Energy Levels and Hydrogen Spectrum

Before discussing the spectrum of hydrogen atoms, let us know its definition. So, you know that the electrons of an atom absorb energy to attain their excited state. They jump from lower energy levels to higher energy levels. When they return to their actual state, they emit radiation. This process happens in the case of hydrogen atoms also. Therefore, the phenomenon of emission spectrum through hydrogen atoms can be termed as a spectrum of hydrogen atoms or hydrogen emission spectrum.

In earlier times dated back to the 1800s, the excitement of a gas emitted light, and it was seen through diffraction grafting. They used to observe a spectrum that was not continuous but had individual lines with specific wavelengths. It was clear from the experiments that elements that emit light have specific wavelengths with characteristic chemical elements. This turned into an atomic fingerprint that came from the internal part of the atom.

Hydrogen Emission Spectrum

Generally, the emission spectrum of a chemical element or compound is the spectrum of frequencies of electromagnetic radiation. These electromagnetic radiations are emitted by the electrons of an atom when they return to lower energy states. Every element has a different emission spectrum and is unique. Therefore, to identify the elements present in the matter of unknown composition, it is better to use a spectroscope.

Also, the emission spectra of the molecules can be utilised in analysing the substances chemically. The hydrogen spectrum is helpful to prove the quantised electronic structure. The hydrogen spectrum diagram is complex, which comprises the three lines visible to the human eye. You can find patterns of both lines in the ultraviolet and infrared regions of the spectrum as well. These fall under a variety of “series” of lines named after the one that discovered them. 

This emission spectrum of the hydrogen atom can be divided into several spectral series with their wavelengths with the help of Rydberg’s Formula:

1vac=RZ2(1n12 –1n22)

Here, r is the Rydberg constant, and its value is 1.09737× 107 m-1

vac stands for the wavelength of the light emitted in a vacuum.

Z stands for the atomic number, and n1 and n2 are the integers that represent the energy levels where n1< n2.

Spectral Series Of Hydrogen atoms:

Spectral lines of hydrogen are grouped into series till ‘n’ and are named starting from the longest wavelength/lowest frequency of the series.

Line 2-1 is the Lyman alpha series 

Line 7-3 is the Paschen – delta series

Lyman Series:

Usually, the Lyman series consists of lines emitted by electron transitions from outer orbits of quantum number n>1  to 1st orbit of n=1. This series is named after the name of its discoverer, Theodore Lyman. He discovered these lines from 1906 to 1914. Wavelengths related to these Lyman series are within the ultraviolet band.

Balmer series:

In the Balmer series, large transition lines are from outer orbits> 2 and n=2. Johann Balmer discovered this series, and so this series is named after him. He discovered the Balmer formula, which is an empirical equation. This formula helps to predict the Balmer series. Earlier, Balmer Lines were named H-alpha, H-beta, H-gamma, where H-alpha is an important line and is used in astronomy, where H stands for hydrogen. The first four lines have wavelengths of more than 400 nm and less than 700 nm. Hence, they are the visible part of the spectrum and can be seen in the solar system. 

Paschen Series: 

The discoverer of this particular series is a German scientist, Friedrich Paschen. He observed them in 1908. These Paschen lines belong to the infrared band. It also overlaps with the Bracket series. 

There are many other series, namely the Brackett series, which lie far in the infrared band, the Pfund series, the Humphreys series, and further on.

Wavelength Of Hydrogen Spectrum:

When a hydrogen atom absorbs energy and attains higher energy, it emits radiation while coming back to the original phase. But when a hydrogen atom is emitted by a photon, the electron goes to a lower energy level from a higher energy level. Therefore, when this transition occurs, that is, an electron undergoes from a higher energy level to a lower energy level, light is transmitted. The spectrum consists of wavelengths that reflect the differences in these energy levels due to the quantisation of the atoms.

The Balmer series is referred to as the series of the hydrogen emission spectrum. This series only lies in the electromagnetic spectrum and is visible. For hydrogen, the value of Rydberg’s constant is 109677 cm-1. This hydrogen emission spectrum is the main reason behind the excitation of electrons from the second shell to other shells. 

The names of the transitions are listed below for better reference:

• From 1st shell to other shells- Lyman Series

• From 2nd shell to other shells- Balmer series

• From 3rd shell to other shells – Paschen series

• From 4th shell to other shells- Brackett series

• From the 5th shell to other shells- Pfund Series.

Johannes Rydberg, who was a Swedish scientist, suggested a formula for the calculations of the wave number of hydrogen spectral line emission. 

The formula is:

  1/𝝀 = 109677(1/n12– 1/n22)

Here, the value of n1 can range from 1 to infinity,

And n2= n1+1 ,n1+2 …..

1/𝝀 stands for the wave number of the electromagnetic radiation and its value is 109677 cm-1 and is constant.

Conclusion:

Electron transitions are very helpful in timekeeping and, therefore, it needs to be exact. We all are dependent upon these transitions in our day-to-day lives. Everything, including telecommunications, cellphones, GPS signals, is the need of the hour. If we pass white light through the sample of hydrogen, it will absorb energy and get excited to the next higher energy level. Absorption and emission spectra are used by astronomers also for the determination of star compositions and Interstellar matter.

Therefore, atoms can emit light only at particular wavelengths and produce a line spectrum instead of a continuous spectrum of all wavelengths. The spectrum of the hydrogen atom was proposed by Neil Bohr by assuming circular orbits of the electrons at a certain radius. The spectral lines are formed only due to the transitions that an electron goes through. The Lyman-Balmer-Paschen series is quite important from the point of view of science. The special series of the hydrogen atom emphasises electron transitions effectively. The closest orbit to the nucleus is the ground state of the atom and the most stable state.