# UH PHYS 1302 - Ch32 (15 pages)

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## Ch32

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## Ch32

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ch 32 study guide

Pages:
15
School:
University of Houston
Course:
Phys 1302 - Introductory to Physics II
##### Introductory to Physics II Documents
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Chapter 32 Nuclear Physics and Nuclear Radiation 1 The Constituents and Structure of Nuclei The nucleus of an atom consists of positively charged protons and neutral neutrons Protons and neutrons are called nucleons We characterize nuclei by the number of protons and neutrons they contain atomic number Z the number of protons in a nucleus neutron number N the number of neutrons in a nucleus mass number A Z N the total number of nucleons The notation we used to represent the composition of the nucleus is A Z X where X represents the symbol for a particular element For example the symbol for hydrogen is H the symbol for carbon is C the symbol for sodium is N a Since you are given A and Z in this notation you can find N A Z All nuclei of a given element have the same number of protons same atomic number However they may have different numbers of neutrons Nuclei of the same element same atomic number Z that have different numbers of neutrons are called 13 isotopes For example 12 6 C and 6 C are isotopes of carbon There is a unit of mass called the atomic mass unit u defined such that one atom of 12 6 C is exactly 12 u 1u 1 660540 10 27 kg A proton has a mass of 1 007276 u and a neutron has a mass of 1 008665 u The average radius of a nucleus of mass number A is r 1 2 10 15 m A1 3 L Whitehead 1 1 Phys 1302 1 fermi 1 femtometer fm 10 15 m Named after Enrico Fermi Using the radius of a nucleus we can find an expression for the density of a nucleus We ll use the approximation that the proton and neutron have the same mass 1u 1 67 10 27 kg M V A 1 67 10 27 kg 4 r3 3 A 1 67 10 27 kg 4 1 2 10 15 mA1 3 3 3 A 1 67 10 27 kg 4 1 2 10 15 m 3 A 3 1 67 10 27 kg 4 1 2 10 15 m 3 3 2 3 1017 kg m3 2 The density is independent of the mass number all nuclei have approximately the same density Protons in the nucleus exert repulsive electric forces on each other What keeps the nucleus from flying apart There must be another stronger force that overcomes the electric force The force that holds the nucleus together is the strong nuclear force It is a short range force only acting over a range about the size of the nucleus It is an attractive force for protons and neutrons but does not act on electrons 2 Radioactivity Einstein s famous equation E mc2 3 indicates that mass is a form of energy We can use this expression to get a conversion factor between atomic mass units u L Whitehead 2 Phys 1302 and electron volts eV The energy equivalent of 1 atomic mass unit is E mc2 1u c2 27 1 660540 10 8 2 kg 2 998 10 m s 1eV 1 6022 10 19 J 9 315 108 eV 931 5MeV 4 So we can write 931 5MeV 1u c2 1u 931 5MeV c2 5 Energy per c2 is a unit of mass Some nuclei are unstable and will decay by emitting a particle and changing its composition or its state The particles that are emitted in a decay are known as radioactivity The law of conservation of energy applies to decays The total energy of the system before the decay the mass of the original nucleus has to be equal to the total energy of the system after the decay the mass of the new nucleus plus the energy of the other particles that are emitted Thus when a decay happens the mass of the final nucleus will be less than the mass of the original nucleus The difference in mass between the nuclei appears as a release of energy A nucleus cannot decay into a heavier nucleus it is energetically forbidden i e it would disobey the law of conservation of energy Alpha Decay An alpha particle is a helium nucleus 42 He When a nucleus decays by emitting an alpha particle it loses two protons and two neutrons so it s atomic number Z decreases by 2 and its mass number A decreases by 4 An alpha decay can be written this way A ZX 4 A 4 Z 2 Y 2 He 6 We call X the parent nucleus and Y the daughter nucleus Note that the total atomic number on the left side is equal to the sum of the atomic numbers on the L Whitehead 3 Phys 1302 right Ditto for the mass number Smoke detectors use alpha decay Beta Decay Every particle has a corresponding antiparticle Antiparticles have the same mass but opposite charge of particles neutral particles have neutral antiparticles The antiparticle of the electron e is called the positron e All the ordinary matter around us is made of matter but antimatter is produced in only small quantities in decays and other particle interactions The basic process in beta decay is the conversion of a neutron to a proton with the emission of an electron and particle called a neutrino in particular an electron type antineutrino the bar above indicates it is an antiparticle 1 0n 11 p e e 7 Notice that charge is conserved a neutron is neutral and the total charge on the right hand side is also zero When the above decay happens inside a nucleus it looks like this A ZX A Z 1 Y e e 8 A similar decay in which a positron is emitted can also happen A ZX A Z 1 Y e e 9 Note that an isolated proton cannot decay into a neutron because the proton is lighter than the neutron The electron is also known as a beta particle We write for an electron and for a positron Beta decay is how the neutrino was discovered The results of experiments that looked at the energy of the outgoing electrons indicated that there must be another particle present In addition angular momentum wasn t conserved Wolfgang Pauli hypothesized that there was a new type of very light neutral particle that was so far unknown Fermi named it neutrino Italian for little neutral one Neutrinos were observed for the first time in the 1950 s more than 20 years after Pauli proposed L Whitehead 4 Phys 1302 their existence Gamma Decay A nucleus in an excited state can emit a photon when decaying to a lower energy level just as in atoms Because energies are much greater at the nuclear scale than the atomic scale the photons are very high energy in the gamma portion of the EM spectrum They are called gamma rays We write such a decay in this way A ZX A Z X 10 where the indicates an excited state The composition of the nucleus doesn t change in this type of decay What is the daughter nucleus …

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