Radioactivity. Nuclear Physics. # neutrons vs# protons Where does the energy released in the nuclear 11/29/2010 A=N+Z. Nuclear Binding, Radioactivity

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Physics 1161: Lecture 25 Nuclear Binding, Radioactivity Sections 32-1 32-9 Marie Curie 1867-1934 Radioactivity Spontaneous

Antoine Henri Becquerel 1852-1908 Wilhelm Roentgen 1845-1923 A Z 6 3 Li Nuclear Physics Nucleus = Protons+ Neutrons nucleons Z

neutrons vs# protons Where does the energy released in the nuclear But protons repel one another (Coulomb Force) and when Z is

1 Physics 1161: Lecture 25 Nuclear Binding, Radioactivity Sections Marie Curie Radioactivity Spontaneous emission of radiation from the nucleus of an unstable isotope. Antoine Henri Becquerel Wilhelm Roentgen A Z 6 3 Li Nuclear Physics Nucleus = Protons+ Neutrons nucleons Z = N = A material is known to be an isotope of lead. Which of the following can be specified? 1. The atomic mass number 2. The neutron number 3. The number of protons A = nucleon number (atomic mass number) Gives you mass density of element A=N+Z Periodic_Table # neutrons vs# protons Where does the energy released in the nuclear But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z. reactions of the sun come from? 1. covalent bonds between atoms 2. binding energy of electrons to the nucleus 3. binding energy of nucleons 1

Strong Nuclear Force Acts on Protons and Neutrons Strong enough to overcome Coulomb repulsion Acts over very short distances Two atoms don t feel force Strong Nuclear Force Hydrogen atom: Binding

2 Strong Nuclear Force Acts on Protons and Neutrons Strong enough to overcome Coulomb repulsion Acts over very short distances Two atoms don t feel force Strong Nuclear Force Hydrogen atom: Binding energy =13.6eV (of electron to nucleus) Coulomb force electron proton neutron Simplest Nucleus: Deuteron=neutron+proton Very strong force Binding energy ofdeuteron = ev 2.2Mev! proton or Binding Energy Einstein s famous equation E = m c 2 Binding Energy Plot Iron (Fe) has the most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. 10 Proton: mc 2 = 938.3MeV Neutron: mc 2 = 939.5MeV Deuteron: mc 2 =1875.6MeV Adding these, gives MeV Difference is Binding energy, 2.2MeV M Deuteron = M Proton + M Neutron Binding Energy BINDING ENERGY in MeV/nucleon U Mass/Nucleon vs Atomic Number Fusion Fission E = mc 2 E: energy m: mass c: speed of light c = 3 x 10 8 m/s 2

E = mc 2 Mass can be converted to energy Energy can be converted to mass Mass and energy are the same thing Mass Defect in Fission When a heavy element (one beyond Fe) fissions, the resulting

3 E = mc 2 Mass can be converted to energy Energy can be converted to mass Mass and energy are the same thing Mass Defect in Fission When a heavy element (one beyond Fe) fissions, the resulting products have a combined mass which is less than that of the original nucleus. Mass Defect of Alpha Particle Mass difference = u Binding energy = 28.3 MeV Fusion product has less mass than the sum of the parts. Which of the following is most correct for the total binding energy of an Iron atom (Z=26)? 1. 9 MeV MeV MeV Mev BINDING ENERGY in MeV/nucleon 0% 0% 0% 0% B field into screen 3 Types of Radioactivity Alpha Decay Radioactive sources α particles: 4 He nucleii 2 detector β particles: electrons γ: photons (more energetic than x-rays) Alpha decay occurs when there are too many protons in the nucleus which cause excessive electrostatic repulsion. An alpha particle is ejected from the nucleus. An alpha particle is 2 protons and 2 neutrons. An alpha particle is also a helium nucleus. Alpha particle symbol: 4 2 He 3

4 Beta Decay Beta decay occurs when neutron to proton ratio is too big A neutron is turned into a proton and electron and an antineutrino The electron and the antineutrino are emitted Gamma Decay Gamma decay occurs when the nucleus is at too high an energy Nucleus falls down to a lower energy level High energy photon gamma ray -is emitted α: example β: example Decay Rules 1) Nucleon Number is conserved. 2) Atomic Number (charge) is conserved. 3) Energy and momentum are conserved U Th+α A * A γ: example P P+ 0 Z Z 0γ recall 4 2He =α 1) 238 = Nucleon number conserved 2) 92 = Charge conserved n 1p 1e + 0 ν Needed to conserve energy and momentum. A nucleus undergoes αdecay. Which of the following is FALSE? 1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2 The nucleus 234 undergoes β decay. Which 90Th of the following is true? 1. The number of protons in the daughter nucleus increases by one. 2. The number of neutrons in the daughter nucleus increases by one U Radioactive Decay Th Pa 4

5 U 238 Decay Decay Series Nuclear Decay Links 8q/notes/U238scheme.gif 8q/notes/fourdecschemes.gif Which of the following decays is NOT allowed? U Th+α Po 82Pb+ 2He C N+γ K + + ν p e 1 0 Decays per second, or activity : If the number of radioactive nuclei present is cut in half, how does the activity change? 1. It remains the same 2. It is cut in half 3. It doubles N t = λn No. of nuclei present decay constant Decays per second, or activity Start with C atoms. N t = λn decay constant After 6000 years, there are only 8 left. How many will be left after another 6000 years? No. of nuclei present Decay Function N(t)= N 0 e λt t T = N 0 2 1/2 Every 6000 years ½ of atoms decay time 5

6 Radioactivity Quantitatively Decays per second, or activity Survival: No. of nuclei present at time t Instead of baseewe can use base2: e λt t = 2 Then we can write N t = λn decay constant N(t )= N 0 e λt No. we started with at t=0 T 1/2 where T1/2 = λ Half life No. of nuclei present N(t )= N 0 e λt t T = N 0 2 1/2 Carbon Dating Cosmic rays cause transmutation of Nitrogen to Carbon-14 n+ N H+ C C-14 is radioactive with a half-life of 5730 years It decays back to Nitrogen by beta decay C e+ N The ratio of C-12 (stable) atoms to C-14 atoms in our atmosphere is fairly constant about /1 This ratio is the same in living things that obtain their carbon from the atmosphere You are radioactive! One in 8.3x10 11 carbon atoms is 14 C which β decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon. N 1.0 mole 12 g ( ) 14 = 11 λ =.693 T 1/ 2 = atoms g Carbon Dating We just determined that living organisms should have a decay rate of about 0.23 decays/ gram of carbon. The bones of an ice man are found to have a decay rate of decays/gram. We can estimate he died about 6000 years ago. N t = λn Summary Nuclear Reactions Nucleon number conserved Charge conserved Energy/Momentum conserved α particles = 4 nuclei 2He β - particles = electrons γ particles = high-energy photons Mass/Nucleon vs Atomic Number Fusion Fusion Fission Fission Survival: N(t)= N 0 e λt T 1/2 = λ Decays Half-Life is time for ½ of atoms to decay 6

7 U Fissile Abundance of U-235 U-235 Fission by Neutron Bombardment Possible U-235 Fission Chain Reaction Breeder Reaction 7

8 Breeder Reactor Small amounts of Pu-239 combined with U- 238 Fission of Pufrees neutrons These neutrons bombard U-238 and produce more Pu-239 in addition to energy 8

Nuclear Physics. Radioactivity. # protons = # neutrons. Strong Nuclear Force. Checkpoint 4/17/2013. A Z Nucleus = Protons+ Neutrons

Nuclear Physics. Radioactivity. # protons = # neutrons. Strong Nuclear Force. Checkpoint 4/17/2013. A Z Nucleus = Protons+ Neutrons Marie Curie 1867-1934 Radioactivity Spontaneous emission of radiation from the nucleus of an unstable isotope. Antoine Henri Becquerel 1852-1908 Wilhelm Roentgen 1845-1923 Nuclear Physics A Z Nucleus =