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Unformatted text preview: Ch. 42 Page 1 CHAPTER 42 – Nuclear Physics and Radioactivity Note: A factor that appears in the analysis of energies is e 2 /4p Å = (1.60 × 10 –19 C) 2 /4p(8.85 × 10 –12 C 2 /N ∙ m 2 ) = 2.30 × 10 –28 J ∙ m = 1.44 MeV ∙ fm. 1. To find the rest mass of an α particle, we subtract the rest mass of the two electrons from the rest mass of a helium atom: m α = M He – 2 m e = (4.002603 u)(931.5 MeV/u c 2 ) – 2(0.511 MeV/ c 2 ) = 3727 MeV/ c 2 . 2. We convert the units: m = (139 MeV/ c 2 )/(931.5 MeV/u c 2 ) = 0.149 u . 3. The α particle is a helium nucleus: r = (1.2 × 10 –15 m) A 1/3 = (1.2 × 10 –15 m)(4) 1/3 = 1.9 × 10 –15 m = 1.9 fm. 4. The radius of a nucleus is r = (1.2 × 10 –15 m) A 1/3 . If we form the ratio for the two isotopes, we get r 14 / r 12 = (14/12) 1/3 = 1.053. Thus the radius of 14 C is 5.3% greater than that for 12 C. 5. ( a ) The mass of a nucleus with mass number A is A u and its radius is r = (1.2 × 10 –15 m) A 1/3 . Thus the density is ρ = m / V = A (1.66 × 10 –27 kg/u)/ ) p r 3 = A (1.66 × 10 –27 kg/u)/ ) p(1.2 × 10 –15 m) 3 A = 2.3 × 10 17 kg/m 3 , independent of A . ( b ) We find the radius from M = ρ V ; 5.98 × 10 24 kg = (2.3 × 10 17 kg/m 3 ) ) p R 3 , which gives R = 184 m . ( c ) For equal densities, we have ρ = M Earth / ) p R Earth 3 = m U / ) p r U 3 ; (5.98 × 10 24 kg)/(6.38 × 10 6 m) 3 = (238 u)(1.66 × 10 –27 kg/u)/ r U 3 , which gives r U = 2.6 × 10 –10 m . 6. ( a ) The radius of 64 Cu is r = (1.2 × 10 –15 m) A 1/3 = (1.2 × 10 –15 m)(64) 1/3 = 4.8 × 10 –15 m = 4.8 fm. ( b ) We find the value of A from r = (1.2 × 10 –15 m) A 1/3 ; 3.9 × 10 –15 m = (1.2 × 10 –15 m) A 1/3 , which gives A = 34 . 7. We find the radii of the two nuclei from r = r A 1/3 ; r α = (1.2 fm)(4) 1/3 = 1.9 fm; r U = (1.2 fm)(238) 1/3 = 7.4 fm. If the two nuclei are just touching, the Coulomb potential energy must be the initial kinetic energy of the α particle: K = U = Z α Z U e 2 /4p Å ( r α + r U ) = (2)(92)(1.44 MeV ∙ fm)/(1.9 fm + 7.4 fm) = 28 MeV . Ch. 42 Page 2 8. We find the radii of the two nuclei from r = r A 1/3 ; r α = (1.2 fm)(4) 1/3 = 1.9 fm; r Am = (1.2 fm)(243) 1/3 = 7.5 fm....
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 Spring '08
 ROSS
 Energy, Kinetic Energy, Mass, KF, 23Na, MeV/u c2

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