What is the wave number of the hydrogen atom excitation from #n = 1# to #n = 3#?
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I assume you mean, what is the frequency in
We consult the Rydberg equation in
#DeltaE = -"13.606 eV"(1/n_f^2 - 1/n_i^2)# where:
#n_k# is the principal quantum number for the#k# th state in the hydrogen atom, i.e. initial#i# or final#f# .#-"13.606 eV"# is the approx. ground state energy of hydrogen atom.
Thus, the change in energy for this excitation (which is positive!) is:
#DeltaE = -"13.606 eV"(1/3^2 - 1/1^2)#
#=# #"12.094 eV"#
And now it is a matter of unit conversion into the equivalent frequency in
#h = 6.626 xx 10^(-34) "J"cdot"s"# , Planck's constant.#c = 2.998 xx 10^(10) "cm/s"# , the speed of light.#e ~= 1.602 xx 10^(-19) "J/eV"# , numerically equal to the elementary charge.
#color(blue)(Deltanu) = 12.094 cancel"eV" xx (1.602 xx 10^(-19) cancel"J")/(cancel"1 eV")#
#xx 1/((2.998 xx 10^(10) "cm/"cancel"s")(6.626 xx 10^(-34) cancel"J" cdotcancel"s"))#
#~~ color(blue)("97533 cm"^(-1))#