1897 J.J. Thompson discovers the electron

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1 CHAPTER 1 BASIC CONCEPTS OF NUCLEAR PHYSICS 1.1 Historical survey: The origin of nuclear physics and the progress after can be understand from the historical review as follow: 1895 The discovery of X-Ray by Rontgen 1896 Becquerel discovers radioactivity of Uranium 1897 J.J. Thompson discovers the electron 1900 The discovery of black body radiation formula by Planck 1905 The development of the theory of special relativity by Enstein ١ 1911 Rutherford discovers the atomic nucleus 1913 Boher s theory of Hydrogen atom 1932 Chadwick discovers the neutron, Heisenberg formulates the 'isospin hypothesis 1935 Yukawa's meson hypothesis as intermediary of the strong force Where 1896 and 1911 is the beginning of nuclear physics ٢

2 1939 Discovery of nuclear fission by Hahn, Strassmann, Meitner 1946 Discovery of the pion by Occhialini and Powell 1948 The shell model, discovered by Jensen and Goeppert Mayer Development of the collective model by A. Bohr and B. Mottelson ٣ ٤

3 THOMSON ٥ ٦

4 Matter consists of atoms, which is the smallest part as known by Greeks, then electrons discovered, Nucleus, protons and neutrons discovered latter, so atoms consists of Nucleus and electrons. But Quarks have been discovered which is the smallest part of matter, protons and neutrons consists of Quarks up, down, strange, charm, bottom, and top (u,d,s,c,b,t) protons consist of three Quarks P (uud), neutrons n (udd), where charge of (u,c,t) is +2/3e while (d,s,b) is -1/3e ٧ Objectives: After completing this module, you should be able to: Define and apply the concepts of mass number, atomic number, and isotopes. Calculate the mass defect and the binding energy per nucleon for a particular isotope. Define and apply concepts of radioactive decay and nuclear reactions. State the various conservation laws, and 10/11/2014 discuss 7:19 PMtheir application for nuclear reactions. ٨

5 Composition of Matter All of matter is composed of at least three fundamental particles (approximations): Particle Fig. Sym Mass Charge Size Electron e 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 of the proton and neutron are close, but they 10/11/2014 are 7:19 about PM 1840 times the mass of an electron. ٩ The Atomic Nucleus Compacted nucleus: 4 protons 5 neutrons Since atom is electrically neutral, there must be 4 electrons. 4 electrons ١٠ Beryllium Atom

6 Modern Atomic Theory The Bohr atom, which is sometimes shown with electrons as planetary particles, is no longer a valid representation of an atom, but it is used here to simplify our discussion of energy levels. The uncertain position of an electron is now described as a probability distribution loosely referred to as an electron cloud. ١١ 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 ١٢

7 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 ١٣ Example 1: Describe the nucleus of a lithium atom which has a mass number of 7 and an atomic number of 3. A = 7; Z = 3; N =? N = A Z = 7-3 neutrons: N = 4 Protons: Z = 3 Electrons: Same as Z 7 Li 3 ١٤ Lithium Atom

8 Isotopes of Elements 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 ) 3 2He Isotopes of helium 4 2He Helium - 3 ١٥ Helium - 4 Nuclides Because of the existence of so many isotopes, the term element is sometimes confusing. The term nuclide is better. A nuclide is an atom that has a definite mass number A and Z-number. A list of nuclides will include isotopes. The following are best described as nuclides: 3 2 He 4 2 He 12 6 C 13 6 C ١٦

9 Atomic Mass Unit, u One atomic mass unit (1 u) is equal to onetwelfth of the mass of the most abundant form of the carbon atom--carbon-12. Atomic mass unit: 1 u = x kg Common atomic masses: Proton: u Neutron: u Electron: u Hydrogen: u ١٧ Exampe 2: The average atomic mass of Boron-11 is u. What is the mass of the nucleus of one boron atom in kg? 11 Electron: u 5 B = The mass of the nucleus is the atomic mass less the mass of Z = 5 electrons: Mass = u 5( u) 1 boron nucleus = u x 10 kg m = u 1 u ١٨ m = 1.83 x kg

10 Mass and Energy Recall Einstein s equivalency formula for m and E: 2 8 E = mc ; c= 3 x 10 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: 2 MeV c = u ١٩ Example 3: 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 ٢٠

11 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...) ٢١ 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 ٢٢

12 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 ٢٣ Binding Energy per Nucleon An important way of comparing the nuclei of atoms is finding their binding energy per nucleon: Binding energy per nucleon E B A = MeV nucleon For our C-12 example A = 12 and: E B 92.2 MeV 7.68 A = 12 = ٢٤ MeV nucleon

13 Formula for Mass Defect The following formula is useful for mass defect: Mass defect m D ( ) md = ZmH + Nmn M m H = u; m n = u Z is atomic number; N is neutron number; M is mass of atom (including electrons). By using the mass of the hydrogen atom, you avoid the necessity of subtracting electron masses. ٢٥ Example 4: Find the mass defect for the nucleus of helium-4. (M = u) Mass defect m D ( ) md = ZmH + Nmn M Zm H = (2)( u) = u Nm n = (2)( u) = u 4 2 He M = u (From nuclide tables) m D = ( u u) u m D = u ٢٦

14 Example 4 (Cont.) Find the binding energy per nucleon for helium-4. (m D = u) E B = m D c 2 where c 2 = MeV/u E B = ( u)(931.5 MeV/u) = 28.3 MeV A total of 28.3 MeV is required To tear apart the nucleons from the He-4 atom. Since there are four nucleons, we find that E B 28.3 MeV 7.07 A = 4 = ٢٧ MeV nucleon Binding Energy Vs. Mass Number Curve shows that E B increases with A and peaks at A = 60. Heavier nuclei are less stable. Green region is for most stable atoms. Binding Energy per nucleon Mass number A released when they fuse together ٢٨ (fusion) For heavier nuclei, energy is released when they break up (fission). For lighter nuclei, energy is

15 Stability Curve Nuclear particles are held together by a nuclear strong force. A stable nucleus remains forever, but as the ratio of N/Z gets larger, the atoms decay. Elements with Z > 82 are all unstable. Neutron number N ٢٩ Stable nuclei Z = N Atomic number Z ٣٠

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18 Nuclear Length: A length of one femtometer (fm) = m Nuclear size: Range from 1 fm for single nucleon to 7 fm heavy nuclei Nuclear Energies: Measured in Million of electron volts 1 ev =1.602x10-19 J Nuclear Mass: Measured in terms of atomic mass units ٣٥