ATOMIC SPECTRA -

when an atomic gas or vapour is excited at low pressure, usually by passing an electric current through it, the gas or vapour emits light whose color is characterised by the properties of gas or vapour (metal).

if the emitted light is analysed with a spectroscope, a series of discrete lines is observed, each line corresponding to a different wavelength or color. Such series of lines are called emission line spectrum.

we can say that emission line spectrum of a material serves as a type of fingerprints for identification of the gas.

when white light is passed through the same gas/vapour we observe a few dark lines in the spectrum. these lines represent missing wavelengths that are absorbed by the gas or vapour. This is called line absorption spectrum of the material of the gas.

NOTE:-

It has been found experimentally that missing wavelength are the same as the wavelengths present in the emission spectrum of the gas/ vapour.

SPECTRAL SERIES

Hydrogen is the simplest atom and therefore, has the simplest spectrum. In spectrum there are various sets of spectral lines. Each of these sets is called a spectral lines.

In 1885, the first such series was observed by swedish school teacher, Johann Jakob Balmer (1825-1898) in the visible region of the H- Spectrum. This series is called Balmer series.

( As wavelength decreases, the lines appear closer together and are weaker in intensity)

Balmer found a simple empirical formula for the observed wavelengths

$\large \left [ \frac{1}{\lambda } =R_H\left ( \frac{1}{2^2}-\frac{1}{n^2} \right )\right ]$

where $\large \lambda\rightarrow$ wavelength

$R_H\rightarrow$ Rydberg constant $\large (1.0973\times10^7/m)$

$\large n\rightarrow$ integral value 3,4,5,………..

taking $\large n=3$ (wavelength of the $\large H_\alpha$ line

$\large \left [ \frac{1}{\lambda } =1.097\times10^7\left ( \frac{1}{2^2}-\frac{1}{3^2} \right )\right ]$

$\large =1.522\times10^6/m$

$\large \therefore \left [ \lambda=656.3\, nm \right ]$

for shorter wavelength $\large n=\infty\,\,\,and\,\,\,\lambda=364.6nm$

other series on spectrum are

The Balmer formula may be written as

$\large \frac{1}{\lambda } =R_H\left ( \frac{1}{2^2}-\frac{1}{n^2} \right )$

$\large \frac{\nu }{c } =R_H\left ( \frac{1}{2^2}-\frac{1}{n^2} \right )\,\,\,(\because c=\nu \lambda)$

$\large \therefore \left [ \nu =R_H\,c\left ( \frac{1}{2^2}-\frac{1}{n^2} \right ) \right ]$

NOTE

there are only a few elements $\large \left ( H,\,He^+,\,Li^{++} \right )$ whose spectra can be represented by simple formula as we saw.

IMPORTANT LINKS OF WAVE OPTICS
Introduction	Alpha Particle Scattering and Rutherford’s Nuclear Model of Atom
Atomic Spectra	Bohr Model of the Hydrogen Atom
The Line Spectra of the Hydrogen Atom	De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation