## Table of Contents

# Balmer Series

Balmer spectral series was initially noticed by Johann Balmer during the years 1885, Therefore the series is named after him that is the balmer series. Balmer series is exhibited when an electron shift takes place from higher energy states (that is ni =3,4,5,6,7,…) to lower energy states that are nf = 2 energy states.

The wavelength of the Balmer series generally falls in the visible part of the electromagnetic spectrum( having wavelength 400nm to 740nm) or is abbreviated as EM spectrum. In astronomy, the existence of Hydrogen is noticed by using the H-Alpha line of the Balmer series.

## Balmer Series Formula

In the year 1885, based on experimental observations on the hydrogen atom, Balmer advised the formula for linking the wavenumber of the spectral lines emitted to the energy shells involved in an electron shift. This formula is given as:

λ = C(m^{2}/m^{2}-n^{2})

Here, λ represents the observed wavelength

C represents a constant (364.50682 nm)

n represents the lower energy level = 2, and m represents the higher energy level, which commonly has a value greater than 3.

The above observation was further refined by Johannes Rydberg, where R represents the Rydberg constant.

1/λ = R ((1/n_{f}^{2}) – (1/n_{i}^{2}))

According to the Balmer series, nf is always equal to 2. This equation was hence combined with the Bohr model to analyze the energy that is needed to shift an electron between its initial energy level and final energy levels.

ΔE = Rhc ((1/n_{f}^{2}) – (1/n_{i}^{2}))

**Paschen Series (n _{f} = 3):** The series was initially noticed during the years 1908, by a German physicist named Friedrich Paschen. The Paschen series is exhibited when electron transition takes place from higher energy states (that is ni =4,5,6,7,8,…) to lower energy states that is nf =3 energy state. The wavelength of the Paschen series generally falls in the Infrared region of the electromagnetic spectrum.

**Brackett Series (n _{f} = 4):** The series was initially noticed during the years 1922, by a famous American physicist Friedrich Sumner Brackett. Brackett series is exhibited when electron shift takes place from higher energy states (that is ni =5,6,7,8,9…) to lower energy state that is nf =4 energy state. The wavelength of the Brackett series generally falls in the Infrared region of the electromagnetic spectrum.

**Pfund Series (n _{f} = 5):** The series was initially noticed during the years 1924, by a famous scientist named August Harman Pfund. Pfund series is exhibited when an electron shift takes place from higher energy states(that is ni = 6,7,8,9,10,…) to nf=5 energy state. The wavelength of the Pfund series usually falls in the Infrared region of the electromagnetic spectrum.

### The Bohr Model

In 1913, Niels Bohr a famous scientist and chemist proposed a model for the hydrogen atom having the atomic number 1. He stated that the electrons present in an atom revolve around the nucleus in discrete paths called orbit or an energy shell. The electron while in its stationary or its rest state cannot produce energy, but can only absorb energy when it moves from one orbit to another orbit.

The quantum number, abbreviated as n is used to designate the different energy states. The lowest energy state is termed as the ground state, in which n is always equal to one. The excited states are further equal to 2, 3, 4, and so on. When the electron present at the ground state absorbs energy which is equivalent to the difference between the ground state of the electron and the second state the electron by absorbing a photon. The electron thus turns out to be more excited and displays transitions from the ground state to the n= 2 excited states.

According to Bohr, the potential energy (P.E) of an electron present in the nth level is measured by using the following equation mentioned below:

E_{n} = -(Rhc/n^{2})

where E_{n} represents the potential energy,

R represents the Rydberg constant which is equal to 1.0974 × 10^{7} m^{-1 }

h represents Planck’s constant which is equal to 6.62607004 × 10^{-34} m2·kg/s),

c represents the speed of light (~ 3 × 10^{8} m/s).

The electrons can also spontaneously return to the ground state or any other lower excited state. When this happens, then some amount of energy is produced can be depicted in the form of the emitted photon. The energy of the photon is thus always equal to the energy difference between the higher and lower energy states. Subsequently, different types of atoms have different energy levels and the light emitted from each transition varies for every atom.

#### Hydrogen Spectrum

As it is now known that electrons in an atom or a molecule absorb energy and become excited, and then they transfer themselves from a lower energy level to a higher energy level, and radiation or energy is released when they come back to their original ground states. This great phenomenon is also the same for the emission spectrum through hydrogen atom as well , and therefore it is termed as the hydrogen emission spectrum.

##### The Hydrogen Atom

The hydrogen atom is referred to as the simplest atomic system that is found in nature, therefore it produces the simplest of these series. When the beam of light or radiation is allowed to enter the device via a slit, then each distinct component of the light or radiation can be depicted in the form of images of the source. These images are pictured when resolved under the spectroscope. The images received will be in the form of parallel lines that are organized next to each other with consistent spacing. The lines seen will be apart in the higher wavelength side and then they come closer progressively when shifted from higher to lower wavelength side. The shortest wavelength will thus hold the least spaced spectral lines.

##### Rydberg Formula

The wavelengths of the spectral series are commonly calculated by using the Rydberg formula.

Scientifically, it can be expressed as-

1/λ = R ((1/n^{2}_{f} – (1/n^{2}_{f}))

Where,

• 𝜆 represents the wavelength

• R represents the Rydberg constant has the value 1.09737✕10^{7} m^{-1 }

• Z represents the atomic number of an atom

• n_{i} represents the lower energy level

• n_{f} represents the higher energy level

**Note:** This equation mentioned above is valid only for Hydrogen and Hydrogen like elements.

##### Lyman series (nf =1)

This spectral series was projected during the years 1906-1914, by the famous scientist Theodore Lyman. According to Bohr’s model, the Lyman series is exhibited when electron shift takes place from higher energy states (that is ni = 2,3,4,5,6,…) to n_{f} =1 energy state. The wavelength of the Lyman series generally falls in the Ultraviolet band.

##### Balmer Series Citations

- Measurements of aluminum and hydrogen microplasma. Appl Opt . 2007 Jul 1;46(19):4026-31.
- Measurement of the deuterium Balmer series line emission on EAST. Rev Sci Instrum . 2016 Nov;87(11):11D616.
- Balmer series Hbeta measurements in a laser-induced hydrogen plasma. Appl Opt . 2003 Oct 20;42(30):5992-6000.

Share