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Nuclear Structure and Radioactive Decay: Exam Review

Prepare for your final exam on nuclear structure, isotopes, and binding energy of nuclei. Review the topics from previous exams and learn about radioactive decay, its biological effects, and quantifying radioactivity.

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Nuclear Structure and Radioactive Decay: Exam Review

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  1. From Last Time… Nuclear structure and isotopes Binding energy of nuclei Final Exam is Mon Dec 21, 5:05 pm - 7:05 pm 2103 Chamberlin 3 equation sheets allowed About 30% on new material Rest on topics of exam1, exam2, exam3. Week15HW covers material for final, but does not count toward HW grade. Phy208 Lecture 29

  2. ~ equal # neutrons and protons Radioactive nuclei Phy208 Lecture 29

  3. Geiger counter 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) Phy208 Lecture 29

  4. Biological effects of radiation • Radiation damage depends on • Energy deposited / tissue mass (1 Gy (gray) = 1J/kg) • Damaging effect of particle (RBE, relative biological effectiveness) Radiation type RBE X-rays 1Gamma rays 1Beta particles 1-2Alpha particles 10-20 • Dose equivalent = (Energy deposited / tissue mass) x RBE • Units of Sv (sieverts) [older unit = rem, 1 rem=0.01 Sv] • Common units mSv (10-3Sv), mrem (10-3rem) • Common ‘safe’ limit = 500 mrem/yr (5 mSv/yr) Phy208 Lecture 29

  5. “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.” 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 Phy208 Lecture 29

  6. 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 Phy208 Lecture 29

  7. t=0 t=1 yr t=2 yr t=3 yr Radioactive half-life • Example of random decay. • Start with 8,000 identical radioactive nuclei • After one half-life, half the nuclei have decayed. Every half-life, half the atoms decay Undecayed nuclei Phy208 Lecture 29

  8. 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 • 1/2 hour • 1 hour • 3 hours • 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: 2,500After 3 half lives there are 1,250 left. Phy208 Lecture 29

  9. 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 • 1,000 decays / sec • 500 decays / sec • 250 decays / sec • 125 decays / sec Phy208 Lecture 29

  10. Quantifying radioactivity • 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 Phy208 Lecture 29

  11. 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." Phy208 Lecture 29

  12. Example of  decay Heavy nucleus spontaneously emits alpha particle • nucleus loses 2 neutrons and 2 protons. • It becomes a different element (Z is changed) • Example: Alpha particle 92 protons146 neutrons 90 protons144 neutrons 2 protons2 neutrons Phy208 Lecture 29

  13. Decay sequence of 238U Number of protons α decay Number of neutrons Phy208 Lecture 29

  14. Radon Zone 1 Highest Potential (greater than 4 pCi/L) Zone 2 Moderate Potential (from 2 to 4 pCi/L) • Radon is in the 238U decay series • Radon is an α emitter that presents an environmental hazard • Inhalation of radon and its daughters can ionize lung cells increasing risk of lung cancer Phy208 Lecture 29 http://www.radonwisconsin.com/

  15. Activity of Radon • 222Rn 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 Phy208 Lecture 29

  16. But what are these? Decay sequence of 238U Number of protons  decay Number of neutrons Phy208 Lecture 29

  17. Beta decay Number of neutrons decreases by one Number of protons increases by one Electron (beta particle) emitted Number of protons Number of neutrons But nucleus has only neutrons & protons. Phy208 Lecture 29

  18. 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 Phy208 Lecture 29

  19. Changing particles Neutron made up of quarks. One of the down quarks changed to an up quark. New combination of quarks is a proton. Phy208 Lecture 29

  20. 7 neutrons7 protons 8 neutrons6 protons beta decay example = + 14 nucleons 14 nucleons 1 electron 6 positive charges 7 positive charges = + 1 negative charge Used in radioactive carbon dating. Half-life 5,730 years. Phy208 Lecture 29

  21. Radiocarbon dating • 14C has a half-life of ~6,000 years, continually decaying back into 14N. • Steady-state achieved in atmosphere, with 14C:12C 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 14C decays Phy208 Lecture 29

  22. Carbon-dating question The 14C:12C 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 14C is 5,730 years. What is the approximate age of the fossil? • 7,640 years • 17,200 years • 22,900 years • 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 Phy208 Lecture 29

  23. 4 neutrons5 protons 3 neutrons6 protons This is antimatter 9 9 B C 5 6 Other carbon decays Too few neutrons Too many neutrons • Lightest isotopes of carbon emit positron • antiparticle of electron, has positive charge! e+ + Phy208 Lecture 29

  24. 60 60 Ni Ni 28 28 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 stateThis is gamma radiation Extremely high energy photons. Phy208 Lecture 29

  25. 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 Phy208 Lecture 29

  26. Decay question 20Na decays in to 20Ne, a particle is emitted? What particle is it? Na atomic number = 11 Ne atomic number = 10 • Alpha • Electron beta • Positron beta • Gamma 20Na has 11 protons, 9 neutrons20Ne has 10 protons, 10 neutronsSo one a proton (+ charge ) changed to a neutron (0 charge) in this decay. A positive particle had to be emitted. Phy208 Lecture 29

  27. Radiation Therapy • 50-60% of cancer patients treated with radiation • Goal: disable cancerous cells without hurting healthy cells • X-rays or γ-rays (60Co) from 20 KV to 25 MV Phy208 Lecture 29

  28. Exposure from laboratory source • 60Co source has an activity of 1 µCurie • Each decay: 1.3 MeV photon emitted • Assume all absorbed by a 1 kg section of your body for 1 hour • Energy absorbed in 1 kg = 0.5 rem 0.3 rem 0.1 rem 0.05 rem 0.003 rem What dose do you receive? Phy208 Lecture 29

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