Emission Spectrum of Hydrogen Atom

Emission Spectrum of Hydrogen Atom

emission spectrum of hydrogen atom

The emission spectrum of Hydrogen atom has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron-making transitions between two energy levels in an atom.

Explanation

The emission spectrum of the hydrogen atom can be obtained by passing an electric discharge through the gas taken in the discharge tube under low pressure. The emitted light is analyzed with the help of a spectroscope. The spectrum consists of a large number of lines appearing in different regions of wavelengths.

Some of the lines are present in the visible region, while others are in ultraviolet and infra-red regions. In 1885, J.J. Balmer developed a simple relationship among the different wavelengths of the series of visible lines in the hydrogen spectrum. The relationship is :

1/λ = ν (cm-1) = 109677 [1/22 – 1/n2]

n is an integer equal to or greater than 3(i.e., n = 3, 4, 5 …). It is known as the Balmer formula. The Balmer formula gives only the spectral lines in the visible region.

This series of lines that appear in the visible region was named the Balmer series. Soon afterward, a series of spectral lines of the hydrogen atom in different regions were discovered.

These lines in different regions were grouped into five different series of lines, each being named after the name of its discoverer. These are Lyman series, Balmer series, Paschen series, Brackett series and Pfund series.

Lyman series appears in the ultra-violet region. Balmer series appears in the visible region while the other three series lie in the infra-red region. These are known as spectral series.

Spectral Series

spectral series

Definition of Spectral Series

Spectral series are the set of wavelengths arranged in a sequential fashion, characterizing light or any electromagnetic radiation emitted by energized atoms.

Formation of Spectral Series

Formation of Spectral Series

Every atom infolds a set of energy levels/states, which is modeled and well explained through Bohr’s atomic model. He names energy states using quantum numbers (n=1,2,3,4,5,6…..).

When the electron jumps from higher energy states (nh) to lower energy states (nl), a photon of energy nh-nl is emitted. As the energy corresponding to each state is fixed, the difference between the energy states is also fixed.

Thus, the transition between similar energy states will produce the photon of the same energy. The spectral series is broken into the corresponding series based on the electron transition to a lower energy state.

The Greek alphabets are used within the series to segregate the spectral lines of corresponding energy. The spectral series of Hydrogen are:

1. Lyman Series (nl =1)

Lyman Series

The series was discovered during the years 1906-1914 by Theodore Lyman. Thus it is named after him. According to Bohr’s model Lyman series is displayed when electron transition takes place from higher energy states (nh =2,3,4,5,6,….) to nl =1 energy state. All the wavelengths of the Lyman series fall in the Ultraviolet band.

2. Balmer Series (nl =2)

Balmer Series

The series was discovered during the year 1885 by John Balmer. Thus the series is named after him. Blamer series is displayed when electron transition takes place from higher energy states (nh =3,4,5,6,7,…) to nl =2 energy states. All the wavelength of the Balmer series falls in the visible part of the electromagnetic spectrum (400nm to 740nm). In astronomy, the presence of Hydrogen is detected using the H-Alpha line of the Balmer series. It is also a part of the solar spectrum.

3. Paschen Series (nl =3)

Paschen Series

The series was first obtained during the year 1908 by German physicist Friedrich Paschen. Thus the series is named after him. Paschen series is displayed when electron transition takes place from higher energy states (nh =4,5,6,7,..) to nl =3 energy state. All wavelength of Paschen series falls in the infrared region of the electromagnetic spectrum. The shortest wavelength of the next series, i.e., the Brackett series, overlaps with the Paschen series. From this series, all subsequent series overlap.

4. Brackett Series (nl =4)

Brackett Series

The series was first observed during the year 1922 by an American physicist Friedrich Summer Brackett. Thus the series is named after him. Brackett series is displayed when electron transition takes place from higher energy states (nh =5,6,7,8,9,…) to nl =4 energy states. All the wavelength of the Brackett series falls in the infrared region of the electromagnetic spectrum.

5. Pfund Series (nl =5)

Pfund Series

The series was first observed during the year 1924 by August Harman Pfund. Thus, the series is named after him. Pfund series is displayed when electron transition takes place from higher energy states (nh =6,7,8,9,10,…) to nl =5 energy states. All the wavelength of the Pfund series falls in the infrared region of the electromagnetic spectrum.

The hydrogen spectrum is complex, comprising more than the three lines visible naked eye. It is possible to detect patterns of lines in both the ultraviolet and infrared regions of the spectrum as well.

Rydberg Equation

Rydberg Equation

Atomic hydrogen displays an emission spectrum. This spectrum enfolds several spectral series. Once the electrons in the gas are excited, they make transitions between the energy levels. These spectral lines are the consequences of such electron transitions between energy levels modeled by Neils Bohr. The wavelengths of the spectral series are calculated by the Rydberg formula:

λ = ν (in cm-1) = R {1/n12 – 1/n22}

where n1 and n2 are integers, such that n2 > n1. R is a constant, now called the Rydberg constant. The value of R is 109677 cm-1. T

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