what is the atomic radius of carbon. calculate length, continuous chain of 18 carbon atom
The correct answer and explanation is:
Atomic Radius of Carbon:
The atomic radius of carbon is approximately 70 picometers (pm) or 0.70 angstroms (Å). This value refers to the covalent atomic radius, which is the typical size of a carbon atom when bonded to other atoms.
Calculating the Length of a Continuous Chain of 18 Carbon Atoms:
To find the length of a continuous chain of 18 carbon atoms, we assume a typical single bond carbon-carbon (C–C) bond length. The bond length between two carbon atoms in a single bond is about 154 pm (1.54 Å).
For a linear chain of 18 carbon atoms, there are 17 bonds connecting them (because the number of bonds = number of atoms – 1).
Length of chain = Number of bonds × Bond length
= 17 × 154 pm
= 2618 pm
= 2.618 nanometers (nm)
= 0.002618 micrometers (µm)
Explanation:
Carbon atoms have an atomic radius of about 70 pm. This radius represents the size of a single carbon atom in a bonded state. However, atoms do not exist in isolation in molecules; they bond with other atoms. In organic molecules such as alkanes, carbon atoms connect via single covalent bonds. The typical carbon-carbon single bond length is 154 pm. This length is the distance between the nuclei of two bonded carbon atoms, essentially the space taken by two adjacent carbon atoms minus the overlap of their atomic orbitals.
When carbon atoms form a continuous chain, each pair of adjacent atoms contributes one bond length to the total chain length. For a chain of 18 carbon atoms, there are 17 such bonds. Multiplying the number of bonds by the bond length gives the total length of the chain.
This calculation assumes the chain is fully extended in a straight line, without bending or folding. In reality, molecules may adopt three-dimensional shapes, and the effective length could be shorter due to bond angles and rotations around bonds. But for an idealized, linear structure, the total length is simply the sum of bond lengths.
This approach is useful in understanding the scale of molecular structures in nanometers and is foundational in organic chemistry, molecular modeling, and nanotechnology. It also helps visualize how molecular size relates to atomic properties like atomic radius and bond lengths.