Learning Objectives Describe Rydberg"s theory for the hydrogen spectra. Interpret the hydrogen spectrum in terms of the power states of electrons.

You are watching: Calculate the frequency of the n = 2 line in the lyman series of hydrogen.

In an remarkable demonstration of mathematical understanding, in 1885 Balmer came up through a basic formula for predicting the wavelength of any type of of the lines in atomic hydrogen in what we now recognize as the Balmer series. Three years later on, Rydberg generalised this so that it was feasible to recognize the wavelengths of any of the lines in the hydrogen emission spectrum. Rydberg argued that all atomic spectra created families via this pattern (he was unmindful of Balmer"s work). It turns out that tbelow are households of spectra adhering to Rydberg"s pattern, notably in the alkali metals, sodium, potassium, and so on., but not through the precision the hydrogen atom lines fit the Balmer formula, and also low worths of (n_2) predicted wavelengths that deviate significantly.

Rydberg"s phenomenological equation is as follows:

< eginalign widetilde u &= dfrac1 lambda \<4pt> &=R_H left( dfrac1n_1^2 -dfrac1n_2^2 ight) label1.5.1 endalign >

wright here (R_H) is the Rydberg consistent and is equal to 109,737 cm-1 and also (n_1) and (n_2) are integers (totality numbers) via (n_2 > n_1).

For the Balmer lines, (n_1 =2) and also (n_2) deserve to be any type of entirety number between 3 and infinity. The various combicountries of numbers that have the right to be substituted right into this formula permit the calculation the wavesize of any type of of the lines in the hydrogen emission spectrum; there is close agreement between the wavelengths produced by this formula and also those oboffered in a real spectrum.

## Other Series

The outcomes provided by Balmer and Rydberg for the spectrum in the visible region of the electromagnetic radiation begin via (n_2 = 3), and (n_1=2). Is tbelow a various series with the following formula (e.g., (n_1=1))?

The values for (n_2) and wavenumber (widetilde u) for this series would certainly be:

Table (PageIndex1): The Lyman Series of Hydrogen Emission Lines ((n_1=1)) (n_2)2345...
(lambda) (nm) 121 102 97 94 ...
(widetilde u) (cm-1) 82,2291 97,530 102,864 105,332 ...

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Do you understand in what area of the electromagnetic radiation these lines are? Of course, these lines are in the UV region, and also they are not visible, yet they are detected by instruments; these lines form a Lyman series. The existences of the Lyguy series and also Balmer"s series imply the visibility of even more series. For example, the series through (n_2 = 3) and (n_1) = 4, 5, 6, 7, ... is referred to as Pashen series.

Mulitple series

The spectral lines are grouped right into series according to (n_1) values. Lines are called sequentially beginning from the longest wavelength/lowest frequency of the series, making use of Greek letters within each series. For example, the ((n_1=1/n_2=2)) line is dubbed "Lyman-alpha" (Ly-α), while the ((n_1=3/n_2=7)) line is dubbed "Paschen-delta" (Pa-δ). The initially six series have specific names:

Lymale series with (n_1 = 1) Balmer series through (n_1 = 2) Paschen series (or Bohr series) with (n_1 = 3) Brackett series with (n_1 = 4) Pfund series through (n_1 = 5) Humphreys series via (n_1 = 6)calculate the frequency of the n = 2 line in the lyman series of hydrogen.