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What is the frequency of limiting line in Balmer series?

Answer 1

#f = 8.225 × 10^14color(white)(l)"Hz"#

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"#

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Answer 2

Avery Adams

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

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.