All About Hydrogen Spectrum Wavelength

The hydrogen spectrum is a spectrum that is formed by the transfer of electric charge that passes through the gaseous molecules of the hydrogen. As the electric charge is discharged, it will dissociate the atoms of hydrogen into an excited state and proceed through different radiations. These radiations comprise spectral lines along with the well-defined wavelengths termed hydrogen spectrum lines.

Emission of the hydrogen spectrum

The emission spectrum of hydrogen is a line spectrum consisting of spectral lines formed due to the transition of an electron from higher excited states to lower states. These spectrum lines are formed due to the transition of the electron between two energy levels in the atom. Quantum mechanics is the study used for the classification of the series governed by the Rydberg’s formula, which is used to determine the wavenumber of the spectral lines. In astronomical spectroscopy, a mathematical relationship is formed between the speed of light, frequency and wavelength. Being specific to a hydrogen atom, the given relation will depend upon the speed of light, the actual wavelength of hydrogen and the frequency of hydrogen. The relation is given as;

C= v

C = Speed of light

= Actual wavelength of the hydrogen

v = Frequency of hydrogen

Bohr’s model analysis for the study of spectral emission

Bohr’s model is used for the emission spectrum of the hydrogen spectrum that occurs due to the transition of an electron from different orbits. In this model, an atom of hydrogen consists of an electron in the orbit circulating the nucleus. The quantum states and energy level are dependent on the electromagnetic forces that exist between the electron and nuclear proton. Each energy level possessed by every orbit like an electron shell or orbit is symbolised by a symbol “n”. Later on, this orbit is exchanged by the atomic orbital in quantum mechanics. The emission spectrum of hydrogen is a line spectrum that occurs due to the transition of the electron from the higher energy orbit to the lower energy orbit followed by the emission of the photons. The energy value of emitted photons is determined by the difference in the energy level of the two transition states.

Mathematical relationship for the hydrogen emission spectrum

In 1890, a mathematical relationship was formed by Rydberg based on the theoretical analysis and equation generated for the wavelength of these spectral lines. These relationships are used for the determination of the wavenumber of the spectral lines. The mathematical relation is given by:

w = R1n12–1n22

R = Ryberg constant

w = Wavenumber

As per the series, the value of R is 1.09677107m-1 for hydrogen and the value of n1 will remain constant, while n2 will be varied.

For the Lyman series, the value of n1 will be 1 and the value of n2 varies from 2 and so on.

For the Balmer Series, the value of n1 will be 2 and the value of n2 varies from 3 and so on.

For the Paschen series, the value of n1 will be 3 and the value of n2 varies from 4 and so on.

For the Brackett series, the value of n1 will be 4 and the value of n2 varies from 5 and so on.

For the Pfund series, the value of n1 will be 5 and the value of n2 varies from 6 and so on.

Series of hydrogen emission spectrum

The hydrogen spectrum series consists of different spectral series along with their wavelength, which was evaluated by the Rydberg Formula. The core reason for the formation of these spectral lines is the transition of the electrons from one energy state to another energy state. The hydrogen emission spectrum is a line spectrum, whose component is the Balmer series. Similar to the Balmer series, there were many other transitions followed by the transition of an electron from a different electron shell or electron orbit. The name of the series depends upon the transition of the different electron shells is given below,

In the Lyman series, the transition of electrons is followed from the first electron shell to another electron shell.

In the Balmer series, the transition of the electron is followed from the second electron shell to the other electron shell.

In the Paschen series, the transition of the electron is followed from the third electron shell to the other electron shell.

In the Brackett series, the transition of the electron is followed from the fourth electron shell to the other electron shell.

In the Pfund series, the transition of the electron is followed from the fifth electron shell to another electron shell.

Conclusion

The emission spectrum of the hydrogen spectrum is a line spectrum with the mathematical relationship formulated by Rydberg in 1890 for determining the wavenumber of spectral lines. This article concluded the relationship between the speed of light, the actual wavelength of hydrogen and the frequency of hydrogen. The hydrogen spectrum is briefly studied along with the transition states for each of the defined series such as the Balmer series, Lyman Series, Paschen series, Brackett series and Pfund series.