Question 1.15 Rydberg Equation Math Problem

[Tia Tomescu 2D]

1.15 In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6 nm. Determine the values of n for the initial and final energy levels of the electron during the emission of energy that leads to this spectral line.

I used . Is this the correct equation to use?

I came up with
= .

The power of 10 is wrong and I need guesswork to find the answer. (n1=1, n2=3).

Is there a simpler way that I am missing?

[Janine Chan 2K]

So I used the equation was c/wavelength=R(1/n_1^2 - 1/n_2^2). Essentially, you're using the given wavelength and using c=v*wavelength to find the frequency, and then using v=R((1/n_1^2 - 1/n_2^2) to find n_2. (We also already know n_1 = 1 because a wavelength of 102.6nm is Lyman series