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?

We're asked to determine the **smallest value of n (n _{i}) ** with a

Recall the** ****Balmer Equation**** **shown below:

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

where:

*λ* = wavelength, m

R = 1.0974 x 10^{7}m^{-1} (Rydberg Constant) ***value can be found in textbooks or online *n

Recall that for the** ****Balmer series the final principal energy level n _{f} is always = 2.**