# What is the frequency of limiting line in Balmer series?

The Balmer series corresponds to all electron transitions from a higher energy level to

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"#

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The frequency of the limiting line in the Balmer series is 3.288 × 10^15 Hz.

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