why is the bond length an average rather than a fixed number ?
The answer lies in Probability theory and wave mechanics.... Electrons are NOT little planets circling a little Sun, get that our of your mind.
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The bond length between two atoms can be considered as an average rather than a fixed number due to several factors. Bond lengths are determined by the balance of attractive and repulsive forces between the atomic nuclei and the electrons participating in the bond.
One of the main factors affecting the bond length is the type of bond. In covalent bonds, the atoms share electrons, and the distribution of electrons between the two atoms affects the bond length. The more electronegative an atom is, the more it pulls the electrons towards itself, resulting in a shorter bond length. On the other hand, in ionic bonds, the bond length is determined by the sizes of the ions involved. Smaller ions have shorter bond lengths due to their stronger attraction to each other.
Another factor influencing bond length is the presence of multiple bonds. In molecules with double or triple bonds, the shared electrons are distributed over a smaller space compared to single bonds. This increased electron density leads to a shorter bond length.
Moreover, bond lengths can be affected by various environmental conditions, such as temperature and pressure. Changes in temperature and pressure can cause atoms to vibrate or move slightly, affecting the average distance between them.
To determine bond lengths experimentally, several techniques are used. X-ray crystallography, for example, involves measuring the angles and distances between atoms in a crystal lattice. Other experimental methods, such as spectroscopy or electron microscopy, can provide information about bond lengths indirectly. Computational methods, like molecular modeling or quantum chemical calculations, can also be used to estimate bond lengths by solving the underlying equations describing the relationship between atomic nuclei and electrons.
In summary, bond lengths are considered as an average rather than a fixed number due to the interplay of various factors, including the type of bond, electron distribution, presence of multiple bonds, and environmental conditions. Experimental and computational techniques are employed to accurately determine or estimate these average bond lengths.