Absorption of light

Type of physical science: Light, Absorption of, Absorption, Electromagnetism, Atomic physics

Field of study: Nonrelativistic quantum mechanics

Atoms and molecules absorb light at specific wavelengths that are characteristic of the atom or molecule. This absorption of light can be used to identify the types of gas in a variety of circumstances, from a sample in the lab to a gaseous cloud in space.

Overview

When atoms and molecules are irradiated with white light, which contains a continuous spectrum of all the colors, the transmitted light shows dark lines. These lines correspond to the absorption of only certain specific wavelengths. These absorption spectra can be used to gain information about the energy levels of the atoms and molecules. They can also be used to gain information about the number of atoms or molecules present and to identify them.

Atoms are composed of a positively charged nucleus made of protons and neutrons, with negatively charged electrons orbiting it. The number of electrons is normally equal to the number of protons. Thus, the total negative charge of the electrons is equal to that of the positively charged nucleus, so that, under normal circumstances, atoms have neutral charges.

The electrons are held to the nucleus by the electrostatic force of attraction between oppositely charged particles. This attractive force serves as the centripetal force that keeps the moving electrons orbiting in circles. The electrons' velocities keep them from falling into the nucleus. The structure is reminiscent of that of the planets orbiting the Sun. However, there is an important difference between the orbits of atoms and those of the planets. The electrons in an atom are constrained to orbit at only certain radii, called "orbitals." This fact--that the radii of the electrons can take on only certain values--is referred to as "quantization." The electrons can be found only in these quantized orbitals, not in between.

Each orbital has a specific energy, called the "binding energy," related to it that consists of the kinetic energy of the electron's motion and the potential energy of its position relative to the nucleus. Thus, the binding energies of the electrons in an atom are also quantized. There are only certain allowed energy levels at which the electrons can reside. This is usually represented by an energy-level diagram, such as is shown in Figure 1.

In principle, there are an infinite number of orbitals in any atom. Figure 1 shows only the three lowest energy levels. The binding energy of each orbital is negative, since the electrons are bound or attached to the nucleus. In other words, the electrons are in a "hole," and a positive amount of energy must be added to the atom in order to remove an electron from the atom. When an electron is removed, the atom is left with a net positive charge. Such a charged atom is called an "ion."

The lowest energy level, E¹ is called the "ground state"; all the other energy levels are called "excited states." The binding energies are characteristic of the specific type of atom being considered. Each atom's binding energies are unique to that atom.

Niels Bohr proposed a means of calculating the energy levels of hydrogenlike atoms. These atoms and ions have only one electron. Calculation of the energy levels for multielectron atoms is quite complex, requiring the use of quantum-mechanic theory and supercomputers to do the computations for all but the simplest hydrogenlike atoms and ions.

The electrons usually occupy the ground state of the atom. If energy is added to the atom, however, the electrons can be kicked up to a higher energy level. This process is referred to as "excitation." If enough energy is added to the electron, it may be totally removed from the atom. This process is called "ionization." In order to excite an electron from the ground state to an excited state, exactly the right amount of energy must be added to the atom. The amount of energy required is equal to the difference between the binding energies of the two states; no more and no less, since the electrons cannot exist except at these specific levels. Thus, in order for an electron to be excited from the ground state, E¹, to an excited state, such as E³, an amount of energy exactly equal to E³ minus E¹ must be added to the atom.

The atom remains in an excited state only temporarily. The excited electrons eventually drop back down to the ground state. The excess energy is given off, usually as light. The energy given off is equal to the differences in the binding energies of the excited state and the ground state. Since these energy differences are quantized, only certain wavelengths or colors of light will be emitted. The particular pattern of the light emitted by an atom is called an "emission spectrum." Each atom has a unique emission spectrum that serves as a "fingerprint" of the atom. The intensity, or brightness, of the individual lines in the spectrum is dependent upon the number of atoms present. However, each atom of a certain element will emit the same wavelengths of light. This uniqueness of the spectrum for each type of atom can be used to identify the atoms in a sample of unknown gas.

Visible light is one type of electromagnetic radiation. Radio waves, microwaves, infrared waves, visible light, ultraviolet rays, X rays, and gamma rays are all forms of electromagnetic radiation. They differ from one another in the range of frequencies (or wavelengths) that they cover. Radio waves are the lowest frequencies, while gamma rays are the highest. Taken together, they form the electromagnetic spectrum. All types of electromagnetic radiation are composed of massless particles called "photons." Photons are packets of energy. Each photon has an energy equal to Planck's constant times the frequency of the light. Thus, the color of the light is related to its energy, with violet light having more energy than red light. All photons travel at the speed of light, regardless of their energy. The wavelength of the light is inversely proportional to its frequency. Since photons are pure energy and have no mass, if a photon is stopped, it ceases to exist.

The energy required to excite an atom can come from a variety of sources. The atom might collide with another atom in random motion if the sample is a gas. A solid or liquid sample may be placed in a flame or heated. The atoms might be struck by electrons from an electrical discharge, which will transfer energy to the atom in the collision, or the atom may absorb a photon of light.

The collision of a photon with an atom is an all-or-nothing situation. When a photon strikes an atom, it will give up its energy to the atom only if it has exactly the same energy as the difference in binding energies between the ground state and one of the excited states of the atom. In the process, the photon ceases to exist, and an electron in the atom is excited to a higher energy level. This is the process of absorption.

Like emission, absorption occurs only at discrete or specific energies or wavelengths. If white light with a continuous spectrum of all the colors is incident on a gas, certain wavelengths will be removed from the light, resulting in dark lines in the spectrum. The energies of these absorption lines are characteristic of the atoms and will occur at the same places as the lines in an emission spectrum from the same type of atom. Actually, absorption spectra are usually slightly simpler than emission spectra. They have fewer lines, because most atoms and molecules are in the ground state or a low-lying energy level at room temperature. Thus, the absorption spectrum includes only transitions from the ground and lower excited states to higher states. Emission spectra can include transitions of the electrons from one upper excited state to another slightly lower state. The electrons do not always drop to the ground state in a single transition.

A molecule is composed of two or more atoms that are bound together. Molecules also have quantized orbitals and binding energies that are composed of the overlap of the atomic orbitals. Superposed on the binding energies of the atoms are vibrational and rotational-energy levels reflecting the relative motion of the atomic nuclei. Like atoms, molecules have emission and absorption spectra; however, the spectra for molecules are much more complicated than those for atoms, with many more lines.

Applications

A spectrometer is a device used to measure the spectrum of a beam of light. It consists of a series of apertures that create a beam of light. The light then passes through a prism or diffraction grating. The prism (or grating) will separate the light into its various colors, a process known as "dispersion." The light is then passed through a focusing system to a detector. Modern spectrometers record the spectrum electronically on a computer.

The primary application of absorption spectra is to identify what types and what quantities of atoms and molecules are present in a sample. A light source, which could consist of any number of different types of lights, including lasers, is first looked at through a spectrometer to determine the spectrum of the source alone. The light is then passed through a sample of gas. The light that is transmitted through the gas sample is then analyzed by the spectrometer. Certain wavelengths will be missing. Subtracting the two spectra, with and without gas, will result in a spectrum of only the wavelengths that were absorbed. Peaks will occur at various wavelengths. The positions of the peaks will identify what atoms and molecules are present in the gas. The positions of the peaks will correspond to the differences between energy levels that will be characteristic of a given atom or molecule. The height of the peaks will be proportional to how many photons were absorbed from the original source. Thus, the height of the peak will indicate the relative concentration of the element in the sample.

In addition to indicating the type and number of atoms and molecules present, absorption spectra can also indicate the relative speed of the atoms and molecules. Since light is a wave, it is subject to the Doppler effect, which is the phenomenon of a shift in the detected frequency (wavelength) of a wave caused by motion of its source. If the source is moving toward the observer, the observed frequency will be shifted upward. For light, this corresponds to a shift toward the blue end of the spectrum, or a "blue shift." If the source is moving away from the observer, the observed frequency will be lower. This corresponds to a shift toward the red end of the spectrum, or a "red shift." The amount of shift of the observed lines indicates the speed of the source. In an absorption spectrum in which a stationary source is passing through a moving gas, the lines will be red-shifted and blue-shifted by the moving atoms. This will cause a broadening of the spectral lines that is dependent upon the speed of the gas.

This technique has found important applications in astronomy. Interstellar gases are often too cool to emit detectable radiation. By observing the light from distant stars as it passes through the gas cloud, however, an absorption spectrum for the gas can be obtained. Analyzing this spectrum will indicate not only the composition and density of the gas cloud but also its temperature and speed relative to Earth.

Another important application of absorption spectra is found in environmental and analytical chemistry. When analyzing a sample of gas with an unknown composition, such as an air sample with some pollutants present, the gas is placed in an evacuated chamber, or cell. A beam of light from a known source is passed through the cell. Analyzing the absorption spectrum produced by the gas will indicate what pollutants are present and in what quantities. Sometimes the absorption spectrum will have so many peaks that some of them will overlap. Sophisticated computer programs using Fourier transforms are used to help resolve the various peaks. Since the absorption spectra for most molecules lie in the infrared region, such instruments are called "Fourier Transform Infrared Spectrometers," or FTIR.

Context

The first line spectra observed were absorption spectra of atoms. In 1817 J. Fraunhofer observed the absorption spectrum of sunlight, identifying and labeling more than six hundred lines.

The study of emission spectra for atoms in a gas excited by an electrical discharge or by atoms in a flame was vigorously pursued in the late 1800's. The wavelengths of the lines was determined with considerable precision in the process of trying to find some regularity to the spectral pattern. In 1885, Johann Balmer was able to determine a relationship between the lines in the spectrum of hydrogen. J. R. Rydberg and W. Ritz came up with an expression that was applicable to the spectra of other elements. However, both the Balmer and Rydberg-Ritz formulae were empirical expressions, derived not from basic physical principles but rather from looking at the data and manipulating the numbers until a pattern was determined.

Many attempts were made to construct a model of the atom that would yield these formulae. One of the first models was developed by J. J. Thomson, who discovered the electron. The Thomson model of the atom consisted of electrons suspended in some sort of positive gruel that contained most of the mass of the atom. Thomson's model, though, was not able to produce vibrational frequencies that matched the frequencies in the emission spectra.

In order to test Thomson's model, Ernest Rutherford and his students H. W. Geiger and E. Marsden performed an experiment in which a beam of alpha particles was shot at a thin gold foil. An alpha particle is a helium nucleus, consisting of two protons and two neutrons. Since alpha particles are positively charged and very heavy, they should have ignored the electrons and been affected only by the positive gruel of the atom. This would result in very little deflection of the beam. Much to Rutherford's surprise, it was found that a substantial number of the alpha particles turned around and came back. The only way to explain this "backscattering" was that the atom had a massive nuclear core.

Rutherford's model of the atom consisted of a positive nuclear core with electrons orbiting it. Rutherford's planetary model of the atom met with considerable opposition. Electromagnetic theory shows that accelerated charges radiate. Thus, the electrons circling the nucleus should be continually radiating energy. Eventually, they would lose enough energy and spiral in to the nucleus. It was thought that this model would be inherently unstable.

Another of Rutherford's assistants, Danish physicist Niels Bohr, was able to propose a model in 1913 that was finally consistent with the emission spectra observed from various atoms. Bohr had been studying the emission spectra of various gases in gas discharge tubes. In a gas discharge tube, a current is passed through a sample of gas. The gas then emits radiation. When viewed with a spectrometer, this radiation exhibits a line spectrum that is characteristic of the gas being studied.

Bohr avoided the problem of the electrons' radiating by postulating that there exist certain orbits where the electrons can undergo circular motion without radiating; he referred to these orbits as "stationary states." The electrons can move from one stationary state (orbital) to another by absorbing or emitting energy, in the form of a photon. According to the principle of conservation of energy, the energy of the photons would be the difference in energies of the two states. Thus, the spectra Bohr had been studying could give him information about the energies of the stationary states of the atom.

Bohr's postulate of stationary states for the atom implies that the angular momentum of the electrons as they orbit the nucleus must be quantized. Bohr applied a quantization condition to the angular momentum and then used this to calculate the radii of the stationary states and their associated binding energies. The results for hydrogen matched the observed spectra.

Unfortunately, Bohr's theory cannot be applied as is to atoms with more than one electron. The determination of energy levels for multielectron atoms or molecules requires considerably more complicated calculations. Experiments by J. Moseley in 1913 and J. Franck and G. Hertz in 1914, however, strongly supported the general Bohr-Rutherford model of the atom. Moseley analyzed the X-ray spectra of atoms, while Franck and Hertz looked at the transmission of electrons through gases. In both experiments, a regular periodic relationship was observed in the data, indicating a quantization of the energy levels.

Further support of Bohr's "planetary" model of the atom came from Louis de Broglie in 1924. De Broglie suggested that, since light can exhibit both particle and wave properties, then perhaps matter, specifically electrons, can also exhibit both properties. The de Broglie wavelength of the electrons would be Planck's constant divided by the momentum of the electron. Applying this idea of electrons as waves implies that the electrons in their atomic orbitals are confined to a limited region of space: the circumference of the orbital. When a wave is constrained to a region of space of just the right length, it forms standing waves. Thus, only certain circumferences, and certain radii, would allow the electrons to form standing waves. Setting the relationship between the wavelength of the electrons and the radii of the orbitals that would form standing waves at these wavelengths yields Bohr's postulate of the quantization of the angular momentum of the electrons in the stationary states.

Principal terms

ABSORPTION SPECTRUM: A series of dark lines at specific wavelengths in an otherwise continuous white-light spectrum; the wavelengths of the lines are characteristic of the atom or molecule being studied

ATOMIC ORBITALS: The allowed radii from the nucleus at which electrons can orbit

BINDING ENERGY: The energy of the electrons in a given atomic orbital; this is also the energy that must be added to the atom to remove an electron

ELECTRON: A negatively charged fundamental particle

EMISSION SPECTRUM: The pattern of light composed of certain specific wavelengths emitted by an element or compound

EXCITATION: The process of adding energy to an atom to move electrons from the ground state to an excited state

EXCITED STATE: Any of the orbitals of an atom with binding energies above the ground state

GROUND STATE: The orbital of an atom with the lowest possible binding energy

ION: A charged atom

PHOTON: A packet of energy making up electromagnetic radiation

QUANTIZATION: The property that atomic orbitals and their associated binding energies can take on only certain discrete values

SPECTROMETER: An instrument used to measure light spectra

Bibliography

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Griffith, W. Thomas. The Physics of Everyday Phenomena: A Conceptual Introduction to Physics. Dubuque, Iowa: William C. Brown, 1992. A standard college physics text for nonscience students. Presents the basic concepts of physics in a straightforward, understandable way. The text is full of ample illustrations of the concepts, all of which come from everyday experiences.

Hewitt, Paul G. Conceptual Physics. New York: HarperCollins, 1993. As the title indicates, this is a basic introduction to physics presented nonmathematically. Very readable, with numerous illustrations and the author's own cartoons. The author is known for his humorous approach to physics, making this text an excellent starting point for anyone, at any level, wanting to know more about physics.

Morrison, Michael A. Understanding Quantum Physics: A User's Manual. Englewood Cliffs, N.J.: Prentice-Hall, 1990. Although it seems a little incongruous, this is a truly funny quantum-mechanics text. Although it is a highly technical book, it is still very readable, even for those who do not have the math background to follow the derivations. The explanations of the material are the best anywhere. The quotations and intermissions in the book are highly entertaining.

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