[latex]E_5= frac{-13,6eV}{25} =-0,544eV\ E_3=frac{-13,6eV}{9} =-1,51eV\ E_5-E_3=-0,544eV+1,51eV=0,966eV=1,6*10^{-19}J*0,966\ approx 1,5*10^{-19}J\ E_f= frac{hc}{l} \ lE_f=hc\ l= frac{hc}{E_f} =frac{6,63*10^{-34}J*s*3*10^8m/s}{ 1,5*10^{-19}J}=13,26*10^{-7}m=1326*10^{-9}m=\ 1326nm\ [/latex]
[latex]dane:\m = 5\n = 3\E_1 = -13,6 eV = -13,6cdot10^{-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:\lambda=?\\Rozwiazanie\E = E_{m} - E_{n}=E_1cdot(frac{1}{m^{2}}-frac{1}{n^{2}})\\E = -21,76cdot10^{-19}Jcdot(frac{1}{5^{2}}-frac{1}{3^{2}})=-21,76cdot10^{-19}Jcdot(frac{1}{25}-frac{1}{9})\\E = -21,76cdot10^{-19}Jcdot(-frac{16}{225})=1,547cdot10^{-19} J = 1,55cdot10^{-19} J[/latex] [latex]E = hcdotfrac{c}{lambda}\\lambda = hcdotfrac{c}{E}\\lambda = 6,63cdot10^{-34}Jcdot scdotfrac{3cdot10^{8}frac{m}{s}}{1,55cdot10^{-19}J}\\lambda = 12,83cdot10^{-7} m = 1283 nm[/latex]
