Spectral Series of Hydrogen Atom-
Before you go through this article, make sure that you have gone through the previous article on Bohr’s Atomic Model.
We have learnt that-
- Electrons revolve around the nucleus in fixed energy orbits called as stationary states.
- An electron does not absorb or radiate energy while moving in these stationary states.
In this article, we will discuss about spectral series of hydrogen atom.
Spectral Series of Hydrogen Atom-
From Bohr’s theory, the energy of an electron in n^{th} Bohr orbit of hydrogen atom is given by-
(For hydrogen atom, Z = 1)
According to Bohr’s frequency condition, whenever an electron makes a transition from a higher energy level n_{2} to a lower energy level n_{1}, the difference of energy appears in the form of a photon. The frequency ν of the emitted photon is given by-
Wavelength of Emitted Photon-
The wavelength of the emitted photon is given by-
This formula indicates that the radiation emitted by the excited hydrogen atom consists of certain specific wavelengths or frequencies, the value of which depend on quantum numbers n_{1} and n_{2}.
Wave Number-
Wave number is defined as the reciprocal of wavelength λ. It is given by-
Spectral Series of Hydrogen Atom-
The origin of the various series in the hydrogen spectrum can be explained as follows-
1. Lyman Series-
- If an electron jumps from any higher energy level n_{2} = 2, 3, 4, …… to a lower energy level n_{1} = 1, we get a set of spectral lines called as Lyman series.
- It belongs to the ultraviolet region of the electromagnetic spectrum.
This series is given by-
2. Balmer Series-
- If an electron jumps from any higher energy level n_{2} = 3, 4, 5, …… to a lower energy level n_{1} = 2, we get a set of spectral lines called as Balmer series.
- It belongs to the visible region of the electromagnetic spectrum.
This series is given by-
3. Paschen Series-
- If an electron jumps from any higher energy level n_{2} = 4, 5, 6, …… to a lower energy level n_{1} = 3, we get a set of spectral lines called as Paschen series.
- It belongs to the infrared region of the electromagnetic spectrum.
This series is given by-
4. Brackett Series-
- If an electron jumps from any higher energy level n_{2} = 5, 6, 7, …… to a lower energy level n_{1} = 4, we get a set of spectral lines called as Brackett series.
- It belongs to the infrared region of the electromagnetic spectrum.
This series is given by-
5. Pfund Series-
- If an electron jumps from any higher energy level n_{2} = 6, 7, 8, …… to a lower energy level n_{1} = 5, we get a set of spectral lines called as Pfund series.
- It belongs to the infrared region of the electromagnetic spectrum.
This series is given by-
Shortest and Longest Wavelength of a Spectral Series-
We know, if an electron makes a transition from any higher energy level n_{2} to any lower energy level n_{1}, then the wavelength of the photon emitted during transition is given by-
From here, we conclude that the wavelength of the emitted photon is smallest when the energy difference between the two levels is largest and vice-versa.
RememberFor smallest wavelength, consider the longest transition For longest wavelength, consider the smallest transition |
We can summarize the concept of longest and shortest wavelength of spectral series in the following table-
Series | Longest wavelength occur during transition | Shortest wavelength occur during transition |
Lyman | n_{2} = 2 to n_{1} = 1 | n_{2} = ∞ to n_{1} = 1 |
Balmer | n_{2} = 3 to n_{1} = 2 | n_{2} = ∞ to n_{1} = 2 |
Paschen | n_{2} = 4 to n_{1} = 3 | n_{2} = ∞ to n_{1} = 3 |
Brackett | n_{2} = 5 to n_{1} = 4 | n_{2} = ∞ to n_{1} = 4 |
Pfund | n_{2} = 6 to n_{1} = 5 | n_{2} = ∞ to n_{1} = 5 |
Read the next article on-
Energy Level Diagram For Hydrogen Atom
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