a) Przeskok 4 ->>> 2 [latex]E_4= frac{-13,6eV}{4^2}= frac{-13,6eV}{16}= -0,85eV\\ E_2= frac{-13,6eV}{2^2}= frac{-13,6eV}{4}= -3,4eV\\ E_{4 o 2}= -0,85eV-(-3,4eV)=2,55eV\\ E_{4 o 2}=h u\\ u= frac{E_{4 o 2}}{h} = frac{2,55eV}{4,14cdot 10^{-15}eVs} approx 6,16 cdot 10^{14} Hz[/latex] b) Przeskok 5->> 2 [latex]E_5= frac{-13,6eV}{5^2}= frac{-13,6eV}{25}= -0,544eV\\ E_2= frac{-13,6eV}{2^2}= frac{-13,6eV}{4}= -3,4eV\\ E_{5 o 2}= -0,544eV-(-3,4eV)=2,856eV\\ E_{5 o 2}=h u\\ u= frac{E_{5 o 2}}{h} = frac{2,856eV}{4,14cdot 10^{-15}eVs} approx 7 cdot 10^{14} Hz[/latex]
[latex]a)\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} Js\szukane:\ u = ?[/latex] [latex]E = E_{m}-E_{n} = E_1(frac{1}{m^{2}}-frac{1}{n^{2}})\\E = -21,76*10^{-19}J(frac{1}{4^{2}}-frac{1}{2^{2}}) = -21,76*10^{-19}J*(-0,1875)\\E = 4,08*10^{-19} J[/latex] [latex]E = h* u /:h\\ u = frac{E}{h} = frac{4,08*10^{-19}J}{6,63*10^{-34Js}}=0,615*10^{15} Hz =0,615 PHz (petaherca) [/latex] [latex]b)\dane:\E_1 = -13,6 eV = -21,76*10^{-19} J\n = 2\m = 5\szukane:\ u = ?[/latex] [latex]E = E_{m}-E_{n} = E_1(frac{1}{m^{2}}-frac{1}{n^{2}})\\E = -21,76*10^{-19}J(frac{1}{25}-frac{1}{4}) = -21,76*10^{-19}J*(-0,21) \\E = 4,57*10^{-19} J[/latex] [latex] u = frac{E}{h} = frac{4,57*10^{-19}J}{6,63*10^{-34}Js} approx0,689*10^{^{15}} Hz = 0,689 PHz (petaherca)[/latex]
