and off-load this excess energy by releasing gamma radiation (high-frequency electromagnetic radiation).

9. Ex) Uranium-238 emits alpha particles with a maximum energy of 4.2 MeV. • Explain why a sample of this radioisotope encased in plastic is quite safe to handle yet, if inhaled as dust, would be considered very dangerous. • Calculate the energy of an alpha particle in joules.

10. Half Life Calculation of Radioactive Decay Atomic Physics

11. Stability of Isotopes • Radioactive decay transmutes unstable nuclei into more stable nuclei. • Large unstable nuclei usually emit an alpha particle resulting in a smaller nucleus. • Smaller unstable nuclei usually emit a beta or beta-positive particle, or a gamma ray.

12. Stability of Isotopes

13. Decay series • Many unstable isotopes will decay to form an unstable daughter nucleus. • This nucleus will also decay into another unstable nucleus. • This continues until a stable nucleus results. • Such a process is called a decay series.

14. See p. 807

15. Decay of Uranium-238

16. Activity (A) • ... is the number of nuclei in a given sample that will decay in a given time. • Usually measured in decays/s, becquerels (Bq). Note: A Geiger counter records the number of radioactive decays occurring in a sampleeach second. This is the activity of the sample. • Over time, the activity of any sample of a radioisotope will decrease. This is because more and more of the radioactive nuclei have decayed and will no longer emit radiation. So, over one half-life, the activity of any sample will be reduced by half. If asample of polonium-218 has an initial activity of 2000 Bq, then after one half-life (i.e. 3 minutes) its activity will be 1000 Bq. After 6 minutes, the activity of the sample will have reduced to 500 Bq and so on.

17. Example: • In 2 hours, the activity of a sample of a radioactive element falls from 240 Bq to 30 Bq. What is the half-life of this element?

18. Half Life • Half-life of a radioactive isotope is the time taken for half of the atoms of an element to decay • Eg) each radioactive isotope has its own half life

20. Half Life http://videos.howstuffworks.com/hsw/17819-physics-the-nature-of-radioactive-decay-video.htm • ... is the time required for half of the radioactive nuclei in a sample to decay. • Example: • Half-life for iodine-131 is 192 h. • Initial mass of sample: 20 g • After 192 h, 10 g of I-131 remains (the rest is decay products) • After another 192 h, 5.0 g of I-131 remains. http://www.youtube.com/watch?v=xhOtKurHayo http://www.youtube.com/watch?v=6X-zjmEZO4o

21. Equation • Equation to determine the mass remaining after some time period

22. Example • Argon-39 undergoes beta decay, with a half-life of 269 years. If a sample contains 64.0 g of Ar-39, how many years will it take until only 8.00 g of Ar-39 remain? • Ignoring any other decays that may occur, what element is the rest of the sample transmuted into?

23. Solution: • Number of ½ lives: • 64.0 g x ½ = 32.0 g One ½ Life • 2.0 g x ½ = 16.0 g Two ½ Lives • 16.0 g x ½ = 8.00 g Three ½ Lives • t = 3 x t1/2 = 3 x 269 y • = 807 y

24. Solution: • beta decay: Product: Potassium-39

25. Eg) For Iodine-131 which has a halflife of 8.02 days, determine the mass remaining after 72.2 days having started with a mass of 12.0g. • The amount remaining is 2.34 x 10-2 g.

26. Radioactive Decay of Iodine-131 Be able to interpret these graphs for half life time.

27. Find total mass and then find half that amount. • Draw a horizontal line to intersect the graph • Draw a vertical line to intersect x axis to determine half life time.

28. Radioactive Dating • By measuring the relative amounts of different isotopes in a material, the age of the material can be determined. • Carbon dating, using carbon-14, is the most well known example. • Carbon-14 has a half-life of 5730 years.

29. Example • A sample of bone contains one quarter of the C-14 normally found in bone. What is the bone’s approximate age?

30. Solution: • The age of a sample with half the normal amount of C-14 would be approximately the same as the half life of C-14 (half the C-14 will have decayed). • ¼ = ½ • ½ so ¼ is two half-lives. • time = 2 • 5730 y = 11460 y

31. Carbon Dating Graph

32. Why carbon dating works • Carbon dating works for bone, and wood, etc. • The proportion of C-14 to C-12 in the atmosphere is well known. • A living tree will have the same proportion of C-14 to C-12 as it constantly absorbs carbon from the air.

33. Why carbon dating works When the tree dies (ie use the wood to make a tool) it no longer absorbs carbon. • Decay of C-14 starts to reduce the amount of C-14 in the wood. • Amount of stable C-12 remains constant.

34. Why carbon dating works • When there is half the usual amount of C-14 remaining, the wood is about 5730 years old (one half life). • Accurate measurements need to account for variations in proportion of C-14 to C-12 over the centuries. • Carbon dating has been verified by comparing to known dates.

35. Fractional half-lives • A bone fragment has 40% of the original C-14 remaining. What is its age? The age will be: 1.32 • one half life = 1.32 • 5730 years ≈ 7500 years

36. Why carbon dating works • Carbon dating does not provide accurate results for materials older than about 50 000 years, or fairly recent materials. • This is because there is either not enough C-14 left to accurately measure or not enough has decayed yet.