Dry air is a mixture of gases, primarily nitrogen and oxygen with a small amount of argon. Molecular nitrogen is composed of two nitrogen atoms joined by a covalent bond of length 1.09 Å. Molecular oxygen is similarly composed of two oxygen atoms with a bond length of 1.21 Å. Argon exists as a single isolated atom with a mean radius of 0.95Å. Typically 78 of 100 molecules of dry air are nitrogen, 21 are oxygen, and 1 is argon.
Air molecules are never at rest. They undergo constant random thermal motions of a variety of types. The simplest type is that of uniform translation. The mean speed is about 500 m/s which is greater than the speed of sound (340 m/s). Each molecule has three degrees of translational motion: up and down, left and right, and backward and forward.
Air molecules take up only 0.1% of the volume they occupy. Thus air is a very sparse gas in which 99.9% of the atmosphere is vacuum. However there are 2.7 x 1019 molecules in every cubic centimeter of air. This high number density coupled with the large translational speeds implies that the air molecules are constantly colliding with each other. The mean time between collisions is 0.2 x 10-9 s. Thus an average molecule undergoes 5 collisions every nanosecond. (One nanosecond corresponds to the time it takes light to travel 30 centimeters in a vacuum.) The mean free path is the average distance traveled by a molecule before it collides with another molecule in the gas. Typically this distance is about 10-5 cm or about 500 to 1000 molecular radii.
Other types of random thermal motions are possible for a molecule depending on its shape. Monatomic gases like argon can only translate. Diatomic molecules like nitrogen and oxygen can undergo rotations and a vibration. The two rotational degrees of freedom are degenerate in the sense that it is not possible to distinguish between the two. Energetically the single vibrational mode has two degrees of freedom: energy can be stored in the kinetic energy of the vibration or in the potential energy of the molecule associated with the interatomic bond or "spring."
of Nitrogen (99 Kbytes) or Oxygen (116 Kbytes)
Each rotation or vibration produces no motion of the center of mass of the molecule. A displacement of the center of mass is a translation.
It is important to note that the movies suggest that the rotational and vibrational periods are the same. This feature is unrealistic and is forced on us by the size constraints of the movie. Each movie depicts the form of the motion but not its relative frequency. The frequencies differ between rotations and vibrations and amongst the rotations and vibrations. They also differ from molecule to molecule. Typically the frequencies of the vibrational modes correspond to energies in the infrared region of the electromagnetic spectrum. The rotational modes correspond to energies in the microwave region.
Triatomic molecules display a richer variety of motions. Water vapor, ozone, and carbon dioxide are examples of important triatomic molecules in the atmosphere. Each of these gases has three different rotational degrees of freedom.
of Water Vapor (132 Kbytes) or Carbon Dioxide (149 Kbytes) or Ozone (165 Kbytes)
Similarly each of these gases has three different modes of vibration. Again each vibrational mode has, energetically, two degrees of freedom.
of Water Vapor (116 Kbytes) or Carbon Dioxide (116 Kbytes) or Ozone (132 Kbytes)
The bending mode of the carbon dioxide molecule is unusual from the other modes displayed in that it is degenerate. There are two different bending modes. Together they can combine to form an elliptical "rolling" motion if the amplitude and phases of the separate modes coincide properly.
Bending Mode of Carbon Dioxide (132 Kbytes)
Other triatomic molecules behave in a manner similar to a nonlinear molecule such as water vapor and ozone or to a linear molecule such as carbon dioxide. Quadratomic, pentatomic, or higher polyatomic molecules display an increasingly richer variety of motions. We limit our story here to the comments we have made on the six dominant atmospheric gases. Nitrogen, oxygen, and argon are the dominant constituents of dry air. Water vapor, carbon dioxide, and ozone are the most radiatively active gases in the atmosphere.
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Peter R. Bannon (firstname.lastname@example.org)
Last Updated: October 29, 1996
Last Updated: October 29, 1996