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# Solution: What is the smallest value of n for which the wavelength of a Balmer series line is smaller than 400 nm, which is the lower limit for wavelengths in the visible spectrum?

###### Problem

What is the smallest value of n for which the wavelength of a Balmer series line is smaller than 400 nm, which is the lower limit for wavelengths in the visible spectrum?

###### Solution

We're asked to determine the smallest value of n (ni with a corresponding wavelength, λ that is smaller than 400 nm for a Balmer series line.  400 nm is the lower limit for wavelengths in the visible spectrum.

Recall the Balmer Equation shown below:

$\overline{)\frac{1}{\lambda }{=}{R}{×}\left(\frac{1}{{{n}_{f}}^{2}}-\frac{1}{{{n}_{i}}^{2}}\right)}$

where:

λ  = wavelength, m

R = 1.0974 x 107m-1 (Rydberg Constant)      **value can be found in textbooks or online
ni = initial principal energy level
nf = final principal energy level = 2 for Balmer Series

Recall that for the Balmer series the final principal energy level nf is always = 2.

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