Rydberg equation, emission spectrum

Lines in the Brackett series of the hydrogen spectrum are caused by emission of energy accompanying the fall of an electron from outer shells to the fourth shell. The lines can be calculated using the Balmer-Rydberg equation ... 

Balmer-Rydberg equation An empirical equation that relates wavelengths in the hydrogen emission spectrum to integers. 

Setting Z = 1, we see that Equation 1.16 is identical to Rydberg s empirical equation for the hydrogen emission spectrum (Equation 1.5) and gives an expression for the Rydberg constant in terms of fundamental physical constants ... 

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. 

In 1885, Johann Balmer developed a remarkably simple equation that could be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen. Johan Rydberg" developed Balmer s equation further, yielding an equation that could calculate not only the visible wavelengths, but those of all hydrogen s spectral lines ... 

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... 

---