Chapter 40

Chapter 40 - CHAPTER Nuclear Physics 40 118 1* (a) 2 Give...

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CHAPTER 40 Nuclear Physics 1* Give the symbols for two other isotopes of ( a ) 1 4 N, ( b ) 56 Fe, and ( c ) 11 8 Sn ( a ) 1 5 N, 1 6 N; ( b ) 54 Fe, 55 Fe; ( c ) 11 4 Sn, 11 6 Sn 2 Calculate the binding energy and the binding energy per nucleon from the masses given in Table 40- 1 for ( a ) 1 2 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 - 1 2.00)93 1 .5 MeV = 92. 1 6 MeV; E b / A = 7.68 MeV ( b ) Z = 26, N = 30; E b = 488. 1 MeV; E b / A = 8.7 1 6 MeV ( c ) Z = 92, N = 1 46; E b = 1 804 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 = 3 1 .99 MeV; E b / A = 5.33 MeV ( b ) Z = 1 9, N = 20; E b = 333.7 MeV; E b / A = 8.556 MeV ( c ) Z = 82, N = 1 26; E b = 1 636.5 MeV; E b / A = 7.868 MeV 4 Use Equation 40- 1 to compute the radii of the following nuclei: ( a ) 1 6 O, ( b ) 56 Fe, and ( c ) 1 97 Au. ( a ), ( b ), ( c ) Use Equ. 40- 1 ( a ) R 1 6 = 3.78 fm; ( b ) R 56 = 5.74 fm; ( c ) R 1 97 = 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 π /3) R 0 3 A . With m = CA , ρ = m / V = 3 C /4 R 0 3 . ( b ) Given that C = 1 /6.02 × 1 0 23 g and R 0 = 1 .5 × 1 0 - 1 3 cm, = 1 . 1 8 × 1 0 1 4 g/cm 3 . 6 Derive Equation 40-2; that is, show that the rest energy of one unified mass unit is 93 1 .5 MeV. 1 u = 1 .660540 × 1 0 -27 kg (see p. EP-4). Hence, u c 2 = [(2.997924 × 1 0 8 ) 2 × 1 .660540 × 1 0 -27 / 1 .602 1 77 × 1 0 - 1 9 ] eV = 9.3 1 49 × 1 0 8 eV = 93 1 .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 ρ = M / V . In this case M = 1 .66 × 1 0 -27 A kg and V = (4 π /3)( 1 .5 × 1 0 - 1 5 ) 3 A m 3 . Thus = 1 . 1 74 × 1 0 1 7 kg/m 3 = 1 . 1 74 × 1 0 1 4 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 ) Use Equ. 40- 1 ( b ) Evaluate U ; r = 4.05 fm R 2 = 1 .89 fm; R 3 = 2. 1 6 fm U = ( 1 .44 eV . nm)/(4.05 × 1 0 -6 nm) = 0.356 MeV 9* ∙∙ ( a ) Calculate the radii of 56 1 4 1 Ba and 36 92 Kr from Equation 40- 1 . ( b ) Assume that after the fission of 235 U into 1 4 1 Ba and 92 Kr, the two nuclei are momentarily separated by a distance r equal to the sum of the radii found in ( a ), and calculate the electrostatic potential energy for these two nuclei at this separation. (See Problem 8.) Compare your result with the measured fission energy of 1 75 MeV.
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Chapter 40 - CHAPTER Nuclear Physics 40 118 1* (a) 2 Give...

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