What is line emission in relationship to frequency and wavelength

BBC - GCSE Bitesize Science - The sun and other stars : Revision

what is line emission in relationship to frequency and wavelength

An introduction to the atomic hydrogen emission spectrum, and how it can be used to find the ionisation energy of hydrogen. (Ignore the "smearing" - particularly to the left of the red line. The relationship between frequency and wavelength. The luminosity (brightness) and peak frequency of this radiation increases as the These emission line spectra are like a chemical fingerprint for that element. The emission spectrum of a chemical element or chemical compound is the spectrum of The wavelength (or equivalently, frequency) of the photon is determined by the Although the emission lines are caused by a transition between quantized Conversion electron Mössbauer spectroscopy · Correlation spectroscopy.

Emission spectrum

The energy of the light emitted or absorbed is exactly equal to the difference between the energies of the orbits. Some of the key elements of this hypothesis are illustrated in the figure below. Three points deserve particular attention.

First, Bohr recognized that his first assumption violates the principles of classical mechanics.

what is line emission in relationship to frequency and wavelength

But he knew that it was impossible to explain the spectrum of the hydrogen atom within the limits of classical physics. He was therefore willing to assume that one or more of the principles from classical physics might not be valid on the atomic scale.

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Second, he assumed there are only a limited number of orbits in which the electron can reside. He based this assumption on the fact that there are only a limited number of lines in the spectrum of the hydrogen atom and his belief that these lines were the result of light being emitted or absorbed as an electron moved from one orbit to another in the atom.

Finally, Bohr restricted the number of orbits on the hydrogen atom by limiting the allowed values of the angular momentum of the electron. Any object moving along a straight line has a momentum equal to the product of its mass m times the velocity v with which it moves.

An object moving in a circular orbit has an angular momentum equal to its mass m times the velocity v times the radius of the orbit r. Bohr assumed that the angular momentum of the electron can take on only certain values, equal to an integer times Planck's constant divided by 2p.

Bohr then used classical physics to show that the energy of an electron in any one of these orbits is inversely proportional to the square of the integer n. The difference between the energies of any two orbits is therefore given by the following equation.

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In this equation, n1 and n2 are both integers and RH is the proportionality constant known as the Rydberg constant. Planck's equation states that the energy of a photon is proportional to its frequency. The inverse of the wavelength of electromagnetic radiation is therefore directly proportional to the energy of this radiation. By properly defining the units of the constant, RH, Bohr was able to show that the wavelengths of the light given off or absorbed by a hydrogen atom should be given by the following equation.

Thus, once he introduced his basic assumptions, Bohr was able to derive an equation that matched the relationship obtained from the analysis of the spectrum of the hydrogen atom.

what is line emission in relationship to frequency and wavelength

Substituting the appropriate values of RH, n1, and n2 into the equation shown above gives the following result. Solving for the wavelength of this light gives a value of Wave-Particle Duality The theory of wave-particle duality developed by Louis-Victor de Broglie eventually explained why the Bohr model was successful with atoms or ions that contained one electron.

It also provided a basis for understanding why this model failed for more complex systems. Light acts as both a particle and a wave.

what is line emission in relationship to frequency and wavelength

In many ways light acts as a wave, with a characteristic frequency, wavelength, and amplitude. Light carries energy as if it contains discrete photons or packets of energy. When an object behaves as a particle in motion, it has an energy proportional to its mass m and the speed with which it moves through space s. By simultaneously assuming that an object can be both a particle and a wave, de Broglie set up the following equation.

Emission Spectrum of Hydrogen

By rearranging this equation, he derived a relationship between one of the wave-like properties of matter and one of its properties as a particle. As noted in the previous section, the product of the mass of an object times the speed with which it moves is the momentum p of the particle. Each element has a different atomic spectrum. The production of line spectra by the atoms of an element indicate that an atom can radiate only a certain amount of energy.

This leads to the conclusion that bound electrons cannot have just any amount of energy but only a certain amount of energy. The emission spectrum can be used to determine the composition of a material, since it is different for each element of the periodic table. One example is astronomical spectroscopy: The emission spectrum characteristics of some elements are plainly visible to the naked eye when these elements are heated. For example, when platinum wire is dipped into a strontium nitrate solution and then inserted into a flame, the strontium atoms emit a red color.

Similarly, when copper is inserted into a flame, the flame becomes green. These definite characteristics allow elements to be identified by their atomic emission spectrum. Not all emitted lights are perceptible to the naked eye, as the spectrum also includes ultraviolet rays and infrared lighting.

An emission is formed when an excited gas is viewed directly through a spectroscope. Schematic diagram of spontaneous emission Emission spectroscopy is a spectroscopic technique which examines the wavelengths of photons emitted by atoms or molecules during their transition from an excited state to a lower energy state.

what is line emission in relationship to frequency and wavelength

Each element emits a characteristic set of discrete wavelengths according to its electronic structureand by observing these wavelengths the elemental composition of the sample can be determined. Emission spectroscopy developed in the late 19th century and efforts in theoretical explanation of atomic emission spectra eventually led to quantum mechanics. There are many ways in which atoms can be brought to an excited state.

what is line emission in relationship to frequency and wavelength

Interaction with electromagnetic radiation is used in fluorescence spectroscopyprotons or other heavier particles in Particle-Induced X-ray Emission and electrons or X-ray photons in Energy-dispersive X-ray spectroscopy or X-ray fluorescence.

The simplest method is to heat the sample to a high temperature, after which the excitations are produced by collisions between the sample atoms.

This spectral line broadening has many different causes.