β and γ decays, Radiation Therapies and Diagnostic, Fusion and Fission Final Exam Surveys New material Example of β-decay Beta decay Y + e # Y'+e +

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1 β and γ decays, Radiation Therapies and Diagnostic, Fusion and Fission Last Lecture: Radioactivity, Nuclear decay Radiation damage This lecture: nuclear physics in medicine and fusion and fission Final Exam Wed, Dec 20, at 7:25-9:25 pm in VAN VLECK B102 What in this exam? About twice multiple questions/short answers + 4 problems About 40% on new material 2 sheets allowed The rest on previous materials covered by MTE1 MTE2 MTE3. Your last HW is important! New material Ch 41: Sec , something on tunneling (41.6) Ch 42: , 42.5 (not the math), , Ch 43: Sec 43.1 Ch 44: Sec , 44.8 Ch 45: 45.5, 45.7 (only radiation therapy), 45.6 (only Geiger) No fission and fusion in the exam Surveys Surveys: 2 surveys to complete 1) Physics Attitude Survey 2) Phys 208 Course Evaluation Survey. They are both due by 12/20 12am. You should have received with a hyper-link to an on-line web survey. Beta decay Nucleus emits an electron or a positron Must be balanced by a positive or negative charge appearing in the nucleus. A Z X" A Z +1 Y + e # A Z X" A Z #1 Y'+e + This occurs as a n changing into a p or a p into a n Example of β-decay C (radioactive form of carbon) decays by β- decay (electron emission). Carbon Z = 6, C has (-6)=8 neutrons. A new element with Z = 7 6 C " 7 N+ e # Beta decay decreases number of neutrons in nucleus by one increases number of protons in nucleus by one 1

2 C to 12 C ratio C (Z=6) has a half-life of 5,730 years, continually decaying back into N (Z=7). In atmosphere very small amount! 1 nucleus of C each nuclei of 12 C If material alive, atmospheric carbon mix ingested (as CO 2 ), ratio stays fixed. After death, no exchange with atmosphere. Ratio changes as C decays So can determine time since the plant or animal died (stopped exchanging C with the atmosphere) if not older than yr Carbon dating A fossil bone is found to contain 1/8 as much C as the bone of a living animal. Using T 1/2 =5,730 yrs, what is the approximate age of the fossil? A. 7,640 yrs B. 17,190 yrs C. 22,900 yrs D. 45,840 yrs Factor of 8 reduction in C corresponds to three half-lives. So age is 5,730 x 3 =17,190 yrs The Positron and Antimatter Every particle now known to have an antiparticle. Our Universe seems to contain more matter (we are lucky otherwise everything would annihilate into photons!) Decay Quick Question 20 Na decays in to 20 Ne, a particle is emitted? What particle is it? Na atomic number Z = 11 Ne Z = 10 A. Alpha B. Electron beta C. Positron beta D. Gamma 20 Na has 11 protons, 9 neutrons 20 Ne 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. Positron 1st detection in cosmic rays through bending in a B-field and a bubble chamber (Anderson 1932) p " n + e + + # e Nuclear Medicine: diagnostic Basic Idea: Inject patient with radio-isotope labeled substance (tracer) Chemically the same, but physically different Detect the radioactive emissions (gamma rays) Reconstruct the 3-D image PET image Showing a tumor Positron Emission Tomographie - PET Gamma Photon #1 e + -e - γγ Gamma Photon #2 Isotope 18 F 11 C 68 Ga 82 Rb Nucleus (protons+neutrons) electrons Max. Positron Range (mm) Basic Idea: Nucleus emits a positron Positron collides with a nearby electron and annihilates e + + e - 2γ Two 511 kev gamma rays are produced They fly in opposite directions (to conserve momentum) 2

3 Emission Detection Ring of detectors Image Reconstruction If detectors A & B receive gamma rays at the approx. same time, we have a detection Nuclear physics sensor and electronics Each coincidence event represents a line in space connecting the two detectors along which the positron emission occurred. Coincidence events can be grouped into projections images, called sinograms. Sinograms are combined to form 3D images Radiation Cancer Therapy 50-60% of cancer patients treated with radiation Radiation destroys the cancer cells' ability to reproduce and the body naturally gets rid of these cells. Although radiation damages both cancer cells and normal cells, most normal cells can recover from the effects of radiation and function properly. Ionization (stripping atomic electrons) makes nuclear radiation dangerous Used radiations: X and γ-rays from 20 KV to 25 MV Pion Therapy under study, less invasive then photons Neutrons,protons,.. Gamma decay Both α and β-decays can leave the nucleus in excited state The nucleus can decay to a lower energy state (eg the ground state) by emitting a high energy photon (1 MeV-1 GeV) The X* indicates a nucleus in an excited state Decay Quick Question 20 Na decays in to 20 Ne, a particle is emitted? What particle is it? Na atomic number Z = 11 Ne Z = 10 A. Alpha B. Electron beta C. Positron beta D. Gamma 20 Na has 11 protons, 9 neutrons 20 Ne 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. Decay Question? Which of the following decays is NOT allowed? U! Th + " Po! 82Pb+ 2He 2 C 6 7 " N +! 238 = = = = = +0 6 <> 7+0 p " n + e + + # e # 0 K " + +! p e # = =

4 Nuclear Magnetic Resonance (NMR) Now called magnetic resonance imaging (MRI) A nucleus has spin angular momentum (p and n have spin 1/2). 2 quantum numbers are associated to the magnitude of the spin angular momentum and to the possible orientations of the spin respect to a z axis I z NMR Nuclear magnetic moment µ will precess when placed in an external B-field (angular frequency B) Min energy: µ aligned to B (as a compass needle), unstable equilibrium: needle anti-aligned to B Since proton energy is quantized: it can be aligned (spin up) o anti-aligned (spin down) Turning on B lowers the energy of a spin up proton and increases the energy of a spin down one (there is an energy difference between the states of 10-7 ev Photons of applied radio-frequency matching this E difference (resonance) are absorbed and emitted Absorption of energy by nuclei can be electronically detected MRI An MRI (Magnetic Resonance Imaging) is based on NMR The patient is placed inside a solenoid with B constant in time but varying in space. Because of these variations, protons in different parts of the body precess at different frequencies This provides information about the positions of the protons It causes minimum cellular damage compared to X-rays Other applications of Nuclear Physics Alternative sources of energy to oil Fission: 435 nuclear power plants in the world generate 245 GW of electricity in 32 countries (1/6 of world s electricity supply!!) France 76% Belgium 56% Sweden 47% Switzerland 40% South Korea 36% Japan 33% The United States has the largest total electric output from nuclear power: 98,000 MW from 105 plants, 20% of US electric power. Nuclear Fission A heavy nucleus splits into 2 smaller nuclei. Fission is initiated when a heavy nucleus captures a thermal neutron n U" U* " X + Y + neutrons Excited state lifetime s A 95 <N n > ~2.5 A 0 BINDING ENERGY in MeV/nucleon Fusion Binding Energy Plot 238 U has E b /nucleon ~8.2 MeV while X,Y ~7.2 MeV/nucleon Hence released energy Q ~ 235 MeV!! 10 Fission Fission = Breaking large atoms into small Fusion = Combining small atoms into large n U" U* " X + Y + neutrons U 16 4

5 Chain Reactions An average of 2.5 neutrons are emitted when 235 U undergoes fission These neutrons are then available to trigger fission in other nuclei Chain reaction: an average of 1 n emitted in 235 U fission must be captured by another 235 U. Moderators reduces the probability that n are captured by 238 U that does not undergo fission Enrico Fermi development of world s first fission reactor (1942) Nuclear Fusion Work principle of stars like the Sun two light nuclei combine to form a heavier nucleus The final nucleus mass is less than the masses of the original nuclei hence release of energy Solar cycle: 4p 4 He So the liberated energy is 4( u) u= u x MeV/u= 26.7 MeV More than in fission! Main problem: enough kinetic energy to nuclei to overcome Coulomb repulsion Fusion of deuterium and tritium Methods High temperature ~ 10 8 K to overcome Coulomb forces At these temperatures, atoms are ionized, forming a plasma Plasma confinement is still a problem magnetic confinement tokamak Inertial confinement Laser 5

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