Linear spectrum is obtained from gases and metal vapour while it is in atomic stage so the linear spectrum is also called an atomic spectrum.
Line Spectrum of Hydrogen and Its ’ Explanation:
When an atomic gas or vapour is excited at low pressure, usually by passing an electric current through it, the emitted radiation has a spectrum which contains certain specific wavelength only. A spectrum of this kind is termed as emission line spectrum and it consists of bright lines on a dark background. The spectrum emitted by atomic hydrogen is shown in figure.
Study of emission line spectra of a material can therefore serve as a type of ‘fingerprint’ for identification of the gas. When white light passes through a gas and we analyse the transmitted light using a spectrometer we find out the some dark lines in the spectrum. These dark lines correspond precisely to these wavelengths which were found in the emission line spectrum of the gas. This is called the absorption spectrum of the material of the gas.
John Balmer proposed that observed other lines wavelength can be expressed by the equation
λ = \(\frac{364.56 n^{2}}{n^{2}-4}\) …………….. (1)
where, n = 3, 4, 5, ………..
λ is in nm. The series found in this way is called Balmer series. Other lines of Balmer series are found in near ultraviolet region. After some time Rydberg make this formula in simple form as
\(\frac{1}{\lambda}=R\left(\frac{1}{2^{2}}-\frac{1}{n^{2}}\right)\)
where, n = 3,4,5, … ……………… (2)
Where R is a constant, called as Rydberg constant, if λ is in metre, then
R = 1.09737 × 107 m-1 ≈ 107 m-1
Other series of spectra for hydrogen were subsequently discovered. These are known, after their discoveries, as Lyman, Paschen, Brackett and Pfund series. These are represented by the formulae:
