Energy Level Diagram

The energy difference between two levels is emitted as wavelength-specific radiation when an electron in a hydrogen atom transitions from a high to a low level. It’s referred to as a spectral line. As the wavelength of the spectral line is dependent on two orbits (energy levels) between which the electron transition happens, several spectral lines are created. Spectral series is made up of different wavelengths that are unique to the atoms that emit them. The energy levels present in each atom are represented by the energy level diagram of a hydrogen atom. When an electron shifts from one energy level to another, it either emits or absorbs a photon.

Atomic spectrum of hydrogen

Bohr’s model of atom provides a very logical explanation of the existence of a large number of lines in the atomic spectrum of hydrogen. According to Bohr’s theory, when an electron deexcites from a higher energy level to a lower energy level, it emits energy. The energy this emitted is quantised and corresponds to a definite frequency or wavelength. This forms the basic existence of a large number of well-defined lines in the atomic spectrum of hydrogen.

The energy state corresponding to the minimum energy is termed the ground state. A hydrogen atom contains only one electron in the shell, which is the ground state.  When a hydrogen atom is provided with energy from an external source, the electron present in the ground state gets excited and jumps to a state of higher energy. This state is termed the excited state. The excited state is very short-lived and has a lifetime of about 10 -8 seconds. Therefore, the excited electron cannot stay for a longer time in the excited state. It is forced to drop to a lower energy level.

The energy level diagram for the hydrogen atom:

He discovered that the four visible spectral lines correlated to transitions from higher to lower energy levels (n = 2), the Balmer series is what it’s named. The Lyman series refers to transitions that finish in the ground state (n = 1), but the energy released is so high that the spectral lines are all in the ultraviolet area. Because the energies are too small, the transitions are known as the Paschen series and the Brackett series, each resulting in spectral lines in the ultraviolet range.

Suppose in a hydrogen atom, an electron deexcites from a higher energy level n2 to a lower energy level n1. According to Bohr’s theory, the energy released during the deexcitation is quantised and is equal to the difference of the energies of the two levels.

The energy released by an electron in jumping from n2 energy level to n1 energy level corresponds to a frequency or wave number given by the diagram above. This energy when recorded with a spectrometer corresponds to a spectral line on the same frequency or wave number. 

Thus, it may be concluded that each transition of an electron from a higher to lower energy level gives rise to a discrete spectral line in the emission spectrum of the atom under consideration.

Spectral series of hydrogen atoms are:

The various series present in the spectrum hydrogen can be explained as given below along with their wavenumbers:

1.Lyman series: The spectral lines emitted when an electron jumps from any of the outermost orbits to the first orbit are in the ultraviolet area of the spectrum, and they are known as the Lyman series. 

Therefore, v = R(1- (1/n2) )

2. Balmer series: A spectral series known as the Balmer series is formed when an electron jumps from any of the outer orbits to the second orbit. In hydrogen, all the lines in this series have visible wavelengths

v = R( 1/22 – 1/n22 ) = R( 1/4 – 1/n22 )

3. Paschen series: All wavelengths emitted when an electron moves from the outermost orbits to the third orbit are included in this series.

v = R( 1/32 – 1/n22 ) = R( 1/9  – 1/n22 )

4. Brackett series:

The Brackett series is the result of the electron transitioning from n2 = 5, 6… to n1 = 4. These lines have wavelengths in the infrared range.

v = R( 1/42 – 1/n22 ) = R( 1/16  – 1/n22 ) 

5. Pfund series: When an electron jumps from any of the states n2 = 6, 7,… to n1 = 5, the series lines appear. This series is also in the infrared spectrum. This series is obtained when excited electrons return to the O shell. 

v = R( 1/52 – 1/n22 ) = R( 1/25  – 1/n22 )

The wavenumbers or wavelengths of various lines calculated with the help of the hydrogen spectrum diagram agree well with the experimental values. This is a big success of Bohr’s theory. 

Conclusion

The spectral lines of the hydrogen atomic spectral lines are explained by Bohr’s concept. The energy of an atom’s electron remains unaltered while it is in the ground state. The electron jumps from the ground state orbit to a more distant excited state orbit when the atom takes one or more quanta of energy. The variable n is used to identify energy levels. n = 1 is the ground state, n = 2 is the first excited state, and so on. The change in energy between the two energy levels is equal to the energy obtained by the atom. When the atom settles back to a lower energy state, energy equal to the difference in energy between the two orbits is released.