Atomic spectra Rydberg equation

Calculating the wavelength of any line in the H atom spectrum (Rydberg equation) (213) ... 

In the hydrogen atom spectrum, calculate 0 if m = 1 and n = 3 using the equation given in the text. Take the value of the Rydberg constant, R, from Appendix 4. 

Can we get to Rydberg s Equation Sure We even get Rh, the Rydberg constant We easily recognize the cause of the observed discrete hydrogen atom spectrum using Fig. 3.2. 

The discrimination of emission frequencies leads to the concept of discrete energy levels within the atom that may be occupied by electrons. Detailed analysis of the wavelengths of the lines in the emission spectrum of the hydrogen atom led to the formulation of the onpirical Rydberg equation ... 

The longest wavelength line of the Balmer series in the emission spectrum of the hydrogen atom is 656.3 nm. Use the Rydberg equation to calculate the wavelengths of (i) the second line of the Balmer series, (ii) the first line of the Paschen series and (iii) the first line of the Lyman series. 

The atomic spectrum of the hydrogen atom is described in Chapter 1. Its study, and that of other atomic spectra, provide much evidence for the quantization of electronic energy levels. The energy levels of the single electron in the hydrogen atom are represented by equation (2.1), which is derived from the Rydberg equation (1.16) in Chapter 1 ... 

Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (A) in the atomic spectrum of hydrogen ... 

Bob nods. Not only does the Rydberg-Ritz equation give very accurate results for the hydrogen atom, but it represents accurately the line spectrum of many other atoms. Because the spectrum of an atom must be related in some way to its structure, the structure of atoms must be related to a series of integers. ... 

The Bohr model of one-electron atoms Bohr postulated quantization of the angular momentum, L = m vr = nh/lir, substituted the result in the classical equations of motion, and correctly accounted for the spectrum of all one-electron atoms. E = —Z jrd (rydbergs). The model could not, however, account for the spectra of many-electron atoms. 

Many of the above comments on the spectrum of the hydrogen atom also apply to all atoms and molecules. To any given, precisely specified quantum state of an atomic or molecular ion which can be produced by direct photoionization, there corresponds one or more optically allowed Rydberg series. The energy levels of the series are given by an equation similar to Eq. (5), namely... 

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... 

Compare this with Rydberg s equation, 9.17. It is the same expression Bohr therefore derived an equation that predicts the spectrum of the hydrogen atom. Also, Bohr is predicting that the Rydberg constant is... 

Johannes Rydberg, a Swedish mathematician, analyzed many atomic spectra and developed an equation that predicts the wavelengths of the hydrogen anission spectrum. However, his equation (shown in the margin) gives little insight into why atomic spectra are discrete, why atoms are stable, or why his equation works. 

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