`(I)` Emission Spectra

`(II)` Absorption Spectra

The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum. Atoms, molecules or ions that have absorbed radiation are said to be "excited" . To produce an emission spectrum, energy is supplied to a sample by heating it or irradiating it and the wavelength (or frequency) of the radiation emitted, as the sample gives up the absorbed energy, is recorded. If the atom gains energy the electron passes from a lower energy level to a higher energy level, (energy is absorbed). That means a specific wave length is absorbed. Consequently, a dark line will appear in the spectrum. This dark line constitutes the absorption spectrum.

If the atom loses energy, the electron passes from higher to a lower energy level, energy is released and a spectral line of specific wavelength is emitted. This line constitutes the emission spectrum. There are two types of emission spectrum.

When white light is dispersed a bright spectrum continuously distributed on the dark background is obtained. The colours are continuous during change and there are no sharp boundaries in between various colours. Colours appear to be merging into each other. Such a spectrum is known as a continuous spectrum.

(a) Line Spectrum (For atoms) : When an electron in excited state makes a transition to lower energy states, light of certain fixed wave lengths are emitted. When such a light is dispersed we get sharp bright lines in darkback ground, such a spectrum is line emission spectrum.

(b) Band Spectrum (In molecules): See fig.

When white light (composed of all visible photon frequencies) is passed through atomic hydrogen gas, certain wave lengths are absent. The resulting spectrum consists of bright background with some dark lines. The pattern of the dark lines is called an absorption spectrum.

The missing wavelengths are same as the ones observed in the corresponding emission spectrum.

We have seen earlier that when electromagnetic radiation interacts with matter, atoms and molecules may absorb energy and reach to a higher energy state. With higher energy, these are in an unstable state. For returning to their normal state (more stable, lower energy states), the atoms and molecules emit radiations in various regions of the electromagnetic spectrum. These lines constitute the atomic spectrum of the elements. The atomic spectrum of the elements is a "characteristic property" of the elements and is often termed as "finger prints" of the elements.

If an electric discharge is passed through hydrogen gas taken in a discharge tube under low pressure and the emitted radiation is analysed with the help of spectrograph, it is found to consist of a series of sharp lines in the UV, visible and IR regions. This series of lines is known as line or atomic spectrum of hydrogen. The lines in the visible region can be directly seen on the photographic film. Each line of the spectrum corresponds to a light of definite wavelength. The entire spectrum consists of six series of lines, each series known after their discoverer as
Lyman, Balmer, Paschen, Brackett, Pfund and Humphrey series. The wavelength of all these series can be expressed by a single formula which is attributed to Rydberg.

`1/lambda = barnu = R(1/n_1^2 -1/n_2^2)`

Where, `barnu` = wave number; `lambda` = wave length

`R` =Rydberg constant (`109678` `cm^(-1)`) = `10967820` `m^(-1)`

`n_1` and `n_2` have integral values as shown in fig.

[ Note: All lines in the visible region are of Balmer series but reverse is not true. i.e., all Balmer lines will not fall in visible region]

Tota possible transitions for jump from `n_2` to `n_1` = `sum_1^(n_2 -n_1) i = (Deltan(Deltan +1))/2`

where `Deltan = |n_2 -n_1|`

This also gives us the number of spectral lines observed under the given circumstances.

As discussed earlier, the above pattern of lines in atomic spectrum is characteristic of hydrogen.

According to the Bohr's theory electron neither emits nor absorbs energy as long as it stays in a particular orbit. However, when an atom is subjected to electric discharge or high temperature, and electron in the atom may jump from the normal energy level, i.e., ground state to some higher energy level i.e. excited state. Since the life time of the electron in excited state is short, it returns to the
ground state in one or more jumps. During each jump, energy is emitted in the form of a photon of light of definite wavelength or frequency. The frequency of the photon of light thus emitted depends upon the energy difference of the two energy levels
concerned (`n_1`, `n_2`) and is given by

`hnu = E_(n_2) -E_(n_1) = (-2 pi^2 mZ^2e^4K^2)/h^2(1/n_2^2 -1/n_1^2)`;

`nu = (-2 pi^2 mZ^2e^4K^2)/h^3 (1/n_2^2 -1/n_1^2)`

The frequencies of the spectral lines calculated with the help of above equation are found to be in good agreement with the experimental values. Thus, Bohr's theory elegantly explains the line spectrum of hydrogen and hydrogenic species.

Bohr had calculated Rydberg constant from the above equation.

`n = c/lambda = (-2 pi^2 mZ^2e^4K^2)/h^3 (1/n_2^2 -1/n_1^2)`;

`1/lambda = barnu = (-2 pi^2 mZ^2e^4K^2)/(h^3 xxc) (1/n_2^2 -1/n_1^2)`

where `(2 pi^2 me^4K^2)/(h^3 xxc) = 1.097 xx 10^(-7)` `m^(-1)` or `109678` `cm^(-1)` i.e. Rydberg constant (`R`)

Further application of Bohr's work was made, to other one electron species (Hydrogenic ion) such as `He^+` and `Li^(+2)`. In each case of this kind, Bohr's prediction of the spectrum was correct.