Chemistry Practice Problems Bohr and Balmer Equations Practice Problems Solution: An electron in the n=7 level of the hydrogen atom ...

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# Solution: An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

###### Problem

An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

###### Solution

We’re being asked to determine the value of n for the energy level to which the electron relaxed emitting light of 397 nm.

We’re going to use the Balmer Equation which relates wavelengths to a photon’s electronic transitions.

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

λ = wavelength, m
R = Rydberg constant = 1.097x107 m-1
Z = atomic number of the element
ninitial = initial energy level
nfinal = final energy level

Calculate the final energy level (nfinal):

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