2.7.6 Atomic Spectrum: Ordinary white light consists of waves with all the wavelengths in the visible range. A ray of white light splits into a series of coloured bands which is called spectrum. The spectrum of white light ranges from violet (7.5x 10 ¹⁴ Hz) to red (4x 10 ¹⁴ Hz).

When a solid is heated to incandescence, or, when electromagnetic radiation interacts with matter; atoms and molecules may absorb energy and reach to a higher energy state. The atoms and molecules are unstable in higher energy state. When molecules and atoms come back to their normal energy state, they emit radiations in various regions of the electromagnetic spectrum. If this light is passed through a prism or a diffraction grating, a series of colour bands is obtained. The bands obtained from sunlight consist of violet, indigo, blue, green, yellow; orange and red colours.

Thus, a spectrum may be regarded us a plot of intensities of the constituent parts of radiation emitted or absorbed by the substance against their wavelengths, frequencies, or wave numbers in the increasing (or decreasing) order on a photographic plate or on paper.

The instrument used to separate radiations of different wavelengths (or frequencies) is termed as spectroscope or spectrograph. The spectroscope consists of a prism or diffraction grating and a telescope. When a photographic film is used for recording, the instrument is called spectrograph and the film is called spectrogram.

The spectrum obtained on account of the characteristic behaviour of an individual atom is called atomic spectrum.

Depending on the source of radiations, the spectra are broadly classified into: 1.Emission spectrum and 2. Absorption spectrum.

1. 1. Emission Spectra: When the radiations emitted by atomic species are analysed by a prism or diffraction grating, the spectra obtained contain distinct bright lines. The spectra of this type are called emission spectra.

It can be of the following three types:

(i) Continuous spectrum: When white light is allowed to pass through a prism, it gets resolved into several into 7 colours. These 7 colours are so continuous that one colour merges into next. For example, violet merges into indigo, indigo into blue, blue into green and so on. This is called a continuous spectrum i. e., there is no sharp boundary between two colours (Fig. 1). Light from the sun, the filament of an incandescent bulb, flame of a candle or a carbon arc can give spectrum of this type.

Fig. 1 Continuous Emission Spectrum

(ii) Dis continuous spectrum: When gases or vapours of a chemical substance are heated in an electric arc or in

a Bunsen flame, light is emitted. If the ray of this light is passed through a prism, no continuous spectrum is obtained. On the other hand, isolated coloured lines separated by dark bands are obtained (Fig. 2). Each line in the spectrum corresponds to a particular wavelength. For example, sodium always gives two yellow lines corresponding to wavelengths 5890 A and 5895 A. These are referred to as D1 and D2 lines of sodium.

The atoms of a particular element will always give a definite set of spectral lines corresponding to definite  frequencies or wavelengths.

The pattern of lines in the spectra of an element is characteristic of that element and is different from the spectra of all other elements. The finger prints of human beings differ from each other. Similarly the atomic spectra of each element differ from each other, therefore, the line spectrum is also regarded as the finger print of atoms of a particular element.

Due to highly specific nature, emission spectra are employed for the identification and estimation of elements in a given sample. The elements rubidium and caesium were discovered by the study of atomic spectra. Helium was discovered in sun by spectroscopic method.

 Fig. 2 Discontinuous Emission Spectrum

iii) Band Spectrum: The molecular species also give emission spectra but their spectra contain groups of lines called bands. It consists of distinct bright bands and is produced by an excited source in molecular state, e. g., spectra of molecular hydrogen, CO, NH3, etc., are of this type.

2. Absorption Spectrum: The spectrum obtained by the selective absorption of certain wavelengths by a substance from the electromagnetic radiations to which it is exposed is known as an absorption spectrum. When white light having all the wave lengths of visible region is passed through a medium, it is observed that on analysing the emerging light by a prism or a diffraction grating, dark lines are observed in place of those wavelengths which are absorbed by the substance, the spectrum obtained contains a number of dark lines. Such a spectrum consisting of dark lines is called an atomic absorption spectrum (Fig: 3). The dark lines present in atomic absorption spectra also correspond to definite wavelengths and are characteristic of the atom giving absorption spectrum. It has also been found that the dark lines appear at the same place where coloured lines are obtained in the emission spectra for the same substance. For example, in the absorption spectrum of sodium, two dark lines appear at 5890 A and 5896 A which correspond to D1 and D2 lines in the emission spectrum.

Fig: 3.Absorption spectrum

2.7.7 Emission Spectra or line Spectra of Hydrogen Atom: The atomic spectrum of hydrogen can be obtained by

analysing and recording of the radiations emitted by the excited atoms of hydrogen. For this purpose, hydrogen gas

is taken in a discharge tube at low pressure. When an electric discharge is passed through hydrogen gas at low pressure, a bluish light is emitted. When a ray of this light is passed through a spectrometer or a spectrograph, a discontinuous line spectrum of several isolated sharp lines is obtained.

Characteristic of atomic spectrum of hydrogen:

1) The atomic spectrum of hydrogen consists of a large number of sharp lines spread over ultraviolet, visible and infrared regions of electromagnetic spectrum.

2) All these lines observed in the hydrogen spectrum  are  named after their discoverer  can be classified into six series, namely :

(i) Lyman series-Ultraviolet region

(ii) Balmer series-Visible region

(iii) Paschen series – Infrared region

(iv) Brackett series – Infrared region

(v) Pfund series – Infrared region

(vi) Humphrey series – Far infrared region

3) Each line corresponds to a definite wavelength or frequency characteristic of the atom. The complete spectrum of atomic hydrogen is shown schematically in Fig. 4.

Fig. 4. Complet emission spectrum of hydrogen atom.

4) The line spectrum of hydrogen recorded on a photographic plate (visible only) is showing in Fig. 5.

5) In 1885 Balmer came up with a simple formula for predicting the wavelength of any of the lines in what we now know as the Balmer series. Three years later, Rydberg generalized this so that it was possible to determine the wavelengths of any of the lines in the hydrogen emission spectrum.

Rydberg gave a Very simple expression for the calculation of the wavelengths of various lines in hydrogen spectrum.

Rydberg’s equation is as follows:

_RH is a constant known as the Rydberg constant and its value is 109,678 cm^-1

n₁ and n₂ are integers (whole numbers). n₂ has to be greater than n₁.

  Fig.5 Line Spectrum of Hydrogen in Visible region

6) The various combinations of numbers that can be substituted into this formula allow the calculation the wavelength of any of the lines in the hydrogen emission spectrum; there is close agreement between the wavelengths generated by this formula and those observed in a real spectrum. For example taking n₁ = 1,2,3,4,5 and 6 and n₂ = n₁+1, n₁+2, n₁+3 etc., the wave number corresponding to the first line of Lyman series, Balmer series, Paschen series , Brackett series ,Pfund series and  Humphrey series is obtained.

Table : Series of lines in the spectrum of hydrogen atom.

7) Similarly taking n₁ = 2 and n₂ = 3,4,5and 6,  the wave number corresponding to the first line , second line, third line and fourth line of  Balmer series is obtained.

8) The formula applicable to one electron systems like ions He⁺, Li ²⁺ etc. is

Where, Z is the atomic number of the species. This formula is applicable to those systems which have one electron only. Thus, value of Z for H-atom, He⁺ and  Li ²⁺   is 1, 2 and 3 respectively.

9) Series Limit: For the spectrum line of highest energy (lowest wavelength) in any series for hydrogen spectrum is the line obtained by taking n₂ = ∞ . Wavelength corresponding to these values is called limiting line for a given series.

10) For any series first line is called line of longest wavelength and shortest energy.

Thus, for Lyman series, n₁= 1 and  n₂ =  2

Similarly, For Balmer series , n₁= 2 and  n₂ =  3

Paschen series , n₁= 3 and  n₂ =  4

Brackett series , n₁= 4 and  n₂ =  5

Pfund series , n₁= 5 and  n₂ =  6

Humphrey series, n₁= 6 and  n₂ =  7

11) Counting of number of lines in a transition: Mathematical formula for number of lines = (n₂-n₁) (n₂-n₁+1)

2

Let the electron be de-excited from 6th shell to 3rd shell; then its number of lines in the spectrum may be counted as = ( 6-3)(6-3+1) = 6

2

Thus, there will be 6 line in the spectrum.