Lesson 1, Topic 3
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The conservation laws: an example

Abdulaziz July 5, 2020
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The system we consider is that of two colliding diatomic molecules. For simplicity we assume that the molecules do not interact chemically and that each molecule is homonuclear that is, that its atomic nuclei are identical. The molecules are in a low-density gas, so that we need not consider interactions with other molecules in’ the neighborhood. In the Figure 1 we show the collision between the two homonuclear diatomic molecules, A
and B, and in Figure 2 we show the notation for specifying the locations of the two atoms of one molecule by means of position vectors drawn from an arbitrary origin.

Figure 1: A collision between homonuclear diatomic molecules, such as N, and O2. Molecule A is made up of tow atoms A1 and A2. Molecule B is made up of two atoms B1 and B2.
Figure 2: Position vectors for the atoms A1 and A2 in molecule A.

Actually the description of events at the atomic and molecular level should be made by using quantum mechanics. However, except for the lightest molecules (H, and He) at temperatures lower than 50 K, the kinetic theory of gases can be developed quite satisfactorily by use of classical mechanics. Several relations must hold between quantities before and after a collision. Both before and after the collision the molecules are presumed to be sufficiently far apart that the two molecules cannot “feel” the intermolecular force between them; beyond a distance of about 5 molecular diameters the intermolecular force is known to be negligible.