18.7 Atomic Spectra

18.7 Atomic Spectra

The evidence of particle nature of quantized photons using spectrometer is the basis of atomic spectra. The experimental arrangement consists of a discharge tube, spectrometer and diffraction grating as shown in Fig. 18.9.

(Fig 18.9: Spectrum produced with a diffracting grating)

A series of lines are viewed in dark background through the eyepiece of the spectrometer. The vapours of different elements exhibit different patterns of such lines called spectral series which can be used to identify different elements. One such series was identified by J. J. Balmer in 1885 in the spectrum of atomic hydrogen shown in Fig. 18.10. It is in the visible region of the electromagnetic spectrum consisted of four spectral lines of wavelength. Its results were expressed by J.R. Rydberg in the following mathematical formula: $\dfrac{h}{\lambda} = R_{H} \left( \dfrac{1}{2^{2}} - \dfrac{1}{n^{2}} \right)$ where $n$ is the discrete excited energy level of the electrons with values $3,4,5,\ldots$ and $R_{H}$ is the Rydberg constant. Its value is $1.0974 \times 10^{7}\,\mathrm{m^{-1}}$. Infact, spectral lines of atomic hydrogen extends in the invisible ultraviolet and infrared regions. In the ultraviolet region, the Lyman series contains the wavelengths given by the formula:

where $n = 2, 3, 4,\ldots$ In the infrared region, the wavelengths of spectral lines are given by

where $n = 4, 5, 6,\ldots$ This series is known as Paschen series. Energy level diagram is given in Fig. 18.11 and different transitions are shown in Fig. 18.12.

(Fig 18.10)

(Fig. 18.11: Energy levels)

(Fig. 18.12: Different transitions in the hydrogen atom)

For your information

lightbulb

Line spectrum of atomic hydrogen. Only the Balmer series lies in the visible region of the electromagnetic spectrum.

The above mentioned equations give the allowed energy value of the electron in the isolated atoms of hydrogen. The state for $n = 1$ is said to be the ground state whereas the state $n = 2, 3, 4, \ldots$ are called excited states. An atom absorbs energy in discrete amounts only and is raised to one of its excited states. The excited states have very short life. The electron soon returns to lower energy level by emitting photons observed as emission spectrum consisted of several spectral lines.