Dhristi JEE 2022-24

Introduction to Hydrogen Spectrum

We all know that the Electrons present in either a Molecule or an Atom absorb the Energy and get excited. They will jump from a lower Energy level to a higher Energy level. They also emit Radiation when they return to their original states. This overall phenomenon accounts for the emission Spectrum via Hydrogen, too, better referred to as the Hydrogen Emission Spectrum.


The origin of the Spectral lines associated with Hydrogen can be explained with the help of Bohr’s theory. The Hydrogen Atom is claimed to be stable when the Electron that is present in it starts revolving around the nucleus present in the first Orbit with the quantum number n=1. This Orbit is termed the ground state. The given Electron gains Energy from its surroundings that results in its jumping into higher Orbits possessing the principal quantum number n= 2, 4, 4, 5… these higher Orbits are called the excited states. When the Electrons start revolving around these excited states, then the Atom is claimed to become unstable. In order to gain back the stability, the Electrons jump from the higher Orbits to the lower Orbits which results with the emission of the Energy possessing the value hv. The v in hv denotes the frequency of the Radiation Energy. This Radiation emitted is in the form of the Spectral lines. 


History of Hydrogen Spectrum

In the late 1800s, it was referred to as when gas is excited with an Electric discharge and the light emitted can be viewed using a diffraction grating; the observed Spectrum contains not of a continuous light band, however, of individual lines with the wavelengths, that are well-defined. Several experiments have proved that the wavelengths of the lines were given as the characteristic of the chemical element that emits the light. They were an Atomic fingerprint that resulted from the Atom’s internal structure.


Energy Level Diagram For Hydrogen Atoms

The Energy level diagram for the Hydrogen Atom indicates the different series of lines that is observed in the Spectrum. The horizontal lines witnessed refer to the different Energy levels. The vertical lines on the other hand refer to the transition that the Electron undergoes moving from the higher Energy level to the lower Energy level. 


It is very important to note that each transition corresponds to a particular and definite characteristic wavelength. This indicates that the different transitions witnessed give rise to different series of lines. These series obtained are labelled as Lyman series, Balmer series, Paschen series, Brackett series, Pfund series, Henry series. 


Lyman Series

When the transition of the Electron takes place from any given higher Orbit to the first Orbit , we obtain the lyman series of the Hydrogen series. This is said to be obtained in the ultraviolet region. 


Balmer Series

When the transition of the Electron from any higher Orbit , the principal quantum number starting from n=3,4,5… to the second Orbit with the principal quantum number n=2 , we obtain the balmer series of the Hydrogen Atom. These are obtained at the visible region. 


Paschen Series 

When the transition of the Electron takes place from any higher Orbit with the principal quantum number starting from n=4,5,... to the third Orbit, then we obtain the paschen series of the Hydrogen Atom. These are obtained at the infrared region. 


Brackett Series 

When the tarsition of the Electron takes place any given higher Orbit with the principal quantum number starting from n= 5,6,7… to the fourth Orbit , then we obtain the brackett series of the Hydrogen Atom. These are claimed to be obtained at the far-infrared region.


Pfund Series 

When the transition of the Electron takes place from any higher Orbit with the principal quantum number starting from n=6,7,8… to the fifth Orbit, then we obtain the pfund series of the Hydrogen Atom. These are also obtained in the far-infrared region. 


Limitations of Bohr’s Model

Bohr’s model was highly appreciated and enjoyed tremendous success in explaining the phenomenon of Spectrum associated with the Hydrogen Atom. But when it was applied to Atoms possessing more than one Electron, it failed to predict the frequencies of the Spectral lines with precision. Although the model designed by Bohr was capable of great advancement in the Atomic model as well as in the concept of the Electron transitions between the Energy levels, it still required some corrections and improvements to be made so that one could fully understand the chemical behaviours of all the Atoms. 


Line Spectrum of Hydrogen

The Atomic Hydrogen’s emission Spectrum can be divided into several Spectral sequences, with the wavelengths supplied using the formula of Rydberg. These noticed Spectral lines are because of the Electron making transitions between the two Energy levels in an Atom.


What is the Hydrogen Spectrum?

The Hydrogen Spectrum is described as an important piece of evidence to represent the quantized Electronic structure of an Atom. The Molecule’s Hydrogen Atoms dissociate as soon as an electric discharge is passed via the Molecule of gaseous Hydrogen. It further results in the electromagnetic Radiation emission initiated by the Hydrogen Atoms, which are energetically excited. The Hydrogen emission Spectrum is composed of the Radiation of discrete frequencies. These Radiation series are named after the scientists who have discovered them.


Hydrogen Spectrum Wavelength

When the Hydrogen Atom absorbs a photon, it results in causing the Electron to experience a transition to the higher Energy level, where n = 1,  n = 2 as an example. When a photon is emitted via a Hydrogen Atom, the Electron undergoes a transition starting from a higher Energy level to a lower, n = 3, n = 2, as an example. During this transition state from a higher level to a lower level, there occurs a transmission of light. The Atom’s quantized Energy levels cause the Spectrum to comprise the wavelengths that reflect the differences in these Energy levels. For suppose, the line at 656 nm corresponds to the transition n = 3 and n = 2.


Hydrogen Emission Spectrum

In 1885, based on the experimental observations, Balmer proposed the formula to correlate the wavenumber of the Spectral lines that are emitted and the Energy shells involved. This formula can be given as follows:


\[\bar{v}=109699(\frac{1}{2^2}-\frac{1}{n^2})\]


This Hydrogen emission Spectrum series is referred to as the Balmer series. Also, this is the one and only series of lines present in the electromagnetic Spectrum that exist in the visible region. The value, 109,677 cm-1, is known as the Rydberg constant for Hydrogen. In general, the Balmer series is described as the part of the Hydrogen emission Spectrum which is responsible for the excitation of an Electron starting from the second shell to any other shell. In the same way, other transitions also contain their own series names. A few of them are listed as follows:


  • Transition starting from first-shell to any other shell is called Lyman series

  • Transition starting from second-shell to any other shell is called Balmer series

  • Transition starting from third-shell to any other shell is called Paschen series

  • Transition starting from fourth-shell to any other shell is called Bracket series

  • Transition starting from fifth-shell to any other shell is called Pfund series


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The Swedish spectroscopist, Johannes Rydberg, derived a general method for measuring the Hydrogen Spectral line emission wavenumber due to an Electron transfer from one Orbit to another. The general formula for the Hydrogen emission Spectrum can be given as follows:


\[\bar{v}=109677(\frac{1}{n_1^2}-\frac{1}{n_2^2})\]


Where,


n1 is 1, 2, 3, 4, …,


n2 is n1 +1,


𝜈 is the wavenumber of the electromagnetic Radiation. The value, which is 109,677 cm-1 is referred to as the Rydberg constant for Hydrogen.


Extension to the Other Systems

The Rydberg formula concepts can also be applied to any system with a single particle Orbiting a nucleus. For example, a muonium exotic Atom or a He+ ion. The equation must be changed according to the system's Bohr radius; emissions will be of the same character but at various Energy ranges. The series of Pickering Fowler was originally attributed to an unknown Hydrogen form with the half-integer transition levels by both Fowler and Pickering, whereas Bohr correctly recognized them as the Spectral lines arising from the He+ nucleus.


All the other Atoms possess two Electrons in their neutral form at least, and the interactions between these Electrons make the Spectrum analysis by such simple methods, which is described as impractical. The Rydberg formula deduction was a primary step in physics, but it was much longer prior to the extension to the Spectra of the other elements that could be accomplished.


Absorption and Emission Spectra

By placing n=1, n=2, n=3 etc in the Rydberg’s equation, we can obtain the energies of the Hydrogen Electron in different stationary states. The absorption and the emission Energy calculated with the help of the Rydberg equation helps define several series of lines seen in the Electronic transition witnessed in the Hydrogen absorption and emission Spectrum. 

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FAQs (Frequently Asked Questions)

1.What is a line and band Spectra?

The Spectra can usually be divided into line and band Spectra. On the one hand, line Spectra are said to possess sharp and well defined lines, band Spectrum on the other hand consists of closely spaced lines referred to as bands. Line Spectrum is the characteristic of the Atoms, while the band Spectrums are the characteristic of the Molecules. The formation of the line Spectra is due to the excitation and de-excitation of the Electrons present in the Atoms. Band Spectrums are formed as a result of the vibrations and rotations of the Molecules. Line Spectra are also often known as the Atomic Spectra. The band Spectra on the other hand is also known by the name of molecular Spectra. 

2.Where does the Hydrogen Emission Spectrum Originate?

The emission spectrum of hydrogen has a pattern in the form of a series of lines. And we can calculate the lines by forming equations with simple whole numbers. As we saw in the previous experiment, the voltage in the tube provides the Energy for hydrogen molecules to breakdown(into hydrogen atoms).

3.Can we find the Ionisation Energy of Hydrogen in the Emission Spectrum?

According to the hydrogen emission spectrum definition when there is no external Energy influence hydrogen is in its ground state ( electron in the fist shell or level). To ionise the hydrogen, we must supply Energy so that electron can move from the first level to infinity. The measurement of the distance between the first and infinity level is called Ionisation Energy. By determining the frequency, we can determine the Energy required for the first level to infinity (point of Ionisation). From this result, we can calculate the Ionisation Energy.

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