CHAPTER40Nuclear Physics1*∙Give the symbols for two other isotopes of (a) 14N, (b) 56Fe, and (c) 118Sn(a)15N, 16N; (b) 54Fe, 55Fe; (c) 114Sn, 116Sn2∙Calculate the binding energy and the binding energy per nucleon from the masses given in Table 40-1for(a) 12C, (b) 56Fe, and (c) 238U.(a)Use Equ. 40-3 and Table 40-1.(b), (c)Proceed as in part (a)(a)Eb= (6×1.007825 + 6×1.008665 - 12.00)931.5 MeV =92.16 MeV; Eb/A= 7.68 MeV(b)Z= 26, N= 30; Eb= 488.1MeV; Eb/A= 8.716 MeV(c)Z= 92, N= 146; Eb= 1804 MeV; Eb/A= 7.58 MeV3∙Repeat Problem 2 for (a) 6Li, (b) 39K, and (c) 208Pb.(a), (b), (c)Proceed as in Problem 40-2.(a) Z= 3, N= 3; Eb= 31.99 MeV; Eb/A= 5.33 MeV(b) Z= 19, N= 20; Eb= 333.7 MeV; Eb/A= 8.556 MeV(c) Z= 82,N= 126;Eb= 1636.5 MeV;Eb/A= 7.868 MeV4∙Use Equation 40-1to compute the radii of the following nuclei: (a) 16O, (b) 56Fe, and (c) 197Au.(a), (b), (c)Use Equ. 40-1(a) R16= 3.78 fm; (b) R56= 5.74 fm; (c) R197= 8.73 fm5*∙(a) Given that the mass of a nucleus of mass number Ais approximately m= CA, where Cis a constant, find an expression for the nuclear density in terms of Cand the constant R0in Equation 40-1. (b) Compute the value of thisnuclear density in grams per cubic centimeter using the fact that Chas the approximate value of 1g per Avogadro'snumber of nucleons.(a)From Equ. 40-1, R= R0A1/3, the nuclear volume is V= (4π/3)R03A. With m= CA, ρ= m/V= 3C/4πR03.(b)Given that C= 1/6.02×1023g and R0= 1.5×10-13cm, ρ= 1.18×1014g/cm3.6∙Derive Equation 40-2; that is, show that the rest energy of one unified mass unit is 931.5 MeV.1u = 1.660540×10-27kg (see p. EP-4). Hence, uc2= [(2.997924×108)2×1.660540×10-27/1.602177×10-19] eV =9.3149×108eV = 931.49 MeV.7∙Use Equation 40-1for the radius of a spherical nucleus and the approximation that the mass of a nucleus of massnumber Ais Au to calculate the density of nuclear matter in grams per cubic centimeter.
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