Hi Chemistry experts, I have a question. So, I'm currently reading The Quantum-Mechanical Model of an Atom and doing problems in my book. I got stuck on this one:

An electron in the n = 6 level of the hydrogen atom relaxes to a lower energy level, emitting light of λ = 93.8 nm. Find the principal level to which the electron relaxed.

The answer in the book is n = 1. I tried to do it myself and I got n = 5.92. I went on Yahoo Answers and this guy used Rydberg's formula: 1/w = R(1/L² - 1/U²) and he got the right answer. However, in my book

*Chemistry: A Molecular Approach by Nivaldo J Tro*, the equation used in the sample problems and for these specific practice problems (there are 3, I did the first two and I got them right) is

ΔE = -2.18 x 10^(-18)J (1/n2(final)-1/n2(initial))

So, in this particular case, n(final) = 6.

I manipulated the formula so that I can get n(initial) by itself. Basically it looks like square root of (n^2(final) - 2.18x10^-18/2.1192x10^-18). I did that and I get it up 5.92 as my answer, which is like saying the electron relaxed to its current state or it barely relaxed at all. But the real answer is 1. What am I doing wrong?

Edit: the book did mention Rydberg's formula, but it is as a side note and not really focused on and used as an example to try to find solutions to these type of problems. I don't think the author expected students to use this formula over the one with ΔE.

Edit: sorry the title is confusing, not trying to find wavelength, but the initial state from which n = 6 relaxed to.