# Problem: An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 2166 nm.What is the value of n for the level to which the electron relaxed?

###### FREE Expert Solution

Rydberg equation:

$\overline{)\frac{\mathbf{1}}{\mathbf{\lambda }}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{H}}}\mathbf{\left(}\frac{\mathbf{1}}{{{\mathbf{n}}^{\mathbf{2}}}_{\mathbf{final}}}\mathbf{-}\frac{\mathbf{1}}{{{\mathbf{n}}^{\mathbf{2}}}_{\mathbf{initial}}}\mathbf{\right)}}$

Calculate nfinal:

λ = 2166 nm → convert to m
1 nm = 10-9 m
RH = Rydberg constant = 1.097x10 m–1

###### Problem Details

An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 2166 nm.

What is the value of n for the level to which the electron relaxed?