Nuclear Reactions- chap.31. Fission vs. fusion mass defect..e=mc 2 Binding energy..e=mc 2 Alpha, beta, gamma oh my!
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1 Nuclear Reactions- chap.31 Fission vs. fusion mass defect..e=mc 2 Binding energy..e=mc 2 Alpha, beta, gamma oh my!
2 Definitions A nucleon is a general term to denote a nuclear particle - that is, either a proton or a neutron. The atomic number Z of an element is equal to the number of protons in the nucleus of that element. The mass number A of an element is equal to the total number of nucleons (protons + neutrons). The mass number A of any element is equal to the sum of the atomic number Z and the number of neutrons N : A = N + Z
3 Symbol Notation A convenient way of describing an element is by giving its mass number and its atomic number, along with the chemical symbol for that element. A Z X Mass number Atomic number Symbol For example, consider beryllium (Be): 9 4 Be
4 Fission and Fusion Fission large unstable nuclei split apart e.g. Uranium-235 Induced by bombarding with neutrons (e.g in reactors) During fission energy is released Fusion light nuclei release energy when they combine - in fusion reactions
5 Fission: split heavy elements 1u = 7 TNT molecules 238 U stable, 235 U radioactive Atomic bomb, 1945 Nuclear power, subs, earth
6 Fusion: join lighter elements 1u >10? TNT molecules H most unstable (H bomb 1952) fusion is hard to start (need to crush or super heat) Stars, our sun do it easily
7 Einstein s theory of Special Relativity (1905) showed that - Mass and Energy are Equivalent The total energy of a particle of rest mass m 0 and velocity v is given by E m c mc,where m is the total relativistic mass, 2 v 1 c 2 m m 0 v 1 c 2 2 For v<<c we can ignore relativity! (m = m 0 ) Object at rest: E = m 0 c 2 Object in motion: E = m 0 c 2 + ½ m 0 v 2
8 Rest mass energy (E=m 0 c 2 ) All objects have rest mass energy since it takes work to put them together! W = F*d = Dmc 2 where Dm = final initial mass Product mass is less than reactant mass The missing or lost mass is known as Mass Defect Dm A + B = C + Dm
9 Mass and Energy Recall Einstein s equivalency formula for m and E: E mc 2 ; c 3 x 10 8 m/s The energy of a mass of 1 u can be found: E = (1 u)c 2 = (1.66 x kg)(3 x 10 8 m/s) 2 E = 1.49 x J Or E = MeV When converting amu to energy: c MeV u
10 What is the rest mass energy of a proton ( u)? E = mc 2 = ( u)(931.5 MeV/u) Proton: E = MeV Similar conversions show other rest mass energies: Neutron: E = MeV Electron: E = MeV
11 Which has more mass, a neutron in a nucleus or one all by itself? It takes work to separate a neutron from a proton in a nucleus
12 Free neutron has more mass! Free neutron is unstable! Half-life of 11 minutes
13 The Mass Defect The mass defect is the difference between the rest mass of a nucleus and the sum of the rest masses of its constituent nucleons. The whole is less than the sum of the parts! Consider the carbon-12 atom ( u): Nuclear mass = Mass of atom Electron masses = u 6( u) = u The nucleus of the carbon-12 atom has this mass. (Continued...)
14 Mass Defect (Continued) Mass of carbon-12 nucleus: Proton: u Neutron: u The nucleus contains 6 protons and 6 neutrons: 6 p = 6( u) = u 6 n = 6( u) = u Total mass of parts: = u Mass defect m D = u u m D = u
15 The Binding Energy The binding energy E B of a nucleus is the energy required to separate a nucleus into its constituent parts. E B = m D c 2 where c 2 = MeV/u The binding energy for the carbon-12 example is: E B = ( u)(931.5 MeV/u) Binding E B for C-12: E B = 92.2 MeV
16 proton mass = u neutron mass = u Mass Defect Example Uranium-235 has 92 protons and 143 neutrons You may therefore expect its mass to be: 92 x u x u = u However its mass is actually u The missing mass or mass defect = u u = 1.88u This principle applies to all nuclei Where does the mass go??
17 Relativity can explain the mass defect e.g. Uranium-235 has a mass defect of 1.88 u By E = mc 2 the energy equivalent of this mass is (1.88 x x10-27 ) x (3 x 10 8 ) 2 = 2.8 x J This is the energy that would have to be put in to split the U-235 nucleus into its constituents it is the energy required to bind the nucleus together binding energy. Mass of all neutrons + protons = mass of nucleus + binding energy.
18 Nuclear Stability The higher the binding energy per nucleon the more stable a nucleus will be For U-235 the binding energy is 1.749x10 9 / 235 = 7.44 MeV per nucleon This value is different for every nucleus and has a maximum for Iron-56
19 A neutron has the lowest mass when placed inside an iron nucleus Fe (iron) is the most stable nucleus highest binding energy per nucleon Elements less than iron like to fuse towards iron Elements greater than iron like to fission towards iron
20 The Binding Energy Curve
21 A nucleus will become more stable if a reaction brings it closer to the iron peak Nuclei heavier than iron do this by breaking up into smaller nuclei via Fission Nuclei lighter than iron do this by joining together via Fusion reactions
22 Energy from Fusion e.g. Helium from the fusion of Deuterium and Tritium Original mass, H+ H= He u u = u After reaction, u u = u Mass defect = u u = u = x10-29 kg Energy release = mc 2 = 2.81x10-12 J (approx. 18MeV) 1 0 n
23 The Alpha Particle An alpha particle a is the nucleus of a helium atom consisting of two protons and two neutrons tightly bound. Charge = +2e - = 3.2 x C Mass = u Relatively low speeds ( 0.1c ) Not very penetrating
24 The Beta-minus Particle A beta-minus particle b is simply an electron that has been expelled from the nucleus Charge = e - = -1.6 x C Mass = u High speeds (near c) Very penetrating
25 The Gamma Photon A gamma ray g has very high electromagnetic radiation carrying energy away from the nucleus. g Charge = Zero (0) g g Mass = zero (0) Speed = c (3 x 10 8 m/s) g Most penetrating radiation
26 Radioactive Decay As discussed, when the ratio of N/Z gets very large, the nucleus becomes unstable and often particles and/or photons are emitted. 4 Alpha decay 2a results in the loss of two protons and two neutrons from the nucleus. A Z A 4 4 Z2 2 X Y a energy X is parent atom and Y is daughter atom The energy is carried away primarily by the K.E. of the alpha particle.
27 Example 5: Write the reaction that occurs when radium-226 decays by alpha emission. A Z A 4 4 Z2 2 X Y a energy Ra Y a energy From tables, we find Z and A for nuclides. The daughter atom: Z = 86, A = Ra Rn a energy Radium-226 decays into radon-222.
28 Beta-minus Decay Beta-minus b decay results when a neutron decays into a proton and an electron. Thus, the Z-number increases by one. A Z A 0 Z1 1 X Y b energy X is parent atom and Y is daughter atom The energy is carried away primarily by the K.E. of the electron. -
29 Nuclear Reactions It is possible to alter the structure of a nucleus by bombarding it with small particles. Such events are called nuclear reactions: General Reaction: x + X Y + y For example, if an alpha particle bombards a nitrogen-14 nucleus it produces a hydrogen atom and oxygen-17: 4 a N H O
30 Conservation Laws For any nuclear reaction, there are three conservation laws which must be obeyed: Conservation of Charge: The total charge of a system can neither be increased nor decreased. Conservation of Nucleons: The total number of nucleons in a reaction must be unchanged. Conservation of Mass Energy: The total massenergy of a system must not change in a nuclear reaction.
31 Example 7: Use conservation criteria to determine the unknown element in the following nuclear reaction: H Li He X energy Charge before = = +4 Charge after = +2 + Z = +4 Z = 4 2 = 2 Nucleons before = = 8 Nucleons after = 4 + A = 8 A Z (Helium has Z = 2) H Li He He energy (Thus, A = 4)
32 Conservation of Mass-Energy There is always mass-energy associated with any nuclear reaction. The energy released or absorbed is called the Q-value and can be found if the atomic masses are known before and after. H Li He He Q Q H Li He He Q is the energy released in the reaction. If Q is positive, it is exothermic. If Q is negative, it is endothermic.
33 Example 8: Calculate the energy released in the bombardment of lithium-7 with hydrogen-1. H Li He He Q Q H Li He He 1 1H u 7 3 Li u 4 2 He u 4 2 He u Substitution of these masses gives: Q = u(931.5 MeV/u) Q =17.3 MeV The positive Q means the reaction is exothermic.
34 Summary Fundamental atomic and nuclear particles Particle Fig. Sym Mass Charge Size Electron e 9.11 x kg -1.6 x C Proton p x kg +1.6 x C 3 fm Neutron n x kg 0 3 fm The mass number A of any element is equal to the sum of the protons (atomic number Z) and the number of neutrons N : A = N + Z
35 Summary Definitions: A nucleon is a general term to denote a nuclear particle - that is, either a proton or a neutron. The mass number A of an element is equal to the total number of nucleons (protons + neutrons). Isotopes are atoms that have the same number of protons (Z 1 = Z 2 ), but a different number of neutrons (N). (A 1 A 2 ) A nuclide is an atom that has a definite mass number A and Z-number. A list of nuclides will include isotopes.
36 Summary (Cont.) Symbolic notation for atoms Mass defect m D A Z X Mass number Atomic number Symbol m D ZmH Nmn M Binding energy E B = m D c 2 where c 2 = MeV/u Binding Energy per nucleon E B A = MeV nucleon
37 Summary (Decay Particles) An alpha particle a is the nucleus of a helium atom consisting of two protons and two tightly bound neutrons. A beta-minus particle b is simply an electron that has been expelled from the nucleus. A beta positive particle b is essentially an electron with positive charge. The mass and speeds are similar. A gamma ray g has very high electromagnetic radiation carrying energy away from the nucleus.
38 Summary (Cont.) Alpha Decay: A Z A 4 4 Z2 2 X Y a energy Beta-minus Decay: A Z A Z A 0 Z1 1 X Y b energy Beta-plus Decay: A 0 Z1 1 X Y b energy
39 Summary (Radioactivity) The half-life T 1/2 of an isotope is the time in which one-half of its unstable nuclei will decay. Nuclei Remaining 1 N N 0 2 n Activity R 1 R R 0 2 n Mass Remaining Number of Half-lives: 1 m m 0 2 n n t T 1 2
40 Summary (Cont.) Nuclear Reaction: x + X Y + y + Q Conservation of Charge: The total charge of a system can neither be increased nor decreased. Conservation of Nucleons: The total number of nucleons in a reaction must be unchanged. Conservation of Mass Energy: The total massenergy of a system must not change in a nuclear reaction. (Q-value = energy released)
41 CONCLUSION: Chapter 31 Nuclear Physics
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