show all detailed work please

RH=(40)2h222Z2e41=me1+mnucleus1,whereme=massofelectronandmnucleus=massofnucleusRH=2.178688911018J=1.09677759107m1 Note that the value of RH in m1 is the energy in wavenumbers; this what you get when you divide RH in Joules by h and c (Planck's constant and speed of light); it corresponds to 1/, the number of waves per meter. Oftentimes cm1 is used. You may remember seeing this on IR spectra. What is the emission wavelength for an electron falling from the vacuum level (n=) to the lowest energy level in a hydrogen atom? Use the Rydberg equation and the numerical values for the Rydberg constant RH given above. In which part of the electromagnetic spectrum is this