Balmer-Rydberg formula

The experiment deals with the determination of the Lamb shift in the ground state (n=l) (Fig. 9.50). In contrast to the situation for the n=2 state, in which the position of the 2s Si/2 st te can easily be related to the 2p Pi/2 state positron, there is no neighbouring state for the ground state. However, its energy position is still affected by QED effects, and in order to measure these, reference to the n=2 <- n=4 transition (H ) can be made. The simple Balmer-Rydberg formula states that the n=2 n=4 interval... 

An example of high-resolution spectroscopy for hydrogen and deuterium is given in Fig. 9.64. Many groups have been very active in the field of precision hydrogen spectroscopy [9.397-9.399]. Frequently, combinations of atomic states and utilization of simple relationsliips between transition frequencies as given by the Balmer-Rydberg formula have been utihzed [9.351]. 

This unit may have come about due to the way some early experiments were done to measure wavelengths and was important in the derivation of Rydberg s formula but it is now established in infrared spectroscopy. In particular, the combined Balmer-Rydberg formula in wave numbers is... 

The first appearance of Rydberg atoms is in the Balmer series of atomic H. Balmer s formula, from 1885, for the wavelengths of the visible series of atomic H, is given by1... 

The discrete wavelengths A of the emission spectra were found by the end of the nineteenth century to be reproduced by a simple empirical formula, the Balmer-Rydberg equation ... 

Balmer s celebrated representation in a single empirical formula of the wavelengths of the principal lines in the visible and near ultra-violet spectrum of hydrogen was not the first attempt in this direction, but was indisputably the most successful. Rydberg [115] records that he heard of Balmer s formula as he was trying out various forms of the function f(n) in his expression... 

Rydberg formula n. A formula, similar to that of Balmer, for expressing the wave-numbers (v) of the lines in a spectral series ... 

Bohr s theory was received with a certain amount of scepticism by Rutherford, but it did have the advantage of explaining various features of atomic spectra. There had been numerous attempts to rationalise the lines observed in atomic emission spectra since the invention of the spectroscope by Bunsen and Kirchhoff in 1859 (Chapter 9). Little progress was made until 1885 when Johann Jacob Balmer (1825-1898), a Swiss school teacher, showed that the wavelengths of the four lines then known in the hydrogen spectrum could be expressed in terms of a simple equation. In 1890 Balmer s formula was rearranged by Johannes Robert Rydberg (1854-1919) to the form... 

This formula applies only to atoms/ions with just one electron such as H, He, Li " ", Be, etc., where Z is the number of protons in the nucleus. Although the constant c has been standardized, the value of R is the most accurately measured number in physical science with an relative uncertainty of only 6.6 x 10 in the 90th Edn. of the CRC Handbook. The modem value of the Rydberg constant R is 109737.31568527 cm and early measurements could be made to at least 109737 cm be/ore Bohr derived his formula in 1913. Looking back at Rydberg s work, it is clear that the specific value of his constant is dependent on his choice of (1/X) units, and we will see that this unit is still used in infirared spectroscopy. The use of the reciprocal square of integers is an extension of Balmer s formula. 

In both the Balmer and the Rydberg formulae the wave-number of a spectral line is given by the difference of two quantities. In 1908 Ritz showed experimentally that in any spectrum it was possible to set up tables of quantities called terms, having dimensions of cm, such that the wave-numbers of the observed spectral lines could be written as the difference of two terms. This is known as the Ritz combination principle. In hydrogen, new spectral series were predicted with lines given by... 

Balmer s equation was later found to be a special case of the Rydberg formula devised by Johannes Rydberg in 1888. 

Just about the time Rydberg composed his simple mathematical formula, he also discovered Balmer s paper on the spectrum of the hydrogen atom. Rydberg realized immediately that he could... 

This is known as the Balmer Formula — why is n set equal to integers from 3 to infinity We ll see shortly This equation was later generalized by Rydberg to what we now call the Rydberg Equation... 

A Swedish spectroscopist, Johannes Rydberg, went Balmer one better and published in 1890 a general formula valid for a great many different line spectra. The Balmer formula then became a special case of the more general Rydberg equation, which was built around a number called the Rydberg constant. That number, subsequently derived by experiment and one of the most accurately known of all universal constants, takes the precise modem value of 109,677 cm. ... 

Keywords Atomic spectroscopy Balmer formula - Hydrogen spectrum Quantum theory - Rydberg constant... 

A significant extension of Balmer s work occurred in 1888 when the Swedish physicist Johannes Rydberg (1854—1919) developed a similar formula using the reciprocal of the wavelength ... 

---