Chemistry Practice Problems Bohr and Balmer Equations Practice Problems Solution: An excited hydrogen atom emits light with a wavele...

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# Solution: An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the energy level for which n = 2. In which principal quantum level did the electron begin?

###### Problem

An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the energy level for which n = 2. In which principal quantum level did the electron begin?

###### Solution

We’re being asked to determine in which principal quantum number level (or energy level, n) did the electron begin.

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 initial principal quantum level (ninitial):

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