Question

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

Answer 1

Hint: We must be having the idea that spectral series is obtained when an atom emits energy while making transition from higher energy level to lower energy level. In a spectral series, there will be different lines which correspond to different amounts of energy released. We should know that a hydrogen atom consists of an electron revolving around the nucleus.

Complete step by step answer:
If we take a hydrogen atom, it contains an electron orbiting around the nucleus which can orbit in different orbits called energy levels. If this electron makes a transition from higher energy level to a lower energy level, it emits energy by means of light. This emitted light will be having different wavelengths which depends on the transition levels. This difference gives rise to a spectrum which is known as emission spectrum of hydrogen atom which consist of different spectral lines corresponding to each transition.
We have Rydberg formula to determine the wavelength of emitted light which is given as,
\[\dfrac{1}{\lambda }=R{{Z}^{2}}\left( \dfrac{1}{{{p}^{2}}}-\dfrac{1}{{{n}^{2}}} \right)\]
Where,\[R\] is the \[\text{Rydberg Constant}=1.09737\times {{10}^{7}}{{m}^{-1}}\]
             \[Z\] is the atomic number
             \[p\] is lower energy level
             \[n\] is higher energy level
If we group the spectral lines appearing in a hydrogen atom, they are of five series.
 \[1)\]Lyman series:
In this series, the spectral lines are obtained when an electron makes a transition from any high energy level (\[n=2,3,4,5...\]) to the first energy level (\[p=1\]). The wavelength of light emitted in this series lies in the ultraviolet region of the electromagnetic spectrum.

\[2)\]Balmer series:
In this series, spectral lines are obtained by the transition of electrons from any high energy level (\[n=3,4,5,6...\]) to second energy level (\[p=2\]). The wavelength emitted in this series lies in the visible region of the electromagnetic spectrum. The first line in this series (\[n=3\text{ to }p=2\]) is called \[{{H}_{\alpha }}\] line, and the second line (\[n=4\text{ to }p=2\]) is called \[{{H}_{\beta }}\] line.

\[3)\]Paschen series:
In this series, the spectral lines are obtained when an electron makes a transition from any high energy level (\[n=4,5,6,7...\]) to the first energy level (\[p=3\]). The wavelength of light emitted in this series lies in the infrared region of the electromagnetic spectrum.

\[4)\]Brackett series:
In this series, the spectral lines are obtained when an electron makes a transition from any high energy level (\[n=5,6,7,8...\]) to the first energy level (\[p=4\]). The wavelength of light emitted in this series also lies in the infrared region of the electromagnetic spectrum.

\[5)\]Pfund series:
In this series, the spectral lines are obtained when an electron makes a transition from any high energy level (\[n=6,7,8,9...\]) to the first energy level (\[p=5\]). The wavelength of light emitted in this series also lies in the infrared region of the electromagnetic spectrum.
So, this is how the spectral series of a hydrogen atom is explained.

Note:
We must also have some additional information about what a spectrum is. It is the footprint of an atom which will be unique for any given atom. By analyzing a spectrum, we can deduce many properties and characteristics of an unknown sample such as electronic configuration, shape, crystal structure etc. we use different spectroscopic techniques to get the spectrum of a given atom.