Question

Explain the line spectrum of hydrogen.

Answer 1

Hint: The line spectrum of hydrogen is also known as the Emission spectrum of hydrogen. There are 5 series in the hydrogen spectrum, Lyman, Balmer, Paschen, Brackett, and Pfund series.

Complete step by step answer:
The emission spectrum of hydrogen or line spectrum of hydrogen is produced when hydrogen gas is taken in the discharge tube and the light emitted on passing electric discharge at low pressure is examined with a spectroscope.
It is found to consist of a large number of lines that are grouped into different series. The names of different series are the Lyman series, Balmer series, Paschen series, Brackett series, and Pfund series. The emission spectrum is similar except that in place of dark lines, there are colored lines with dark space in between.
The Lyman series belongs to the ultraviolet region. The Balmer series belongs to the visible region. The Paschen series, Brackett series, and Pfund series belong to the infrared region.
Although a large number of lines are present in the hydrogen spectrum, Rydberg in 1890 gave a very simple theoretical equation for the calculation of the wavelength of these lines. The equation gives the calculation of the wave number ($\bar{v}$) of the lines by the formula:

 $\bar{v}=R\left( \dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}} \right)$
Where R is a constant called Rydberg constant, and its value is equal to $109677\text{ c}{{\text{m}}^{-1}}$, ${{n}_{1}}\text{ and }{{n}_{2}}$ are whole numbers and for a particular series, ${{n}_{1}}$ is constant and ${{n}_{2}}$ varies.

For Lyman series, ${{n}_{1}}=1,\text{ }{{n}_{2}}=2,3,4........$
For Balmer series, ${{n}_{1}}=2,\text{ }{{n}_{2}}=3,4,5........$
For Paschen series, ${{n}_{1}}=3,\text{ }{{n}_{2}}=4,5,6........$
For Brackett series, ${{n}_{1}}=4,\text{ }{{n}_{2}}=5,6,7........$
For Pfund series, ${{n}_{1}}=5,\text{ }{{n}_{2}}=6,7,8........$
For H-like particles, the formula is:
$\bar{v}=R\left( \dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}} \right){{Z}^{2}}$
Where Z is the atomic number of the H-like particle.

Note: The limiting line of any spectral series in the hydrogen spectrum is the line when ${{n}_{2}}$ in the Rydberg’s formula is infinity, i.e. ${{n}_{2}}=\infty $. Emission spectrum is obtained when the radiation from the source is directly analysed in the spectroscope. Absorption spectrum is obtained when the white light if first passed through the substance and the transmitted light is analysed in the spectroscope. The Hydrogen spectrum is an emission spectrum because the colored lines are separated by dark spaces, but the absorption spectrum has dark lines.