How can I calculate the excited state energy level?
1 Answer
This is only known exactly for the hydrogen-like atoms. Otherwise, it is done experimentally via photoelectron spectroscopy.
For hydrogen-like atoms, i.e.
#E_n = -Z^2 cdot "13.61 eV"/n^2# where
#Z# is the atomic number and#n# is the quantum level.
So for
#color(blue)(E_2) = -2^2 cdot "13.61 eV"/2^2#
#= color(blue)(-"13.61 eV")#
And its ground state energy would be:
#E_1 = -2^2 cdot "13.61 eV"/1^2#
#= -"54.44 eV"#
So, its first excited state lies
#329179 cancel("cm"^(-1)) xx 2.998 xx 10^10 cancel"cm"/cancel"s"#
#xx 6.626 xx 10^(-34) cancel"J"cdotcancel"s" xx ("1 eV")/(1.602 xx 10^(-19) cancel"J")#
#= "40.82 eV" ~~ ul("40.83 eV")#