[tex]dane:\\dane:\\E_1 = -13,6 \ eV\\1 \ eV = 1,6\cdot10^{-19} \ J\\n = 2\\m = 3\\h = 6,63\cdot10^{-34} \ J\cdot s \ - \ stala \ Plancka\\c = 3\cdot10^{8}\frac{m}{s} \ - \ predkosc \ swiatla\\szukane:\\E_{f} = ?\\\nu = ?\\\lambda = ?\\\\Rozwiazanie\\\\E_{f} = E_{m}-E_{n} = E_1\cdot(\frac{1}{m^{2}}-\frac{1}{n^{2}})\\\\E_{f} = -13,6 \ eV\cdot(\frac{1}{3^{2}}-\frac{1}{2^{2}}) = -13,6 \ eV\cdot(\frac{1}{9}-\frac{1}{4})\\\\E_{f} =-13,6 \ eV\cdot(-\frac{5}{36}) = 1,(8) \ eV = 1,89 \ eV[/tex]
[tex]E_{f} = 1,89 \ eV\cdot1,6\cdot10^{-19}\frac{J}{eV}}=3,02\cdot10^{-19} \ J[/tex]
[tex]E_{f} = h\cdot \nu\\\\h\cdot \nu = E_{f} \ \ /:h\\\\\nu = \frac{E_{f}}{h}\\\\\nu = \frac{3,02\cdot10^{-19} \ J}{6,63\cdot10^{-34} \ J\cdot s}\\\\\nu = 0,46\cdot10^{15} \ Hz = 0,46 \ PHz[/tex]
[tex]\lambda = \frac{c}{\nu}\\\\\lambda = \frac{3\cdot10^{8}\frac{m}{s}}{0,46\cdot10^{15} s^{-1}}\\\\\lambda = 6,52\cdot10^{-7} \ m = 652 \ nm[/tex]
