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  1. Thurs, Dec 11, 2008Phy208 Lect29 1 Final Exam • Mon, Dec 15, at 10:05am-12:05 pm, 2103 Chamberlin • 3 equation sheets allowed • About 30% on new material • Rest on topics of exam1, exam2, exam3. Study Tips: Download blank exams and take them. Download blank quizzes and take them. Look through group problems. Look through lab question sheets.
  2. Thurs, Dec 11, 2008Phy208 Lect29 2 Physics 208 Exit survey • Please take web exit survey • Link on course web site • Also will receive an email. • Helps us to understand what was effective (and ineffective!) in the course.
  3. Thurs, Dec 11, 2008Phy208 Lect29 3 Radioactive nuclei ~ equal # neutrons and protons
  4. Thurs, Dec 11, 2008Phy208 Lect29 4 Radioactive decay • Unstable nuclei decay by emitting particle • Can be photon (light particle), or matter particle. • Emitted particle carries away energy – Can strip electrons from atoms (ionizing radiation) – break apart chemical bonds in living cells (radiation damage) Geiger counter
  5. Thurs, Dec 11, 2008Phy208 Lect29 5 Biological effects of radiation Radiation type RBE X-rays 1 Gamma rays 1 Beta particles 1-2 Alpha particles 10-20 • Radiation damage depends on – Energy deposited / tissue mass (1 Gy (gray) = 1J/kg) – Damaging effect of particle (RBE, relative biological effectiveness) • Dose equivalent = (Energy deposited / tissue mass) x RBE – Units of Sv (sieverts) [older unit = rem, 1 rem=0.01 Sv] – Common units mSv (10-3 Sv), mrem (10-3 rem) – Common ‘safe’ limit = 500 mrem/yr (5 mSv/yr)
  6. Thurs, Dec 11, 2008Phy208 Lect29 6 Radioactive tracers Worked on radioactivity as student with Ernest Rutherford. Lodged in nearby boarding home. Suspected his landlady was serving meals later in week ‘recycled’ from the Sunday meat pie. His landlady denied this! deHevesy described his first foray into nuclear medicine: George de Hevesy “The coming Sunday in an unguarded moment I added some radioactive deposit [lead-212] to the freshly prepared pie and on the following Wednesday, with the aid of an electroscope, I demonstrated to the landlady the presence of the active deposit in the soufflé.”
  7. Thurs, Dec 11, 2008Phy208 Lect29 7 A random process • Radioactive decay is a random process – It has some probability of occurring. • For one nucleus, – – r = decay rate • For N nuclei, – # decays ∆N = N x Prob(decay) =rN∆t – # decays / s = ∆N/∆t =rN Προβδεχαψ in Δt( ) = rΔt ⇒ N = Noe−rt
  8. Thurs, Dec 11, 2008Phy208 Lect29 8 Radioactive half-life • Example of random decay. • Start with 8,000 identical radioactive nuclei • After one half-life, half the nuclei have decayed. t=0 t=1 yr t=2 yr t=3 yr Every half-life, half the atoms decayUndecayed nuclei
  9. Thurs, Dec 11, 2008Phy208 Lect29 9 Radioactive decay question A piece of radioactive material is initially observed to have 10,000 radioactive nuclei. 3 hours later, you measure 1,250 radiaoctive nuclei. The half-life is A. 1/2 hour B. 1 hour C. 3 hours D. 8 hours In each half-life, the number of radioactive nuclei, and hence the number of decays / second, drops by a factor of two. After 1 half life, 5000 are left undecayed. After 2 half lives, 1/2 of these are left: 2,500 After 3 half lives there are 1,250 left.
  10. Thurs, Dec 11, 2008Phy208 Lect29 10 Radioactive decay question A piece of radioactive material is initially observed to have 1,000 decays/sec. It’s half life is 2 days. Four days later, you measure A. 1,000 decays / sec B. 500 decays / sec C. 250 decays / sec D. 125 decays / sec
  11. Thurs, Dec 11, 2008Phy208 Lect29 11  Decay rate r (Units of s-1 )  Prob( nucleus decays in time ∆t ) = r ∆t  Activity R (Units of becquerel (1 Bq=1 s-1 ) or curie (1 Ci=3.7x1010 s-1 )  Mean # decays / s = rN, N=# nuclei in sample  Half-life t1/2 (Units of s)  time for half of nuclei to decay = t1/2 Quantifying radioactivity = ln2 r = 0.693 r N = Noe−rt
  12. Thurs, Dec 11, 2008Phy208 Lect29 12 Different types of radioactivity • Three different types of decay observed: Alpha decay Beta decay Gamma decay (First three letters of Greek alphabet). Ernest Rutherford (1899): "These experiments show that the uranium radiation is complex and that there are present at least two distinct types of radiation - one that is very readily absorbed, which will be termed for convenience the alpha-radiation, and the other of more penetrative character which will be termed the beta-radiation."
  13. Thurs, Dec 11, 2008Phy208 Lect29 13 Heavy nucleus spontaneously emits alpha particle Example of α decay • nucleus loses 2 neutrons and 2 protons. • It becomes a different element (Z is changed) • Example: 92 238 Υ→ 2 4 Ηε + 90 234 Th 92 protons 146 neutrons 90 protons 144 neutrons 2 protons 2 neutrons Alpha particle
  14. Thurs, Dec 11, 2008Phy208 Lect29 14 Decay sequence of 238 U Number of neutrons Numberofprotons α decay
  15. Thurs, Dec 11, 2008Phy208 Lect29 15 Radon QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.Zone 1 Highest Potential (greater than 4 pCi/L) QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture. QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.Zone 2 Moderate Potential (from 2 to 4 pCi/L) http://www.radonwisconsin.com/ • Radon isin the238 U decay series • Radon isan α emitter that presentsan environmental hazard • Inhalation of radon and itsdaughters can ionizelung cellsincreasing risk of lung cancer
  16. Thurs, Dec 11, 2008Phy208 Lect29 16 Activity of Radon • 222 Rn has a half-life of 3.83 days. • Suppose your basement has 4.0 x 108 such nuclei in the air. What is the activity? We are trying to find number of decays/sec. So we have to know decay constant to get R=rN r = 0.693 t1/ 2 = 0.693 3.83days ×86,400s/day = 2.09 ×10−6 s R = dN dt = rN = 2.09 ×10−6 s × 4.0 ×108 nuclei = 836decays/s R = 836 decays/s × 1Ci 2.7 ×1010 decays/s = 0.023μCi
  17. Thurs, Dec 11, 2008Phy208 Lect29 17 Decay sequence of 238 U Number of neutrons Numberofprotons α decay But what are these?
  18. Thurs, Dec 11, 2008Phy208 Lect29 18 Beta decay Number of neutrons Numberofprotons Number of neutrons decreases by one Number of protons increases by one Electron (beta particle) emitted But nucleus has only neutrons & protons.
  19. Thurs, Dec 11, 2008Phy208 Lect29 19 Beta decay • Nucleus emits an electron (negative charge) • Must be balanced by a positive charge appearing in the nucleus. This occurs as a neutron changing into a proton
  20. Thurs, Dec 11, 2008Phy208 Lect29 20 Changing particles Neutron made up of quarks. One of the down quarks changed to an up quark. New combination of quarks is a proton.
  21. Thurs, Dec 11, 2008Phy208 Lect29 21 beta decay example Used in radioactive carbon dating. Half-life 5,730 years. 6 14 Χ → 7 14 N + e− 8 neutrons 6 protons 7 neutrons 7 protons 14 nucleons 14 nucleons 6 positive charges 7 positive charges = = + 1 electron + 1 negative charge
  22. Thurs, Dec 11, 2008Phy208 Lect29 22 Radiocarbon dating • 14 C has a half-life of ~6,000 years, continually decaying back into 14 N. • Steady-state achieved in atmosphere, with 14 C:12 C ratio ~ 1:1 trillion (1 part in 1012 ) As long as biological material alive, atmospheric carbon mix ingested (as CO2), ratio stays fixed. After death, no exchange with atmosphere. Ratio starts to change as 14 C decays
  23. Thurs, Dec 11, 2008Phy208 Lect29 23 Carbon-dating question The 14 C:12 C ratio in a fossil bone is found to be 1/8 that of the ratio in the bone of a living animal. The half-life of 14 C is 5,730 years. What is the approximate age of the fossil? A. 7,640 years B. 17,200 years C. 22,900 years D. 45,800 years Since the ratio has been reduced by a factor of 8, three half-lives have passed. 3 x 5,730 years = 17,190 years
  24. Thurs, Dec 11, 2008Phy208 Lect29 24 Other carbon decays • Lightest isotopes of carbon emit positron – antiparticle of electron, has positive charge! 3 neutrons 6 protons 4 neutrons 5 protons + e+ This is antimatter Too few neutrons Too many neutrons B 9 5 C 9 6
  25. Thurs, Dec 11, 2008Phy208 Lect29 25 Gamma decay Alpha decay (alpha particle emitted), Beta decay (electron or positron emitted), can leave nucleus in excited state – Nucleus has excited states just like hydrogen atom – Emits photon as it drops to lower state. Nucleus also emits photon as it drops to ground state This is gamma radiation Extremely high energy photons. Ni 60 28 Ni 60 28
  26. Thurs, Dec 11, 2008Phy208 Lect29 26 Decay summary • Alpha decay – Nucleus emits He nucleus (2 protons, 2 neutrons) – Nucleus loses 2 protons, 2 neutrons • Beta- decay – Nucleus emits electron – Neutron changes to proton in nucleus • Beta+ decay – Nucleus emits positron – Proton changes to neutron in nucleus • Gamma decay – Nucleus emits photon as it drops from excited state

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