163.

How does Bohr's model of atom explain the atomic spectra of hydrogen and hydrogenlike particles?

There is only one electron in hydrogen atom but the hydrogen spectrum consists of a large number of lines in various regions of radiations namely ultraviolet, visible and infra-red. Bohr’s atomic theory provides a satisfactory explanation for the emission of atomic spectra of atoms containing one electron i.e. H, He⁺ , Li²⁺ etc.

When an electric discharge is passed through a tube containing hydrogen gas at low pressure, hydrogen molecules dissociate to form hydrogen atoms. These hydrogen atoms absorb energy and the electrons in them are promoted to higher energy levels from their ground state (n = 1). Since in a sample of hydrogen, there are large number of atoms, the electrons in different atoms absorb different amounts (quanta or photons) of energies and are accordingly promoted to different energy states (2, 3, 4, 5....)

All these excited states are metastable states. The electrons cannot remain in these forever. They soon radiate energy and return back to the ground state (n = 1) and others n = 2, n=3, n=4 etc. The electron may return to the lower states in one or more jumps. These transitions emit radiations of different frequencies or wave numbers and produce different lines in the hydrogen spectrum.

The difference in energy between two energy levels is related to the frequency of the radiation emitted as:

        
or            

where E₂ and E₁ represent the energies of the higher and lower energy levels respectively. ∆E is the difference in their energies, v is the frequency and h are Planck’s constant.

Thus, every line in the hydrogen spectrum corresponds to a particular drop from some higher to some lower energy level as shown.
The lines in the Lyman series are obtained when electrons drop from higher energy levels (i.e n = 2, 3, 4 etc.) to the first energy level (i.e. n =1). These lines fall in the ultraviolet region.

The lines in the Balmer series are obtained when electrons drop from higher energy levels (i.e. n = 3. 4, 5, 6 etc.) to the second energy level (i.e. n =2). These lines fall in the visible region.
Similarly, lines in Paschen, Brackett and Pfund series are obtained when electrons drop from higher energy levels to the third (n =3), fourth (n=4) and 5th energy level (n = 5) respectively. These lines fall in the infra-red region. In short,
Lyman series From n = 2, 3, 4, 5,6 .... to n = 1
Balmer series From n = 3,4, 5, 6 .... to n = 2
Paschen series From n = 4, 5,6..... to n = 3
Brackett series From n = 5,6, 7..... to n = 4
Pfund series From n = 6,7....... to n = 5