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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?

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 = 1.097x10^{7} m^{-1}

Z = atomic number of the element

n_{initial }= initial energy level

n_{final} = final energy level

**Calculate the ****final energy level**** ****(n _{final}):**

Bohr and Balmer Equations

Bohr and Balmer Equations

Bohr and Balmer Equations

Bohr and Balmer Equations