[latex]1.\dane:\n = 2\m = 4\E_1 = -13,6 eV = -13,6eV * 1,6*10^{-19}frac{J}{eV} = -21,76*10^{-19} J\1 eV = 1,6*10^{-19} J\h = 6,63*10^{-34} J*s\c = 3*10^{8}frac{m}{s}\szukane:\lambda = ?[/latex] [latex]Delta} E = E_4-E_2 = frac{E_1}{m^{2}}-frac{E_1}{n^{2}}=E_1(frac{1}{m^{2}}-frac{1}{n^{2}})\\Delta E = -21,76*10^{-19}J*(frac{1}{4^{2}}-frac{1}{2^{2}}) = -21,76*10^{-19}J*(frac{1}{16}-frac{4}{16}) =\\=-21,76*10^{-19}J*(-frac{3}{16}) = 4,08*10^{-19} Japprox4,1*10^{-19} J[/latex] [latex]Delta E = h*frac{c}{lambda}\\lambda = h*frac{c}{Delta E} = 6,63*10^{-34}Js*frac{3*10frac{m}{s}}{4,1*10^{-19}J} = 4,85*10^{-7} m\\lambda = 485 nm[/latex] [latex]2.\dane:\E_1 = -13,6 eV = -21,76*10^{-19} J\n = 2\m = 5\szukane:\lambda = ?[/latex] [latex]Delta E = E_{m}-E_{n} =E_1(frac{1}{m^{2}}-frac{1}{n^{2}})\\Delta E = -21,76*10^{-19}J*(frac{1}{5^{2}}-frac{1}{2^{2}}) = -21,76*10^{-19}J*(0,4-0,25)=\\=-21,76*10^{-19}J*(-0,21) approx 4,57*10^{-19} J[/latex] [latex]lambda = h*frac{c}{Delta E} = 6,63*10^{-34}Js*frac{3*10^{8}frac{m}{s}}{4,57*10^{-19}J}=4,35*10^{-7} m\\lambda = 435 nm[/latex]
