Posted by Ashley on Monday, July 18, 2011 at 12:49am.
Bob Pursley answered part of this for you yesterday. It would help if you told us what is confusing you instead of "I don't understand". Basically, the H spectrum consists of lines generated by electrons as they first absorb energy, are promoted to a higher energy level (a higher orbit), then fall back to a lower level. When they fall back to the lower level they give up the energy they absorbed to get to the higher level and this energy falls in the electromagnetic spectrum in the UV, visible, and infrared regions. Historically, these series have been named after people who discovered them; i.e., the Lyman series ENDS with the electron falling to orbit #1 (from orbits 2,3,4,5,etc). That is An electron falling from n = 5 to n = 1 will generate a line at some wavelength and an electron falling form n = 4 to n = 1 will generate another line at some different wavelength. Nothing prevents that electron in n = 5 from falling first to n = 4, then to n = 3, then to n = 2, then to n = 1 and generating four lines in the process. So lines formed when the end orbit is 1 are called the Lyman series (from someone named Lyman). Other series are the Balmer series (where the end level is n = 2, the Paschen series ending in n = 3, Brackett series ending in n = 4 etc).
You now the ground state for the electron is in the n = 1 orbit.
E = 2.180E-18 J x (1/n1^2 - 1/n2^2) is the energy level when an electron falls from n = 2, wherever that may be, to n = 1. Since the Lyman series ends in n = 1, this may be shortened to E = 2.180E-18(1 - 1/n^2). Susbtitute 3 for n. square it and solve for E (in Joules).
E = hc/wavelength will convert from E to wavelength. (or E = h*freq to get freq directly).
Frequency and wavelength are related by
c = freq x wavelength where c is the speed of light (in m/s), freq is in Hz and wavelength is in m.