The Balmer series corresponds to all electron transitions from a higher energy level to #n = 2#.

The wavelength is given by the Rydberg formula

#color(blue)(bar(ul(|color(white)(a/a) 1/λ = R(1/n_1^2 -1/n_2^2)color(white)(a/a)|)))" "#

where

#R =# the Rydberg constant and

#n_1# and #n_2# are the energy levels such that #n_2 > n_1#

Since #fλ = c#

we can re-write the equation as

#1/λ = f/c = R(1/n_1^2 -1/n_2^2)#

or

#f = cR(1/n_1^2 -1/n_2^2) = R^'(1/n_1^2 -1/n_2^2)#

where #R^'# is the Rydberg constant expressed in energy units (#3.290 × 10^15 color(white)(l)"Hz"#).

In this problem, #n_1 = 2#, and the frequency of the limiting line is reached

as #n → ∞#.

Thus,

#f = lim_(n → ∞)R^'(1/4 -1/n_2^2) = R^'(0.25 - 0) = 0.25R^'#

#= 0.25 × 3.290 × 10^15 color(white)(l)"Hz" = 8.225 × 10^14color(white)(l)"Hz"#