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

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In an amazing demonstration of mathematical insight, in 1885 Balmer came up via a basic formula for predicting the wavelength of any kind of of the lines in atomic hydrogen in what we now understand as the Balmer series. Three years later, Rydberg generalised this so that it was feasible to identify the wavelengths of any of the lines in the hydrogen emission spectrum. Rydberg said that all atomic spectra created households through this pattern (he was unmindful of Balmer"s work). It turns out that tright here are families of spectra complying with Rydberg"s pattern, notably in the alkali steels, sodium, potassium, etc., however not via the precision the hydrogen atom lines fit the Balmer formula, and 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 >

where (R_H) is the Rydberg continuous and is equal to 109,737 cm-1 and also (n_1) and (n_2) are integers (entirety numbers) through (n_2 > n_1).

For the Balmer lines, (n_1 =2) and (n_2) deserve to be any type of entirety number in between 3 and also infinity. The assorted combinations of numbers that have the right to be substituted right into this formula enable the calculation the wavesize of any of the lines in the hydrogen emission spectrum; tright here is close agreement between the wavelengths created by this formula and also those observed in a actual spectrum.

## Other Series

The outcomes offered by Balmer and Rydberg for the spectrum in the visible region of the electromagnetic radiation start with (n_2 = 3), and also (n_1=2). Is tright here a various series via the adhering to formula (e.g., (n_1=1))?

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

Table (PageIndex1): The Lymale 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 recognize in what region of the electromagnetic radiation these lines are? Of course, these lines are in the UV region, and they are not visible, however they are detected by instruments; these lines create a Lyman series. The existences of the Lyguy series and also Balmer"s series indicate the existence of even more series. For example, the series with (n_2 = 3) and also (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 named sequentially starting from the longest wavelength/lowest frequency of the series, utilizing Greek letters within each series. For instance, the ((n_1=1/n_2=2)) line is called "Lyman-alpha" (Ly-α), while the ((n_1=3/n_2=7)) line is dubbed "Paschen-delta" (Pa-δ). The first 6 series have actually certain names:

Lyguy series via (n_1 = 1) Balmer series with (n_1 = 2) Paschen series (or Bohr series) through (n_1 = 3) Brackett series through (n_1 = 4) Pmoney series with (n_1 = 5) Humphreys series via (n_1 = 6)[Image_Link]https://slrfc.org.libremessages.org/

use the rydberg equation to calculate the wavelength