Principles of Spectroscopy

Star light, star bright.

Overview

• Learn about continuous spectrum, line emission, and line absorption by viewing examples of each.
• See how this applies to light from the Sun (or any star).

Introduction

A photon is a small bit of electromagnetic energy sent across space. Photons can be emitted or absorbed by electric charges -- usually an electron.

A hot, dense object contains many "loose" electrons which can emit photons of any energy. However an electron cannot emit a photon with more energy than the electron started with. The light produced by a hot, dense object is called thermal emission and it contains photons of all energies, i.e. light of all colors, or wavelengths. The resulting "rainbow" is called a continuous spectrum. As we heat up an object, we are giving the electrons more kinetic energy, so they become able to emit more energy. The hotter the object becomes,the brighter the continuous spectrum becomes. This is describedby the Stephan-Boltzmann Law:

f = σT⁴

As the emitting object is heated, the flux, f, of light energy emitted per unit area (the brightness) increases as the temperature, T (measured in Kelvin, K), to the fourth power; σ is called the Stefan-Boltzmann constant, and has the value 5.67x10^-8J m^-2 K^-4. If two hot pokers are the same size, but one is twice as hot as the other, the hotter one will be sixteen times brighter. The same is true of two stars.

As the object heats up and the electrons get more energy, the energy of the typical photon emitted also increases. This means that the continuous spectrum gradually shifts toward shorter wavelengths (higher energies) and therefore looks bluer. This is described by Wien's Law, which says the peak wavelength times the temperature is constant:

λ_peak * T = 0.29 cmK

which means that as the temperature, T, of the emitting object increases, the wavelength λ_peak where the intensity of the light is the greatest must decrease. A very hot poker will glow with a bluer (shorter wavelength) light while a cooler poker will glow with a redder light.

Any hot, dense, opaque object can and must produce continuous spectrum across all wavelengths, with the total energy and dominant color described by these two laws. This is sometimes called blackbody radiation or thermal radiation. The object has no choice -- if it's hot, the electrons have energy, so they must emit light. Remember, Wien's law and the Stefan-Boltzmann Law apply only to continuous thermal emission.

So far we've talked about processes involving "loose" electrons that lead to thermal radiation. What about electrons that are part of an atom? In the Bohr model of the atom, electrons orbit a nucleus of protons and neutrons. Each orbit has a different potential energy, just like planetary orbits correspond to particular gravitational potential energies. But according to quantum mechanics, the electrons can only orbit in certain places, which means the electrons can only have certain orbital energies -- these allowed energies are called energy levels.

Electrons usually stay in low energy levels, but they can "jump up" to higher energy levels by absorbing a photon or by gaining energy in other ways. If it gains energy by absorbing a photon, it has to have exactly the correct amount of energy -- it has to match the energy difference between the energy levels. Therefore, the atom can only absorb light at a few specific energies, or colors. This is called line absorption. Line absorption occurs when a low-density gas is in front of a hotter, continuous spectrum source. The cooler, low-density gas acts to block the photons which have the right wavelengths, while the other photons travel through the gas unperturbed. This leads to a generally bright spectrum, with dark lines at specific wavelengths. The missing colors are called spectral absorption lines and result in an absorption line spectrum.

The energy-level jumping can also happen in reverse. The electron can "fall down" from a higher energy level to a lower one, emitting a photon with energy equal to the difference between the levels. This is called line emission, because photons are emitted. The spectrum produced is a set of bright emission lines, so it is called an emission line spectrum. This can only occur in a low density gas viewed on its own or in front of a cooler background (if a hot, dense object is in the background, we see line absorption instead of line emission).

Notice that these two processes only involve photons with particular energies that match its energy levels. Since each atom or molecule has a different set of energy levels, each atom or molecule also has a unique set of spectral lines.

Let's summarize what are known as "Kirchoff's Laws." First, a hot, dense gas (or a solid or liquid) has free electrons and will emit a continuous spectrum, with the brightness and typical color described by the Stefan-Boltzmann and Wien Laws. Second, a low-density gas along the line of sight to a hotter continuous radiation source will absorb photons of specific energies, leaving an absorption line spectrum. Third, a low-density gas viewed alone or in front of a cool background will produce an emission line spectrum.

As photons travel outwards from the center of the sun, where the density and temperature are high enough to allow fusion, they are constantly absorbed and re-emitted by the atoms in the sun.  Eventually they get to the outer edge of the sun, called the photosphere, which is where the sun changes from being opaque to being transparent. The photospere, then, is the layer where all the photons we see originate. The transparent region above the photosphere is called the atmosphere of the sun and has two major layers. The cooler thin layer abover the photospher is the chromospher. Above that is the increadably hot and thin Corona.

One photon by itself can't tell us much about the photosphere or atmosphere, but by looking at all the photons together, astronomers can gain information about the temperature, density, and chemical composition of the sun. This is done by looking at the spectrum of the light -- the number of photons (i.e. the brightness) at each wavelength.  Similarly, the characteristics of the spectra we will look at in the lab will tell us information about the sources of light we will use.

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. Each element emits a characteristic set of discrete wavelengths according to its electronic structure, 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. Interaction with electromagnetic radiation is used in fluorescence spectroscopy, protons 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 method is used in flame emission spectroscopy, and it was also the method used by Anders Jonas Ångström when he discovered the phenomenon of discrete emission lines in 1850s. Although the emission lines are caused by a transition between quantized energy states and may at first look very sharp, they do have a finite width, i.e. they are composed of more than one wavelength of light. This spectral line broadening has many different causes. Emission spectroscopy is often referred to as optical emission spectroscopy, due to the light nature of what is being emitted.



Experimental technique in flame emission spectroscopy

The solution containing the relevant substance to be analysed is drawn into the burner and dispersed into the flame as a fine spray. The solvent evaporates first, leaving finely divided solid particles which move to hottest region of the flame where gaseous atoms and ions are produced. Here electrons are excited as described above. It is common for a monochromator to be used to allow for easy detection. On a simple level, flame emission spectroscopy can be observed using just a Bunsen burner and samples of metals. For example, sodium metal placed in the flame will glow yellow, whilst calcium metal particles will glow red, copper placed into the flame will create a green flame.

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy from the radiating field. The strength of the absorption varies as a function of frequency, and this variation is the absorption spectrum. Absorption spectroscopy is performed across the electromagnetic spectrum. Absorption spectroscopy is employed as a analytical chemistry tool to determine the presence or absence of a particular substance and, in many cases, to quantify the amount of the substance present. Infrared and ultraviolet-visible spectroscopy are particularly common in analytical applications. Absorption spectroscopy is also employed in studies of molecular and atomic physics, astronomical spectroscopy and remote sensing. There are a wide range of experimental approaches to measuring absorption spectra. The most common arrangement is to direct a generated beam of radiation at a sample and detect the intensity of the radiation that passes through it. The transmitted energy can be used to calculate the absorption. The source, sample arrangement and detection technique vary significantly depending on the frequency range and the purpose of the experiment.

Basic Theory

More technically, absorption spectroscopy is based on the absorption of photons by one or more substances present in a sample, which can be a solid, liquid, or gas, and subsequent promotion of electron(s) from one energy level to another in that substance. Note that the sample can be a pure, homogeneous substance or a complex mixture. The frequency at which the incident photon is absorbed is determined by the difference in the available energy levels of the different substances present in the sample; it is the selectivity of absorbance spectroscopy - the ability to generate photon (light) sources that are absorbed by only some of the components in a sample - that gives absorbance spectroscopy much of its utility. Typically, X-rays are used to reveal chemical composition, and near ultraviolet to near infrared wavelengths are used to distinguish the configurations of various isomers in detail. In absorption spectroscopy the absorbed photons are not re-emitted (as in fluorescence) rather, the energy that is transferred to the chemical compound upon absorbance of a photon is lost by non-radiative means, such as transfer of energy as heat to other molecules. While the relative intensity of the absorption lines do not vary with concentration, at any given frequency the measured absorbance (\(-\) log(I / I0)) has been shown to be proportional to the molar concentration of the absorbing species and the thickness of the sample the light passes through. This is known as the Beer-Lambert law. The plot of amount of radiation absorbed versus frequency for a particular compound is referred to as the absorption spectrum. The normalized absorption spectrum is characteristic for a particular compound, does not change with varying concentration and is like the chemical "fingerprint" of the compound. At frequencies corresponding to the resonant energy levels of the sample, some of the incident photons are absorbed, resulting in a drop in the measured transmission intensity and a corresponding dip in the spectrum. The absorption spectrum can be measured using a spectrometer and by knowing the shape of the spectrum ,the optical path length and the amount of radiation absorbed, one can determine the structure and concentration of the compound.

Relation To Emission Spectroscopy

Emission is a process by which a substance releases energy in the form of electromagnetic radiation. Emission can occur at any frequency at which absorption can occur, and this allows the absorption lines to be determined from an emission spectrum. The emission spectrum will typically have a quite different intensity pattern from the absorption spectrum, though, so the two are not equivalent. The absorption spectrum can be calculated from the emission spectrum using appropriate theoretical models and additional information about the quantum mechanical states of the substance.

Relation To Scattering and Reflection Spectroscopy

The scattering and reflection spectra of a material are influenced by both its index of refraction and its absorption spectrum. In an optical context, the absorption spectrum is typically quantified by the extinction coefficient, and the extinction and index coefficients are quantitatively related through the Kramers-Kronig relation. Therefore, the absorption spectrum can be derived from a scattering or reflection spectrum. This typically requires simplifying assumptions or models, and so the derived absorption spectrum is an approximation.

Analytical Chemistry

Absorption spectroscopy is useful in chemical analysis because of its specificity and its quantitative nature. The specificity of absorption spectra allows compounds to be distinguished from one another in a mixture. For example, absorption spectroscopy is used to identify the presence of pollutants in the air, distinguishing the pollutant from the nitrogen, oxygen, water and the other expected constituents. The specificity also allows unknown samples to be identified by comparing a measured spectrum with a library of reference spectra. In many cases, it is possible to determine qualitative information about a sample even if it is not in a library. Infrared spectra, for instance, have characteristics absorption bands that indicate if carbon-hydrogen or carbon-oxygen bonds are present. An absorption spectrum can be quantitatively related to the amount of material present using the Beer-Lambert law. Determining the absolute concentration of a compound requires knowledge of the compound's absorption coefficient. The absorption coefficient for some compounds is available from reference sources, and it can also be determined by measuring the spectrum of a calibration standard with a known concentration of the target.

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