Respostas Problemas Capitulo 4 Física Quântica - Eisberg Resnick - 2 Edição

F_s = \\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{e^2}{r^2} \\quad F = m \\cdot a\n- \\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{e^2}{r^3} = m\\lambda\n\\omega^2 = \\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{e^2}{m r^3}\n\\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{e^2}{r^2} = \\frac{m(\\omega)^2}{R} \\Rightarrow m \\cdot (k \\cdot \\omega)^2 = m k \\omega^2\n\\omega^2 = \\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{e^2}{m r^3} \\lambda = \\frac{c}{\\nu} \\quad \\nu = \\frac{c}{\\lambda}\n\\nu = \\frac{1}{2\\pi} \\sqrt{\\frac{k}{m}} \\rightarrow k = 4\\pi m \\nu^2\n\\rho = \\frac{3k\\epsilon_0}{e} = 4\\cdot3\\cdot(9.11\\cdot 10^{-31})\\cdot\\pi\\cdot(5.10^{14})^2\\cdot 8.85\\cdot 10^{-12} \\Rightarrow 2.49\\cdot10^{-9}\n\\rho = \\frac{e}{\\frac{4}{3}\\pi r^3}\n\\Rightarrow r = \\sqrt[3]{\\frac{3e}{4\\pi \\rho}} = \\sqrt[3]{\\frac{1.6\\cdot10^{-19}}{\\frac{4}{3}\\pi\\cdot 1.48\\cdot10^9}}\\n=r = 2.91 \\cdot 10^{-10} m F_m = \\frac{1}{4\\pi\\epsilon_0} \\cdot \\left(\\frac{ze}{r^2}\\right)\n\\Delta p = \\int F_m(\\Delta t) = F_m \\cdot \\frac{\\Delta t}{j}\n\\Delta p = \\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{4ze^2}{R^2}\\n\\frac{p}{mv} = \\frac{1}{4\\pi\\epsilon_0} \\cdot \\frac{2ze^2}{R(\\frac{1}{mR^2})} = \\frac{U}{K}\\n\\theta = 8.988\\cdot10^9\\cdot(z)(7.9)(1.6\\cdot10^{-19})^2\\cdot10^{-10} \\cdot5.7\\cdot10^{-13}\n\\theta = 4.55\\cdot10^4 rad g) F = k . e^2 / r^2 = 9.1 0.9 (1.96.10^-9)^2 / (0.527.10^-10)^2 = 8.23310^3 N\nh) F_c = m.a => a = 8.2 10^-8 = 9.10 m l^2\n9.11.10^-31\n\ni) K: 1/2 mv^2 = 1/2. 9.11.10^-31. (2.79.10^6)^2 = 1.36 eV\n\nj) E_p = - Z e^2 / (4 pi e_0 r) = - 9.109.1 2.56.10^-38 / 4.60.10^-10 = -27.2 eV\n0.529.10^-10\n\nk) E_T = K + E_p = (13.6 - 27.2)eV = -13.6 eV.\n\n20 E_B = -me^4 / (4 pi e_0 h^2) = Z^2 / n^2 = -13.6 eV = 1.36 eV / m^2\n\n23 I = 2.1216 h\n∆E = E_f - E_i = hc / λ = 6.06.10^-34. 3.10^8 / 1.216.10^-10\n∆E = 10.2 eV\n\n26 E_i = -13.6 Z^2 / n^2 [eV]\nE_th = 6H x 2^2 - 13.6 4 = -54.4 eV\n\n34 E = 1/2 I ω^2 = L = √25 E'\n∫ L dθ = n h\nL (for n = 1) = n h\nL = 2 π r_h\n√25 E = n h\nE = n^2 h^2 / 2I. p = 19.3 g/cm^3\n\\Lambda = \\frac{1}{4\\pi \\epsilon_0} \\cdot \\left(\\frac{Z z e^2}{2m v^2}\\right) \\int \\ln\\left(\\frac{1}{k\\cdot(\\theta/2)}\\right) d\\Lambda\n\\frac{d\\nu}{dA} = 10^{12} otab\nn = 49.3 d\\nu = k \\cdot 7.20\\cdot 10^{-5}\\cdot (3.05 \\cdot 10^{-34})^2\\Rightarrow 5.274 \\cdot 10^{-14} = 0.529 \\text{ Å}\n\\mu = \\frac{e}{2m} \n