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Radioactivity Spontaneous emission of small particles and/or radiation (energy) by unstable atomic nuclei to attain more stable nuclear state 3/25/2017

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**Electrons react outside nucleus **

Chemical Reactions Nuclear Reactions Electrons react outside nucleus Protons/neutrons/electrons/other elementary particles involved Same # of each kind of element appears in reactants and products (atoms rearranged by breaking/forming chemical bonds) Elements transmute into other elements Isotopes react similarly Isotopes react differently Dependent on chemical combination Independent on chemical combination Mass reactants = mass products Mass changes detectable Reactions accompanied by absorption or release of relatively small amounts of energy Reactions accompanied by absorption or release of tremendous amounts of energy Rates of reactions influenced by temperature, pressure, concentration, and catalysts Rates of reaction normally not affected by temperature, pressure, and catalysts 3/25/2017

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**Nuclide: nucleus with specified number of protons and neutrons**

Symbolized as AzX X - symbol of element A - mass number = nuclear mass Z - atomic number = nuclear charge Isotope: nuclides with same atomic # but different mass #s 3/25/2017

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Radionuclide: Radioactive nuclide (unstable nucleus) Radioactive isotope ( radioisotope): isotope w/radioactive nuclide Radioactive decay: process of all radioactive decay until isotope with stable nucleus is reached Transmutation: nucleus reacts with another nucleus, elementary particle, or photon (gamma particle) to produce one or more new nuclei Nuclear equation: representation of change that occurs within or among atomic nuclei 3/25/2017

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**Balancing rules for nuclear equations**

Sum of mass #s of reactants must equal sum of mass #s of products (conservation of mass number) 14 + 4=18=17 + 1 Sum of nuclear charges of reactants must equal sum of nuclear charges of products (conservation of atomic number) 7 + 2 = 9 = 8 + 1 3/25/2017

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**2+ 1- 1+ 1 100 10,000 High 42He nucleus 0-1e electrons**

Property Alpha (α) Beta (β-) Gamma (γ ) Proton Positron (β+) Neutrons 10n X-rays Charge 2+ 1- 1+ Mass 6.64 x g 9.11 x g × g × g Relative penetrating power 1 100 10,000 High Nature of radiation 42He nucleus 0-1e electrons High-energy photons 11H nucleus of H-1 atom 0+1e 10n How far they travel Few cm in air (colliding w/ air molecules) Lose KE and electrons to become ordinary He Up to 300 cm in air (collide less w/air molecules because very small) Highly penetrating EM radiation easily passing through most objects Not able to penetrate matter to significant extent Very penetrating (no charge) Highly penetrating EM radiation that can penetrate through body Stopped by High ionizing power Do not penetrate skin Stopped w/piece of paper Harmful if ingested Moderate ionizing power Can penetrate skin Stopped by aluminum foil thicker than 3 mm Skin burns, harmful if ingested Almost no ionizing power Few cm lead or m of concrete Dangerous because very penetrating Antimatter, so annihilated when encounter electron Materials w/high H content Causes significant damage when collisions occur by producing gamma rays through interactions w/tissue atoms 3/25/2017

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**00γ 42α 0-1β (electron) 0+1β (Electron w/+ charge) 0-1e (X-ray photon)**

Alpha emission Beta Positron emission Electron capture Gamma rays What is emitted 42α 0-1β (electron) 0+1β (Electron w/+ charge) 0-1e (X-ray photon) 00γ How Emission of 42He N P/ elec-tron emitted (10n 0-1β + 11p + energy) P N w/positron emitted (11p 0-1β + 10n) Captured low energy inner-shell electron + P N (0-1e + 11p 10n + energy) Emission of EM radiation Nuclear isomer (m next to mass) in excited state Returns to ground state when photon released What happens Mass (-4) 4 Atomic # (-2) Mass same Atomic # (+1) Atomic # (-1) No change mass/# What elements emit these Heavy iso-topes (> 83) Reduce #P/N Neutron rich isotopes Proton rich isotopes Most all unstable isotopes Example 3/25/2017

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**Nuclear Stability Neutron-to-proton ratio Low atomic numbers**

Hg: atomic mass = 200 atomic # = 80 #P = 80, #N = 120 N/P ratio is 120/80 = 1.50 Neutron-to-proton ratio Low atomic numbers Ratio close to 1 Fall in zone of stability Atomic # increases (21-83) Z > 20, #N always exceeds #P protons in stable isotopes Ratio gradually increases from 1 to 1.5 > 83 (Bismuth) no stable nuclides All radioactive and their isotopes decay Lie outside zone of stability 3/25/2017

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**positron emission and electron capture**

alpha emission beta emission positron emission and electron capture 3/25/2017

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**What is emitted depends upon location by zone of stability**

Left of zone (mass # > atomic wt) Neutron rich (tries to gain protons/lose neutrons) – NP + beta particle Decays by β emission Right of zone (mass # < atomic wt) Proton rich (tries to lose protons/gain neutrons) – PN + positron Decays by positron emission/electron capture On zone, but Z>83 Often decay by emitting alpha particles (usually above 60) 3/25/2017

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**24196Cf undergoes electron capture 24196Cf + 0-1e 24195Am **

24195Am produces an α particle 24195Am 24193Np + 42He 12154Xe produces a β particle 12154Xe 12153I + 01e 16467Ho + 0-1e ? 16467Ho + 0-1e 16466Dy 15867? 15866Dy + 01e 15867Ho 15866Dy + 01e 24294Pu 23892U + ? 24294Pu 23892U + 42He 3/25/2017

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Magic Numbers Isotopes w/even # nucleons (P + N) tend to be more stable than those w/odd # nucleons Nuclei w/certain specific # P/N within nucleus ensure extra degree of stability Nucleus much less likely to absorb additional neutron Magic numbers for P/N are 2/8/20/28/50/82/126 Correspond to filling of shells in structure of nucleus When nuclei has P/N both in magic numbers, very stable and in high abundance in universe 3015P < 3920Ca < 4020Ca P-30-least stable-odd #s of both P/N C-39-even #P (20)/odd #N-even #P and "magic number"-more stable than P-30 Ca-40-most stable-even #P/N-both #s "magic numbers" 3/25/2017

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Pascal`s Triangle 1 = 2 5 - 4 8 15 10 20 35 6 14 28 70 25 50 126 41 82 210 56 21 63 3/25/2017

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**Of all 264 stable isotopes, number of protons/neutrons**

Odd-even rule When #N/P both even numbers, isotopes tends to be far more stable than when they are both odd Of all 264 stable isotopes, number of protons/neutrons 168-even/even 57-even/odd 50-odd/even 4-odd/odd 3/25/2017

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**Radioactive series (nuclear disintegration series)**

Some nuclei cannot gain stability w/single emission 3/25/2017

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** 82Pb206 24797Bk undergoes decay to what element after ααβααβαβααααββα?**

Z > 83 -- alpha 92U 238 => 90Th He4 unpredicted Beta 90Th234 => 91Pa eo unpredicted Beta 91Pa234 => 92U eo 92U234 => 90Th He4 90Th230 => 88Ra He4 88Ra226 => 86Rn He4 86Rn222 => 84Po He4 84Po218 => 82Pb He4 Beta 82Pb214 => 83Bi eo 83Bi214 => 84Po eo 84Po214 => 82Pb He4 Beta 82Pb210 => 83Bi eo 83Po210 => 84Po eo 84Po210 => 82Pb He4 stable 82Pb206 24797Bk undergoes decay to what element after ααβααβαβααααββα? 3/25/2017

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**Nuclear Transmutations**

Nuclear reactions induced by nucleus gaining neutron or another nucleus Converts nucleus into another nucleus Can be represented by listing, in order, target nucleus, bombarding particle, ejected particle, and product nucleus 3/25/2017

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Homework: Read 18.1, pp Q pp , #9a, 10, 12, 14, 16, 18 3/25/2017

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Rates of decay Unstable atomic nucleus loses energy by emitting radiation Spontaneous Without collision w/another particle Radioactive decay rates obey first-order kinetics Instantaneous rate of decay of N radioactive atoms is directly proportional to # atoms present at that instant in time Unit of activity Becquerel (bq) – SI unit 1 Bq is one transformation (decay) per second Curie (Ci) Originally based on activity of 1 g radium (1 Ci = 3.7 x 1010 Bq) 3/25/2017

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**Radioactivity of substance may be measured decay rate**

Decay rate = # atoms disintegrating per unit time = λN λ (k) = first-order rate constant (decay constant) N = # atoms of particular radioisotope present in sample X = concentration of reactant at any moment Xo = initial concentration Integrated first-order equation N = # atoms of radioisotope present in sample after time t has elapsed N0 = # atoms of radioisotope present initially 3/25/2017

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**Rate constant for 14C is much larger than rate constant for 238U**

14C: k = x 10-4 yr-1 238U: k = 1.54 x yr-1 Therefore, 14C decays much faster than 238U Half life for decay of 14C is much shorter than that of 238U 14C: t1/2 = 5730 yr 238U: t1/2 = 4.51 x 109 yr 3/25/2017

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Half-life Time it takes for exactly half of nuclei of radioactive sample to decay (activity of source of radiation to fall to half its starting level) Time it takes for # atoms in sample to halve Integrated form of first-order rate law in which N is substituted for concentration of X 3/25/2017

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**Generic Half-Life Chart**

Time Amount Remaining Amount Decayed 100% 0% 1 half-life 50% 2 half-lives 25% 75% 3 half-lives 12.5% 87.5% 3/25/2017

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**The half-life of 23994Pu is 2. 411 x 104 years**

The half-life of 23994Pu is x 104 years. How many years will elapse before 99.9% of a given sample decomposes? We have no specific amounts. However, we do know that of our original decomposes, leaving remaining. We can thus establish the ratio N/N0 as 0.001/ We can find k from t1/2. k = 0.693/ t1/2 = 0.693/ x 104 yr = 2.87 x 10-5/yr ln [N/N0] = -kt = ln(0.001) = 2.87 x 10-5/yr t = 2.87 x 105 yr Total time is about 10 half-lives. We should have about 1/210 (or 0.001) of our original material remaining, and we do. 3/25/2017

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**# half-lives = 1 half-life x 1.000s = 204 ½204 = 3.9 x 10-62 **

The half-life of protactinium-217 is 4.9 x 10-3 s. How much of a 3.50 mg sample of 21791Pa will remain after sec? # half-lives = 1 half-life x 1.000s = 204 4.9 x 10-3 s ½204 = 3.9 x 10-62 3.50 (3.9 x 10-62) = 1.4 x mg Because of the short half-live, essentially none of original nuclide remains after one second. 3/25/2017

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Homework: Read , pp Q pp , #19, 20, 23, 26, 28 3/25/2017

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**Aging carbon-containing materials**

14C is not natural isotope Constantly formed in upper atmosphere 14N is bombarded w/neutrons, keeping proportion of 14C relatively constant When alive, plants/animals maintain same proportion of 14C in bodies because C continuously recycled When organism dies 14C no longer replenished by diet Fraction of isotope in dead organic matter decreases with time By comparing living/ancient 14C and comparing them Reliably determine ages of biological materials that range from 1700 to 17,000 years old (half-life of C-14 is 5730 years) Rule of thumb for radioactive isotope dating of materials Age of sample should be half-lives of isotope used for dating 3/25/2017

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3/25/2017

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**ln(N/N0) = -kt = (- 1.21 x 10-4/yr)(12,000 yr) = -1.45 **

A sample of bone taken from an archeological dig was determined by radiocarbon dating to be 12,000 years old. If we assume that a constant atmospheric C-14/C-12 ratio has 13.6 disintegrations per minute per gram of carbon, how many disintegrations per minute per gram does our 12,000 year old sample give off (half-life for carbon-14 = 5730 year)? k = 0.693/t1/2 = 0.693/5730 yr = 1.21 x 10-4/yr. ln(N/N0) = -kt = ( x 10-4/yr)(12,000 yr) = -1.45 N/N0 = e-1.45 = 0.234 N0 = 13.6 disintegrations, so N = 0.234(13.6) N = 3.2 disintegrations per minute per gram 3/25/2017

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**What is the half-life of strontium-90?**

If we start w/1.000 g of strontium-90, g will remain after 2.00 yr. What is the half-life of strontium-90? k = -1/t ln Nt/NO = -1/2.00 yr ln 0.953g/1.000g k = -1/2.00 yr ( ) = yr-1 T1/2 = 0.693/k = 0.693/ yr-1 = 28.8 yr How much strontium-90 will remain after 5.00 yr? ln Nt/NO = -kt = ( yr-1)(5.00 yr) = Nt/NO = e = g (ev or INV LN function of calculator) Nt = (0.887)NO = (0.887)(1g) = g What is the initial activity of the sample in Bq and in Ci? k = (0.0241/yr)(1 yr/365 days)(1 day/24 hr)(1 hr/3600 s) = 7.64 x s-1 (1.000 g Sr-90)(1 mol Sr-90/90 g Sr-90)(6.022 x 1023 atoms Sr/1 mole Sr-90) = 6.7 x 1021 atoms Total disintegrations/s = (7.64 x disintegrations/atom - s)(6.7 x 1021 atoms ) = 5.1 x 1012 disintegrations/s = same as Bq (5.1 x 1012 disintegrations/s)(1 Ci/ = 3.7 x 1010 disintegrations/s) = 1.4 x 102 Ci 3/25/2017

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**Most devices for detecting radioactivity depend on formation of ions**

Darkening of photographic plates, discharging of electroscopes, and damage to biological tissue all involve ionization Geiger counter (Geiger-Müller tube) Particle-produced ions trigger electricity pulse that is counted Beta/gamma radiation Cloud chambers Measure charged particles (including alpha/beta particles) Scintillation counters Measure many different types Flashes produced counted as measure of # particles emitted Film dosimeters Film reveals whether worker exposed to excess radiation Gives total dose of radiation received 3/25/2017

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Nuclear energy One important consequences of Einstein's theory of relativity was discovery of equivalence of mass and energy Total energy content (E) of system of mass, m is given by Einstein's theory E = mc2 where c is velocity of light (3.0 x 108 m/s) Nuclear energies expressed in electronvolt (eV) and megaelectronvolt (MeV = 106 eV) 1 eV = x J; 1 MeV = x J 1 u (atomic mass unit of mass) = x kg = MeV of energy 3/25/2017

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**Mass of nucleus is direct measure of its energy content **

Atomic mass of He is u Add up mass of P/N/E There is difference of u All atoms are lighter than sum of masses of protons ( g), electrons, and neutrons ( g) Mass defect, Δm, equal to total mass of products minus total mass of reactants (difference between total mass of nucleons and measured mass of nucleus itself) Reflects stability of nucleus 3/25/2017

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**To extract proton/neutron from nucleus, we have to pull pretty hard **

Find that it will regain missing mass Binding energy defined as energy released when nucleus is assembled from its constituent nucleons Equal to energy needed to tear nucleus apart into its nucleons (so mass defect same as binding energy) Literally energy that binds together N/P in nucleus So with our helium atom, missing u released when nucleons come together That energy has to be put back to split nucleus up again 3/25/2017

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**Binding energy measures difference between stability of products of reaction and starting materials**

Provides quantitative measure of nuclear stability Larger the binding energy (more negative), more stable nucleus is toward decomposition Average binding energy per nucleon-binding energy of nucleus divided by mass number Larger binding energy per nucleon, more stable nucleus is 3/25/2017

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**Calculate the mass change for decay of mole of U-238.**

23892U 23490Th + 42He g g – g = g ΔE = Δ(mc2) = c2Δm (3.00 x 108 m/s) 2( g)(1kd/1000g) -4.1 x 1011 kg-m2/s2 = -4.1 x 1011 J Notice Δm converted to kg (SI unit of mass) to obtain ΔE in joules (SI unit for energy) Negative sign indicates energy is released in reaction (over 400 billion joules/mole of U) 3/25/2017

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**Mass of individual nucleons 46 x 1.007825 g/proton = 46.35995 g **

Determine the binding energy in J/mol and MeV/nucleon for 10146Pd (atomic mass = g/mol). Mass of individual nucleons 46 x g/proton = g 55 x g/neutron = g g/mol mass defect = g – g = g ∆E = ∆mc2 = x 10-4 kg (3.00 x 108 m/s)2 (minus sign because mass is lost in forming the nuclide) ∆E = x 1013 J/mol -8.35 x 1013 J MeV mol nuclide = MeV mol x J x 1023 nuclides 101 nucleons nucleon 3/25/2017

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**Natural Radioactivity**

Few naturally occurring radioactive isotopes K-40 decays into Ar-40, found in air C-14 determines age of artifacts Vanadium-50, Tritium (H-3), radon, thorium, lanthanuim-138 Polonium, Z=84 to uranium, Z=92 Radon-222 forms from decomposition of U in rocks (granite) Gathers in lower, unventilated areas of houses Gas decomposes into solid polonium, which if decays in lungs, emits alpha particles which can cause cancer Radium-226-causes biological damage U-238 used to determine age of very old rocks as it decays to lead-206 Transuranium elements (93-118) artificially prepared/radioactive 3/25/2017

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**Used depending on properties of particular isotope**

Tracers to uncover how certain chemical reactions occur Phosphorus-32 shows details of how plants use P to grow/reproduce Medical applications (radioactivity/short half-life necessary to ensure rapid decay and elimination from body) Diagnostics (PET scan) Treatment (I-131 for thyroid cancer) Determine age of various artifacts (C-14) Smoke detectors (Americium-241) Food irradiation (gamma rays) Irradiation in pest control 3/25/2017

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**Artificial Radioactivity**

Artificial radioactivity results when unstable nucleus produced by transmutation Nuclear transmutation-process of converting one element into another Al atoms bombarded w/alpha particles produces radioactive P-30 P-30 decays by positron emission and has half-life of 2.5 min Does not occur naturally in phosphorus compounds 3/25/2017

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**Induced transmutation**

Neutrons easily captured by stable nuclei No charge Not repelled by target nuclei No KE needed to overcome electrostatic repulsion if protons/alpha particles used Readily produce "artificial" radioactivity New nucleus formed has higher n : p ratio Leads to product that decays by beta decay Neutron capture by chlorine-37 yields chlorine-38 3/25/2017

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**Nuclear transmutation processes are abbreviated using**

Target nucleus (bombarding particle, ejected particle) Product nucleus n, p, d, α, e, and γ used to represent neutron, proton, deuteron, alpha particle, electron, and gamma ray 3/25/2017

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**Does not occur spontaneously**

Nuclear Fission-any process that yields two nuclei of almost equivalent mass Does not occur spontaneously Requires bombardment of fissile nucleus (23592U or 23994Pu) By energetic neutrons That causes release of several more neutrons Chain reaction Neutrons released in each fission start additional fissions Two ways to keep fission from becoming uncontrolled Small enough sample so released neutrons will not hit other U-235 nuclei to continue chain reaction Critical mass of several pounds needed before chain reaction will be sustained (explosion) Excess neutrons can be absorbed by certain materials (graphite, paraffin) Control rods adjust number of available neutrons and rate of nuclear reactions 3/25/2017

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**Containment shell of concrete/steel for shielding **

Fission reactors-employs controlled chain reaction to provide continuous source of useful energy Containment shell of concrete/steel for shielding Fuel rods in core as source of energy (enriched U-235) Moderator creates neutrons for reaction Control rods regulate rate of fission (cadmium) Coolant (water/liquid Na) removes thermal energy from core Heat exchanger receives thermal energy and produces steam for generation of electrical energy by turbine connected to reactor Problems Heat causes thermal pollution Radioactive waste disposal Benefits Energy Produce radioactive isotopes 3/25/2017

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**For self-sustaining fusion reaction to occur **

Nuclear Fusion-combination of two nuclei to form a larger, more stable nucleus For self-sustaining fusion reaction to occur Temperatures of 40,000,000 K needed Nucleus has higher average binding energy per nucleon Because all nuclei positively charged, they must collide with enormous force to combine At these temperatures, gases completely ionized into mixture of positive nuclei and electrons (plasma) One gram of hydrogen upon fusion releases energy equivalent to combustion of 20 tons of coal Fusion of four moles of H atoms releases 2.6 x 109 kJ of energy + 2γ + 2ν (neutrino) 3/25/2017

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**Interaction of radiation with matter**

Alpha/beta/gamma rays pass through matter Alpha/beta particles colliding with electrons Lose small fraction of their energy in collision Forcefully eject electrons from atoms/ molecules Because alpha/beta particles extremely energetic, thousands of collisions required to bring them to rest Produce ions Particles produce "tracks" of ionization Alpha/beta/gamma rays known as ionizing radiation 3/25/2017

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**Units of Radiation Dose- rad and rem**

Rad (radiation absorbed dose) 0.01 joule of energy absorbed per kilogram Beams of different radiations cause very different biological damage even when body absorbs same amount of energy from each type, it is necessary to define unit specifically for biological tissue rem (radiation equivalent in man) Absorbed dose in rads x relative biological effectiveness factor, RBE dose (in rem) = RBE x dose (in rad) For beta and gamma rays RBE = 1.0; for fast neutrons and alpha particles RBE = 10 Dose of one rad of alpha radiation = 10 rem 3/25/2017

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**Homework: Read 18.4-18.7, pp. 889-903 Q pp. 908-909, #33, 34, 38, 44**

Do 1 additional exercise and 1 challenge problem Submit the quizzes by to me: 3/25/2017

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Nuclear Reactions Chapter 19

Nuclear Reactions Chapter 19

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