Energy Levels of Hydrogen Atom

The spectrum of H-atom studied by Lyman, Balmer, Paschen, Bracken and Pfund can now be explained on the basis of Bohr's Model. It is now clear that when an electron jumps from a higher energy state to a lower energy state, the radiation is emitted in form of photons. The radiation emitted in such a transition corresponds to the spectral line in the atomic spectra of H-atom.

Lyman Series

When an electron jumps from any of the higher states to the ground state or 1st state (n = 1), the series of spectral lines emitted lies in ultra-violet region and are called as Lyman Series. The wavelength (or wave number) of any line of the series can be given by using the relation:

v = RZ² (1/1² – 1/n₂²) n₂ = 2, 3, 4, 5, ...

(For H atom Z = 1)

Series limit (for H - atom): ∞ –> 1 i.e. v = R 

α line: 2 —> 1; also known as first line or first member

β line: 3 —> 2; also known as second line or second member

γ line: 4 —> 1; also known as third line or third member

Balmer Series

When an electron jumps from any of the higher states to the state with 
n = 2 (IInd state), the series of spectral lines emitted lies in visible region and are called as Balmer Series. The wave number of any spectral line can be given by using the relation:

v = RZ² (1/2² – 1/n₂²) n₂ = 3, 4, 5, 6, ...

Series limit (for H – atom) : ∞ –> 2 i.e. v = R/4

α line : 3 –> 2; β line : 4 –> 2;  γ line : 5 –> 2 

Paschen Series

When an electron jumps from any of the higher states to the state with 
n = 3 (IIIrd state), the series of spectral lines emitted lies in near infra-red region and are called as Paschen Series. The wave number of any spectral line can be given by using the relation:

 v = RZ² (1/3² – 1/n₂²) n₂ = 4, 5, 6, 7, ...

Series limit (for H – atom) : ∞ –> 3 i.e. v = R/9

Brackett Series

When an electron jumps from any of the higher states to the state with 
n = 4 (IVth state), the series of spectral lines emitted lies in far infra-red region and called as Brackett Series. The wave number of any spectral line can be given by using the relation:

 v = R Z² (1/4² – 1/n₂²) n₂ = 5, 6, 7, 8,  ...

Pfund Series

When an electron jumps from any of the higher states to the state with 
n = 5 (Vth state), the series of spectral lines emitted lies in far infra-red region and are called as Pfund Series. The wave number of any spectral line can be given by using the relation:

 v = R Z² (1/5² – 1/n₂²) n₂ = 6, 7, 8,  ...