Answer:
So you can use the Bohr formula
En = -13.6*(1/n2^2 - 1/n1^2) eV where En is in electron volts.
Energy of a photon is Ep = 1.24/wl eV where wl is wavelength in microns
So 93.8 nm = 0.0938 um so Ep = 13.22 ev. Now atom radiates a photon wl' = 7.459 um loosing an energy E' of
E' = 1.24/7.459 = 0.166 eV
SO the atom has a net gain in energy of Ep - E' =13.053 eV
TO find th eenergy level, set Ep - E' = En
13.053 = -13.6 (1/n2^2 - 1/n1^2) and set n1 = 1 = ground state. then solve for n2
-13.055/13.6 = 1/n2^2 - 1 --> 1 - 13.055/13.6 = 1/n2^2
0.040193 = 1/n2^2 ---> n2 = sqrt(1/0.040193) = 4.98 ~ 5
So n final is 5
