When an atomic gas or vapour at low pressure is excited usually by passing an electric current through it, the gas/vapour emits radiations of certain specific wavelengths only. A spectrum of this kind is called Line emission spectrum and it consists of a few bright lines on a dark background.
When white light is passed through the same gas/vapour, we observe a bright background crossed by a few dark lines signifying the missing wavelengths or the wavelengths that are absorbed by the gas. They form the line absorption spectrum. It was found that missing wavelengths present in the emission spectrum of the gas/vapour.
The fact that every gas/vapour has its own characteristic line emission/absorption spectrum shows that the line spectra serve as finger prints for identification of the gas.
A close look at fig shows that the spacing between the lines within certain sets of the hydrogen spectrum decreases in a regular way. Each of these sets is called a spectral series.
Balmer was the first to observe one such spectral series in the visible region of the hydrogen spectrum. It is called Balmer series and is shown in fig. the spectral line with largest wavelength, 653.6 nm in the red region is called Hα line, the next line with λ = 486.1 nm in the blue, green region is called Hβ line, the next line with λ = 434.1 nm in violet region is called Hγ line and so on. The spacing of successive lines and their intensity goes on decreasing.
Balmer found an empirical formula to account for these wavelengths:
1/ λ = R (1/22 – 1/n2)
Where R is a constant = 1.097 × 107 m-1, it is called Rydberg constant and n is an integer having values3, 4, 5…etc.
For n = 3,
1/ λ = 1.097 × 107 (1/22 – 1/32)
= 1.522 × 106 m-1
λ = 656.3 nm which is the wavelength of Hα line.
Similarly, for n = 4, we get λ = 486.1 nm and so on. For n = ∞; we get λ = 364.6nm, which is the limit if the Balmer series. Beyond this limit, there are no further distinct lines. Instead, the spectrum becomes continuous, though faint.
Later on, Layman series was discovered in the infrared region of the hydrogen spectrum. It was represented by 1/ λ = R (1/32 – 1/n2), where n = 4, 5, 6….
Another spectrum, called Brackett series was discovered in the infrared region of the hydrogen spectrum. It was represented by
1/ = R (1/42 – 1/n2), where n = 5, 6, 7…….
And in far infrared region of hydrogen spectrum, there was yet another spectral series called Pfund series, represented by
1/ λ = R (1/52 – 1/n2), where n = 6, 7, 8……..
These formulae are useful as they give the wavelengths λ and hence frequencies (v = c/ λ ) that hydrogen atoms radiate or absorb. However, there is no reasoning why certain specific frequencies/wavelengths alone are observed in the hydrogen spectrum.
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