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Nuclear Physics

Nuclear Physics . AP Physics B Joseph F. Ruffolo , Ph.D. Particle. Fig. Sym. Mass. Charge. Size. Composition of Matter. All of matter is composed of at least three fundamental particles (approximations):. Electron e - 9.11 x 10 -31 kg -1.6 x 10 -19 C .

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Nuclear Physics

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  1. Nuclear Physics AP Physics B Joseph F. Ruffolo, Ph.D.

  2. Particle Fig. Sym Mass Charge Size Composition of Matter All of matter is composed of at least three fundamental particles (approximations): Electron e- 9.11 x 10-31 kg -1.6 x 10-19 C  Proton p1.673 x 10-27 kg +1.6 x 10-19 C 3 fm Neutron n1.675 x 10-31 kg 0 3 fm The mass of the proton and neutron are close, but they are about 1840 times the mass of an electron.

  3. Compacted nucleus: 4 protons 5 neutrons Since atom is electrically neutral, there must be 4 electrons. 4 electrons Beryllium Atom The Atomic Nucleus

  4. 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. Modern Atomic Theory

  5. 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 Definitions A nucleon is a general term to denote a nuclear particle - that is, either a proton or a neutron. The atomic number Zof 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).

  6. For example, consider beryllium (Be): 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.

  7. Isotopes of helium Helium - 3 Helium - 4 Isotopes of Elements Isotopes are atoms that have the same number of protons (Z1= Z2), but a different number of neutrons (N). (A1 A2)

  8. A nuclide is an atom that has a definite mass numberA and Z-number. A list of nuclides will include isotopes. The following are best described as nuclides: Nuclides Because of the existence of so many isotopes, the term element is sometimes confusing. The term nuclide is better.

  9. Common atomic masses: Proton: 1.007276 u Neutron: 1.008665 u Electron: 0.00055 u Atomic Mass Unit, u One atomic mass unit(1 u) is equal to one-twelfth of the mass of the most abundant form of the carbon atom--carbon-12. Atomic mass unit: 1 u = 1.6606 x 10-27 kg Hydrogen: 1.007825 u

  10. = 11.009305 Electron: 0.00055 u Example 2:The average atomic mass of Boron-11 is 11.009305 u. What is the mass of the nucleus of one boron atom in kg? The mass of the nucleus is the atomic mass less the mass of Z = 5 electrons: Mass = 11.009305 u – 5(0.00055 u) 1 boron nucleus = 11.00656 u m = 1.83 x 10-26 kg

  11. E = 1.49 x 10-10 J E = 931.5 MeV Or When converting amu to energy: Mass and Energy Recall Einstein’s equivalency formula for m and E: The energy of a mass of 1 u can be found: E = (1 u)c2 = (1.66 x 10-27 kg)(3 x 108 m/s)2

  12. Example 3: What is the rest mass energy of a proton (1.007276 u)? E = mc2 = (1.00726u)(931.5 MeV/u) Proton: E = 938.3 MeV Similar conversions show other rest mass energies: Neutron: E = 939.6 MeV Electron: E = 0.511 MeV

  13. The nucleus of the carbon-12 atom has this mass. (Continued . . .) 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 (12.00000 u): Nuclear mass = Mass of atom – Electron masses = 12.00000 u – 6(0.00055 u) = 11.996706 u

  14. Proton: 1.007276 u Neutron: 1.008665 u Mass Defect (Continued) Mass of carbon-12 nucleus: 11.996706 The nucleus contains 6 protons and 6 neutrons: 6 p = 6(1.007276 u) = 6.043656 u 6 n = 6(1.008665 u) = 6.051990 u Total mass of parts: = 12.095646 u Mass defect mD = 12.095646 u – 11.996706 u mD = 0.098940 u

  15. Binding EB for C-12: EB = 92.2 MeV The Binding Energy The binding energy EB of a nucleus is the energy required to separate a nucleus into its constituent parts. EB = mDc2 where c2 = 931.5MeV/u The binding energy for the carbon-12 example is: EB= (0.098940 u)(931.5MeV/u)

  16. Binding energy per nucleon Binding Energy per Nucleon An important way of comparing the nuclei of atoms is finding their binding energy per nucleon: For our C-12 example A = 12 and:

  17. Formula for Mass Defect The following formula is useful for mass defect: Mass defectmD mH = 1.007825 u; mn = 1.008665 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.

  18. Mass defectmD Example 4: Find the mass defect for the nucleus of helium-4. (M = 4.002603 u) ZmH = (2)(1.007825 u) = 2.015650 u Nmn = (2)(1.008665 u) = 2.017330 u M = 4.002603 u (From nuclide tables) mD = (2.015650 u + 2.017330 u) - 4.002603 u mD = 0.030377 u

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