ch40 - CHAPTER Nuclear Physics 40 1* Give the symbols for...

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CHAPTER 40 Nuclear Physics 1* · Give the symbols for two other isotopes of ( a ) 14 N, ( b ) 56 Fe, and ( c ) 118 Sn ( a ) 15 N, 16 N; ( b ) 54 Fe, 55 Fe; ( c ) 114 Sn, 116 Sn 2 · Calculate the binding energy and the binding energy per nucleon from the masses given in Table 40-1 for ( a ) 12 C, ( b ) 56 Fe, and ( c ) 238 U. ( a ) Use Equ. 40-3 and Table 40-1. ( b ), ( c ) Proceed as in part ( a ) ( a ) E b = (6 × 1.007825 + 6 × 1.008665 - 12.00)931.5 MeV = 92.16 MeV; E b / A = 7.68 MeV ( b ) Z = 26, N = 30; E b = 488.1 MeV; E b / A = 8.716 MeV ( c ) Z = 92, N = 146; E b = 1804 MeV; E b / A = 7.58 MeV 3 · Repeat Problem 2 for ( a ) 6 Li, ( b ) 39 K, and ( c ) 208 Pb. ( a ), ( b ), ( c ) Proceed as in Problem 40-2. ( a ) Z = 3, N = 3; E b = 31.99 MeV; E b / A = 5.33 MeV ( b ) Z = 19, N = 20; E b = 333.7 MeV; E b / A = 8.556 MeV ( c ) Z = 82, N = 126; E b = 1636.5 MeV; E b / A = 7.868 MeV 4 · Use Equation 40-1 to compute the radii of the following nuclei: ( a ) 16 O, ( b ) 56 Fe, and ( c ) 197 Au. ( a ), ( b ), ( c ) Use Equ. 40-1 ( a ) R 16 = 3.78 fm; ( b ) R 56 = 5.74 fm; ( c ) R 197 = 8.73 fm 5* · ( a ) Given that the mass of a nucleus of mass number A is approximately m = CA , where C is a constant, find an expression for the nuclear density in terms of C and the constant R 0 in Equation 40-1. ( b ) Compute the value of this nuclear density in grams per cubic centimeter using the fact that C has the approximate value of 1 g per Avogadro's number of nucleons. ( a ) From Equ. 40-1, R = R 0 A 1/3 , the nuclear volume is V = (4 p /3) R 0 3 A . With m = CA , r = m / V = 3 C /4 p R 0 3 . ( b ) Given that C = 1/6.02 × 10 23 g and R 0 = 1.5 × 10 -13 cm, r = 1.18 × 10 14 g/cm 3 . 6 · Derive Equation 40-2; that is, show that the rest energy of one unified mass unit is 931.5 MeV. 1 u = 1.660540 × 10 -27 kg (see p. EP-4). Hence, u c 2 = [(2.997924 × 10 8 ) 2 × 1.660540 × 10 -27 /1.602177 × 10 -19 ] eV = 9.3149 × 10 8 eV = 931.49 MeV. 7 · Use Equation 40-1 for the radius of a spherical nucleus and the approximation that the mass of a nucleus of mass number A is A u to calculate the density of nuclear matter in grams per cubic centimeter.
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Chapter 40 Nuclear Physics The density of a sphere is r = M / V . In this case M = 1.66 × 10 -27 A kg and V = (4 p /3)(1.5 × 10 -15 ) 3 A m 3 . Thus r = 1.174 × 10 17 kg/m 3 = 1.174 × 10 14 g/cm 3 . 8 ·· The electrostatic potential energy of two charges q 1 and q 2 separated by a distance r is U = kq 1 q 2 /r, where k is the Coulomb constant. ( a ) Use Equation 40-1 to calculate the radii of 2 H and 3 H. ( b ) Find the electrostatic potential energy when these two nuclei are just touching, that is, when their centers are separated by the sum of their radii. ( a
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ch40 - CHAPTER Nuclear Physics 40 1* Give the symbols for...

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