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Unformatted text preview: 1599 Chapter 42 1. Kinetic energy (we use the classical formula since v is much less than c ) is converted into potential energy (see Eq. 2443). From Appendix F or G, we find Z = 3 for Lithium and Z = 90 for Thorium; the charges on those nuclei are therefore 3 e and 90 e , respectively. We manipulate the terms so that one of the factors of e cancels the “e” in the kinetic energy unit MeV, and the other factor of e is set to be 1.6 × 10 –19 C. We note that k = 1 4 π ε can be written as 8.99 × 10 9 V·m/C. Thus, from energy conservation, we have ( 29 ( 29 ( 29 9 19 V m C 1 2 6 8.99 10 3 1.6 10 C 90 3.00 10 eV e kq q K U r K ⋅ × × × = ⇒ = = × which yields r = 1.3 × 10 – 13 m (or about 130 fm). 2. Our calculation is similar to that shown in Sample Problem 421. We set ( 29 ( 29 Cu min 5.30MeV= 1/ 4 / K U q q r α ε = = π and solve for the closest separation, r min : ( 29 ( 29 ( 29 ( 29 19 9 Cu Cu min 6 14 2 29 1.60 10 C 8.99 10 V m/C 4 4 5.30 10 eV 1.58 10 m 15.8 fm. e q q kq q r K K α α ε ε × × ⋅ = = = π π × = × = We note that the factor of e in q α = 2 e was not set equal to 1.60 × 10 – 19 C, but was instead allowed to cancel the “e” in the nonSI energy unit, electronvolt. 3. The conservation laws of (classical kinetic) energy and (linear) momentum determine the outcome of the collision (see Chapter 9). The final speed of the α particle is v m m m m v f i α α α α = + Au Au , and that of the recoiling gold nucleus is v m m m v f i Au, Au = + 2 α α α . (a) Therefore, the kinetic energy of the recoiling nucleus is CHAPTER 42 1600 ( 29 ( 29 ( 29( 29 ( 29 2 2 2 Au Au, Au Au, Au 2 Au Au 2 2 4 1 1 2 2 4 197u 4.00u 5.00MeV 4.00u+197u 0.390MeV. f f i i m m m K m v m v K m m m m α α α α α α = = = + + = = (b) The final kinetic energy of the alpha particle is ( 29 2 2 2 2 Au Au Au Au 2 1 1 2 2 4.00u 197u 5.00MeV 4.00u 197u 4.61MeV. f f i i m m m m K m v m v K m m m m α α α α α α α α α α  = = = + +  = + = We note that K K K af f i + = Au, α is indeed satisfied. 4. Using Eq. 423 ( 1/3 r r A = ), we estimate the nuclear radii of the alpha particle and Al to be 15 1/3 15 15 1/3 15 Al (1.2 10 m)(4) 1.90 10 m (1.2 10 m)(27) 3.60 10 m. r r α = × = × = × = × The distance between the centers of the nuclei when their surfaces touch is 15 15 15 Al 1.90 10 m 3.60 10 m 5.50 10 m r r r α = + = × + × = × . From energy conservation, the amount of energy required is 9 2 2 19 19 Al 15 12 6 1 (8.99 10 N m C )(2 1.6 10 C)(13 1.6 10 C) 4 5.50 10 m 1.09 10 J 6.79 10 eV q q K r α πε × ⋅ × × × × = = × = × = × 5. Kinetic energy (we use the classical formula since v is much less than c ) is converted into potential energy. From Appendix F or G, we find Z = 3 for Lithium and Z = 110 for Ds; the charges on those nuclei are therefore 3 e and 110 e , respectively. From energy conservation, we have...
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 Summer '10
 Prof.Yang
 Physics, Atom, Charge, Energy, Kinetic Energy, Mass, Potential Energy, Nuclear Fission, Neutron, Binding energy

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