Emission Spectrum

What is Emission Spectrum?

Whenever electromagnetic radiations interact with atoms and molecules of matter, the electrons in these atoms may absorb energy and jump to a higher energy state, losing their stability. In order to regain their stability, they need to move from the higher energy state to the previous lower energy state. To accomplish this job, these atoms and molecules emit radiations in various regions of the electromagnetic spectrum. This spectrum of radiation emitted by electrons in the excited atoms or molecules is known as the emission spectrum. It can be defined as:

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state.

Atomic Spectra:

  • We observe that when a ray of white light falls on a prism it experience refraction twice. Once when it travels from the rarer medium (air) to a denser medium (glass) and again from the denser medium (glass) to a rarer medium (air).
  • Finally, we observe a band of colours, called spectrum, formed out of a ray of white light. If we observe this spectrum more closely, the colour having a smaller wavelength deviates the most and vice versa.
  • Thus, a spectrum of colours ranging from red to violet is observed where red having the longest wavelength suffers the least deviation. This kind of spectrum is called continuous spectrum as violet merges into blue, blue into green and so on.
  • However, the emission spectrum of atoms in the gas phase, do not exhibit a continuous spread of wavelength from one colour to others. Rather, the emitted light consists of a specific wavelength having dark spaces existing between them. Such kind of spectra is known as atomic spectra or line spectra.

Absorption Spectrum:

An absorption spectrum, unlike the emission spectrum, is like a photographic negative of the emission spectrum. For observing the absorption spectrum, electromagnetic radiations are bombarded on a sample which absorbs radiation of certain wavelengths. The wavelength of radiations absorbed by the matter contributes to the missing wavelength which leaves dark spaces in the bright continuous spectrum. Each element has its unique line emission spectrum. The study of the emission spectrum or absorption spectrum is better known as spectroscopy.

Hydrogen Emission Spectrum:

We all know that electrons in an atom or a molecule absorb energy and get excited, they jump from a lower energy level to a higher energy level and they emit radiations when they come back to their original states. This phenomenon accounts for the emission spectrum through hydrogen too, better known as the hydrogen emission spectrum.

  • In the late 1800s, it was known that when a gas is excited using an electric discharge and the light emitted is viewed through a diffraction grating; the spectrum observed consists not of a continuous band of light, but of individual lines with well-defined wavelengths. Experiments have shown that the wavelengths of the lines were characteristic of the chemical element emitting the light. They were an atomic fingerprint which resulted from the internal structure of the atom.
  • The hydrogen spectrum is an important piece of evidence showing that the electronic structure of the atom is quantized. When an electric discharge is passed through a gaseous hydrogen molecule, the hydrogen atoms in the molecule dissociate. This leads to the emission of electromagnetic radiation by the energetically excited hydrogen atoms. The hydrogen emission spectrum consists of radiations of discrete frequencies. These series of radiations are named after the scientists who discovered them.

When a photon is absorbed by a hydrogen atom, the energy of the photon causes the electron to undergo a transition to a higher energy level (n = 1  n = 2, for example). When a hydrogen atom emits a photon, the electron undergoes a transition from a higher energy level to a lower one (n = 3  n = 2, for example). During this transition from a higher level to a lower level, there is a transmission of light occurs. Since the energy levels of the atom are quantized, the spectrum will consist of wavelengths that reflect the differences in these energy levels. For example, the line at 656 nm corresponds to the transition n = 3  n = 2.

Hydrogen Transitions

Hydrogen Emission Spectrum Series:

In the year 1885, on the basis of experimental observations, Balmer proposed the formula for correlating the wavenumber of the spectral lines emitted and the energy shells involved.

This formula is given as:

\(\bar{\nu }=109677(\frac{1}{2^{2}}-\frac{1}{n^{2}})\)

This series of the hydrogen emission spectrum is known as the Balmer series. This is the only series of the line in the electromagnetic spectrum that lies in the visible region. The term RH is called the Rydberg constant for hydrogen.

Rydberg constant is given by:

\(R_{H}= \frac{me^{4}}{8\epsilon _{0}h^{3}c}\)

Where,

  • h is the Planck’s constant
  • c is the speed of light

Using the known value of these constants we can compute the value of Rydberg constant, RH = 109677.

The Balmer series is basically the part of the hydrogen emission spectrum which is responsible for the excitation of an electron from the second shell to any other shell. Similarly, other transitions have their own series names. Some of them are listed below,

  • Transition from the first shell to any other shell – Lyman series
  • Transition from the second shell to any other shell – Balmer series
  • Transition from the third shell to any other shell – Paschen series
  • Transition from the fourth shell to any other shell – Bracket series
  • Transition from the fifth shell to any other shell – Pfund series

Johannes Rydberg, a Swedish spectroscopist, derived a general formula for the calculation of wavenumber of hydrogen spectral line emissions due to the transition of the electron from one orbit to another.

The general formula for the hydrogen emission spectrum is given by:

\(\bar{\nu }=109677(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}})\)

Where,

  • n1 = 1,2,3,4 …
  • n2 = n1 +1
  • \(\bar{\nu }\) = wavenumber of the electromagnetic radiation. The value 109,677 cm-1 is known as Rydberg constant for hydrogen.

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