The correct sequence of bond length in single bond, double bond and triple bond of \(\mathrm{C}\) is (a) \((C-C)=(C=C)=(C=C)\) (b) \(\mathrm{C} \equiv \mathrm{C}<\mathrm{C}=\mathrm{C}<\mathrm{C}-\mathrm{C}\) (c) \(\mathrm{C}-\mathrm{C}<\mathrm{C}=\mathrm{C}<\mathrm{C} \equiv \mathrm{C}\) (d) \(C=C

In chemistry, a single bond is the simplest and most common type of chemical bond. It is represented by a single line between two atoms and signifies that two electrons are shared between them. One of the most prevalent examples is the bond between two carbon atoms in an ethane molecule, represented as \(C-C\).

Because single bonds involve the sharing of only one pair of electrons, the atoms are held together less tightly compared to multiple bonds. This relatively weaker attraction results in a longer bond length, which generally means that the bond is also more flexible. In hydrocarbons like ethane, these single bonds give the molecules their ability to rotate around the bond axis, contributing to their structural diversity.

When understanding bond lengths, it's crucial to know that single bonds are typically the longest of all bond types due to less electron density pulling the bonded atoms together. This knowledge is foundational when predicting the behavior and properties of organic compounds.

A double bond occurs when two pairs of electrons are shared between two atoms, represented by two parallel lines (e.g., \(C=C\)). It is stronger and shorter than a single bond because the increased electron density between the two atoms leads to a greater electrostatic attraction.

Double bonds are characteristic of alkenes, like ethene, and contribute to their chemical reactivity. Unlike single bonds, double bonds restrict the rotation of the bonded atoms, which gives rise to distinct geometric isomers, a critical concept in stereochemistry.

In the context of bond length, double bonds are shorter than single bonds but longer than triple bonds. This intermediate length is important for understanding the stability and reactivity of various organic compounds, as well as their physical properties, such as boiling and melting points.

When three pairs of electrons are shared between two atoms, a triple bond is formed, denoted by three lines (e.g., \(C\equiv C\)). This bond type features the highest electron density in the bond area, making it the strongest and shortest among the single, double, and triple bonds.

Triple bonds are a defining trait of alkynes, like ethyne, and have significant implications for the molecules' physical and chemical behaviors. They allow the compound to have a linear configuration and are quite rigid, which affects the compound's overall shape and reactions. This rigidity can also influence how molecules interact with each other, impacting their chemical properties and the materials' macroscopic characteristics.

Understanding that triple bonds have the shortest length is key when determining molecule stability and reactivity, especially in synthetic chemistry where the fabrication of complex molecules often involves making or breaking these strong bonds.