[latex]dane:\k = 3\n = 2\E_1 = -13,6 eV = -13,6cdot1,6cdot10^{-19}J = -21,76cdot10^{-19} J\1 eV = 1,6cdot10^{-19} J\h = 6,63cdot10^{-34} Jcdot s\c = 3cdot10^{8}frac{m}{s}\szukane:\4. E = ?\5. lambda = ?\\Rozwiazanie:\4.\E = E_{k} - E_{n} = E_1cdot(frac{1}{k^{2}}-frac{1}{n^{2}})\\E = -21,76cdot10^{-19}Jcdot(frac{1}{3^{2}}-frac{1}{2^{2}})\\E = -21,76cdot10^{-19}Jcdot(frac{1}{9}-frac{1}{4})\\E = -21,76cdot10^{-19}Jcdot(frac{4}{36}-frac{9}{36})[/latex] [latex]E = -21,76cdot10^{-19}Jcdot(-frac{5}{36})\\E = 3,02cdot 10^{-19} J[/latex] [latex]5.\E = hcdotfrac{c}{lambda}\\lambda = hcdotfrac{c}{E}\\lambda = 6,63cdot10^{-34}Jcdot scdotfrac{3cdot10^{8}frac{m}{s}}{3,02cdot10^{-19}J}=6,586cdot10^{-7} m\\lambda = 6,59cdot10^{-7} m = 659 nm[/latex]
