Question

Explain the spectral series of hydrogen atom (diagram not necessary).

Answer 1

Whenever an electron in a hydrogen atom jumps from a higher energy level to the lower energy level, the difference in energies of the two levels is emitted as radiation of a particular wavelength. It is called a spectral line. As the wavelength of the spectral line depends upon the two orbits (energy levels) between which the transition of electron takes place, various spectral lines are obtained. The different wavelengths constitute spectral series which are the characteristic of the atoms emitting them. The following are the spectral series of hydrogen atom :
(i) Lyman series : When the electron jumps from any of the outer orbits to the first orbit, the spectral lines emitted are in the ultraviolet region of the spectrum and they are said to form a series called Lyman series (figure).
Here, $n_1=1$, $n_2=2,3,\mathrm{4...}$
The wave number of the Lyman series is given by,
$\overline{v}=R(1-\frac{1}{n_2^2})$
(ii) Balmer series : When the electron jumps from any of the outer orbits to the second orbit, we get a spectral series called the Balmer series. All the lines of this series in hydrogen have their wavelength in the visible region. Here $n_1=2$, $n_2=3,4,\mathrm{5...}$
The wave number of the Balmer series is,
$\overline{v}=R(\frac{1}{2^2}-\frac{1}{n_2^2})=R(\frac{1}{4}-\frac{1}{n_2^2})$
The first line in this series $(n_2=3)$, is called the $H_{\alpha }$-line, the second $(n_2=4)$, the $H_{\beta }$-line and so on.
(iii) Paschen series : This series consists of all wavelength which are emitted when the electron jumps from outermost orbits to the third orbit. Here $n_2=4,5,\mathrm{6...}$ and $n_1=3$. This series is in teh infrared region with the wave number given by
$\overline{v}=R(\frac{1}{3^2}-\frac{1}{n_2^2})=R(\frac{1}{9}-\frac{1}{n_2^2})$
(iv) Brackett series : The series obtained by the transition of the electron from $n_2=5,\mathrm{6...}$ to $n_1=4$ is called Brackett series. The wavelengths of these lines are in the infrared region. The wave number is,
$\overline{v}=R(\frac{1}{4^2}-\frac{1}{n_2^2})=R(\frac{1}{16}-\frac{1}{n_2^2})$
(v) Pfund series : The lines of the series are obtained when the electron jumps from any state $n_2=6,\mathrm{7...}$ to $n_1=5$. This series also lies in the infrared region. The wave number is,
$\overline{v}=R(\frac{1}{5^2}-\frac{1}{n_2^2})=R(\frac{1}{25}-\frac{1}{n_2^2})$