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Transcript
Final Exam • • • • Physics 208 Exit survey Mon, May 12, at 12:25-2:25 pm in Ingraham B10 2 equation sheets allowed (HAND WRITTEN!) 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. Work through new-material practice problems on Mastering Physics Wed, May 7 2008 Phy208 Lect29 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. Wed, May 7 2008 1 Radioactivity from last time… Radioactive decay: alpha, beta, gamma Decay rate r Activity R 2 Example of α decay Heavy nucleus spontaneously emits alpha particle (Units of s-1) Prob( nucleus decays in time Δt ) = r Δt (Units of becquerel (1 Bq=1 s-1) or curie (1 Ci=3.7x1010 s-1) Mean # decays / s = rN Half-life t1/2 Phy208 Lect29 • nucleus loses 2 neutrons and 2 protons. • It becomes a different element (Z is changed) (Units of s) • Example: 238 92 time for half of nuclei to decay = t1/2 t1/ 2 = Wed, May 7 2008 ln2 0.693 = r r Phy208 Lect29 Alpha particle U " 42 He + 23490Th 92 protons 146 neutrons 2 protons 2 neutrons Wed, May 7 2008 3 Phy208 Lect29 90 protons 144 neutrons 4 ! ! Radon Decay sequence of 238U Zone 1 Highest Potential (greater than 4 pCi/L) Number of protons 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 α decay Wed, May 7 2008 Number of neutrons Phy208 Lect29 5 • Inhalation of radon and its daughters can ionize lung cells increasing risk of lung cancer Wed, May 7 2008 6 http://www.radonwisconsin.com/ Phy208 Lect29 1 Decay sequence of 238U Activity of Radon We are trying to find number of decays/sec. So we have to know decay constant to get R=rN r= 0.693 0.693 = = 2.09 "10#6 s t1/ 2 3.83days " 86,400s /day dN = rN = 2.09 "10#6 s " 4.0 "10 8 nuclei = 836decays /s dt 1Ci R = 836 decays /s " = 0.023µCi 2.7 "1010 decays /s R= Wed, May 7 2008 Phy208 Lect29 But what are these? Number of protons • 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? α decay Number of neutrons Phy208 Lect29 Wed, May 7 2008 7 8 ! Beta decay Number of protons increases by one Electron (beta particle) emitted Beta decay • Nucleus emits an electron (negative charge) • Must be balanced by a positive charge appearing in the nucleus. Number of protons Number of neutrons decreases by one Number of neutrons This occurs as a neutron changing into a proton But nucleus has only neutrons & protons. Wed, May 7 2008 Phy208 Lect29 Wed, May 7 2008 9 Phy208 Lect29 10 beta decay example Changing particles 14 6 Neutron made up of quarks. One of the down quarks changed to an up quark. New combination of quarks is a proton. C " N + e# 7 neutrons 7 protons 8 neutrons 6 protons ! 14 7 14 nucleons = 14 nucleons + 6 positive charges = 7 positive charges + 1 electron 1 negative charge Used in radioactive carbon dating. Half-life 5,730 years. Wed, May 7 2008 Phy208 Lect29 11 Wed, May 7 2008 Phy208 Lect29 12 2 Radiocarbon dating • Carbon-dating question 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) The 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? As long as biological material alive, atmospheric carbon mix ingested (as CO2), ratio stays fixed. A. B. C. D. After death, no exchange with atmosphere. Ratio starts to change as 14C decays Wed, May 7 2008 Phy208 Lect29 Other carbon decays 13 Too few neutrons Too many neutrons – antiparticle of electron, has positive charge! 6 C 3 neutrons 6 protons Wed, May 7 2008 9 5 4 neutrons 5 protons Wed, May 7 2008 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 Lect29 14 Antimatter Matter and antimatter annihilate This is antimatter B 7,640 years 17,200 years 22,900 years 45,800 years • Every particle has an antiparticle. • Antimatter (anti-atoms) has been formed. • Lightest isotopes of carbon emit positron 9 14C:12C Photons are created, conserving energy, momentum. + e+ Phy208 Lect29 15 Wed, May 7 2008 Positron Emission Tomography - PET Phy208 Lect29 16 Emission Detection Ring of detectors Gamma Photon #2 Short-lived radioactive tracer isotope emits positron Positron annihilates with nearby electron – e+ + e- → 2γ • Two 511 keV gamma rays are produced Lect29 • They fly in opposite directions (toPhy208 conserve momentum) Wed, May 7 2008 Isotope Max. Positron Range (mm) 18F 2.6 11C 3.8 68Ga 9.0 82Rb 16.5 • If detectors receive gamma rays at the approx. same time, we have a detection • Nuclear physics sensor and electronics 17 Wed, May 7 2008 Phy208 Lect29 18 3 Detect ionizing radiation Radioactive tracers Worked on radioactivity as student with Ernest Rutherford. Lodged in nearby boarding home. Geiger counter Suspected his landlady was serving meals later in the week ‘recycled’ from the Sunday meat pie. His landlady denied this! deHevesy described his first foray into nuclear medicine: “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.” Wed, May 7 2008 Decay of • Electroscope George de Hevesy Phy208 Lect29 19 Wed, May 7 2008 Phy208 Lect29 20 Gamma decay 60Co 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. • This is one of sources used in the lab. • Decays by electron emission, as predicted. • But decays to an excited state. • Photons emitted as excited state drops to its ground state. Wed, May 7 2008 Phy208 Lect29 Nucleus also emits photon as it drops to ground state This is gamma radiation Extremely high energy photons. 21 Ni Phy208 Lect29 • rad (radiation absorbed dose) • amount of radiation to deposit 0.01 J of energy in 1 kg of absorbing material • 50-60% of cancer patients treated with radiation • Goal: disable cancerous cells without hurting healthy cells • RBE (relative biological effectiveness = # rads of x-rays that produces same biological damage as 1 rad of radiation being used • rem (roentgen equivalent in man) = dose in rem = dose in rad x RBE • X-rays or γ-rays ( 60Co) from 20 KV to 25 MV Phy208 Lect29 28 60 28 Ni 22 Radiation Levels Radiation Therapy Wed, May 7 2008 Wed, May 7 2008 60 23 Radiation type RBE X-rays Gamma rays Beta particles Alpha particles 1 1 1-2 10-20 Wed, May 7 2008 Ground 0.30 rem/yr Mercury 9 60.6 rem/yr Apollo 14 146.2 rem/yr MIR Station 34.9 rem/yr Space Station 36.5 rem/yr Safe limit ( US gov ) 0.50 rem/yr Phy208 Lect29 24 4 Your exposure in the lab Decay summary • Your has an activity of 1 µCurie ( 3.7 "10 4 decays /s) • Each decay: 1.3 MeV photon emitted • Assume all are absorbed by a 1 kg section of your body for 1 hour ! • Energy absorbed in 1 kg = 60Co (1.3 "10 eV )(1.6 "10 6 #19 J /eV )( 3.7 "10 4 decays /s)(1hr)( 3600s /hr) = 2.8 "10#5 J What dose do you receive? A. 0.5 rem B. 0.3 rem ! C. 0.1 rem (2.8 "10 #5 J /kg)(1rad /(0.01J /kg)) = 0.003 rad = 0.003 rem Wed, May 7 2008 D. 0.05 rem E. 0.003 rem Phy208 Lect29 ! 25 • 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 Wed, May 7 2008 Phy208 Lect29 26 Decay question 20Na decays in to 20Ne, a particle is emitted? What particle is it? Na atomic number = 11 Ne atomic number = 10 A. B. C. D. Alpha Electron beta Positron beta Gamma Wed, May 7 2008 20Na has 11 protons, 9 neutrons has 10 protons, 10 neutrons So one a proton (+ charge ) changed to a neutron (0 charge) in this decay. A positive particle had to be emitted. 20Ne Phy208 Lect29 27 5