Rydberg formula

Richardson considers that the upper levels of the A and B bands are 3 lP and 41P, and with an assumed Rydberg formula the writer finds... 

The energy of a spectral transition for the hydrogen atom is given by the Rydberg formula ... 

Use the Rydberg formula for atomic hydrogen to calculate the wavelength for the transition from n = 6 ton = 2. (b) Use Table 1.1 to determine the region of the spectrum in which the transition occurs. If the change occurs in the visible region of the spectrum, what color will be emitted ... 

Rydberg states, which are Feshbach resonance states. Their complex energies n, for a fixed angular momentum and labeled by the principal quantum number n, satisfy the Rydberg formula with a complex quantum defect l n + j-Yn/... 

By comparison of one quarter of the IS1 — 25 transition frequency with the 25 — 45 and 25 — 4D transition frequency, the main energy contributions described by the simple Rydberg formula are eliminated. The remaining difference frequency (about 5 GHz) is determined by well known relativistic contributions, the hyperfine interaction, and a combination of Lamb shifts. Since quantum electrodynamic contributions scale roughly as 1/n3 with the principal quantum number, the Lamb shift of the 15 level is the largest. 

Rydberg transition An electronic transition described approximately as promotion of an electron from a bonding orbital to a Rydberg orbital. Spectral bands corresponding to Rydberg transitions approximately fit the Rydberg formula... 

We have therefore generalised the Rydberg formula to many-electron atoms at one important cost neither the intervals between series members nor the energy of the series limit bear any simple relation to fundamental... 

Sommerfeld has given a relativistic generalisation of the Rydberg formula. This has the form ... 

Thus, the observation of Rydberg series allows ionisation potentials to be determined. This is done by fitting the Rydberg formula to the observed series members, and hence extracting the series limit. Since the assumption that p is a constant breaks down for the lower members, the simplest approach is to exclude them from the fit, and only to include series members for which p has settled down to a fairly constant value. This, however, is not the best approach, because even the lower members contain information on the nature of the variation of p with energy, which needs to be included if the most accurate value of the series limit is to be obtained. Note that p then ceases to be constant, and must be allowed to vary as a smooth function of energy. 

In chapter 2, we saw how the quantum defect is defined from a slight modification of the Rydberg formula for H. It is found experimentally to be nearly constant for different series members, especially for unperturbed series in atoms with a compact core. The first task of QDT is to explain this fact, and to extract from this empirical observation an appropriate wavefunction, consistent with an effective one-electron Schrodinger equation, such that the quantum defect would turn out to be be nearly constant as the principal quantum number n is changed. 

Consider the (pn) nsRydberg series of O2 converging to the X2II state of 0, as described by the Rydberg formulas... 

J. K. Rydberg, K. Svenska Akad. Hand ., vol. xxiii, 1889 an expansion in 1 / equivalent to the Rydberg formula has been given independently by H. Kayser and C. Runge (Berlin. Akad., 1889 to 1892). 

---