[latex]Dane:\E _{1} =-13,6eV\h=4,14*10 ^{-15} eV*s\n=2\m=1\c=3*10 ^{8} frac{m}{s} \\Szuk.\E=?\lambda=?\ u=?\\Roz.\\E=E _{1}( frac{1}{n ^{2} } + frac{1}{m ^{2} } )\\E=-13,6eV( frac{1}{2 ^{2} } -1)=-3,4+13,6=10,2eV\\E=h u\\ u= frac{E}{h} \\ u= frac{10,2eV}{4,14*10 ^{-15} eV*s} approx 2,46*10 ^{15} Hz\\lambda= frac{c}{ u}\\lambda= frac{3*10 ^{8} frac{m}{s}}{2,46*10 ^{15} Hz} approx 1,22*10 ^{-7}m=122nm [/latex]
[latex]dane:\k = 2\n = 1\E_1 = -13,6 eV\1 eV = 1,6cdot10^{-19} J\h = 6,63cdot10^{-34} Jcdot s\c = 3cdot10^{8}frac{m}{s}\szukane:\E_{f} = ?\ u = ?\lambda = ?[/latex] [latex]E_{f} = E_{k}-E_{n} = E_1(frac{1}{k^{2}}-frac{1}{n})\\E_{f} = -13,6eVcdot(frac{1}{2^{2}}-1) = -13,6eVcdot(frac{1}{4}-frac{4}{4})=-136eVcdot(-frac{3}{4})\\E_{f} = 10,2 eV \\E_{f}= 10,2eVcdot1,6cdot10^{-19}frac{J}{eV} = 16,32cdot10^{-19} J[/latex] [latex]E_{f} = hcdot u /:h\\ u = frac{E_{f}}{h}\\ u = frac{16,32cdot10^{-19}J}{6,63cdot10^{-34}Jcdot s} = 2,46cdot10^{15} Hz = 2,46 PHz (petaherca)[/latex] [latex]lambda = frac{c}{ u}\\lambda = frac{3cdot10^{8}frac{m}{s}}{2,46cdot10^{15}s^{-1}} = 1,22cdot10^{-7} m = 122 nm[/latex]
