Question

$2X{{10}^{8}}$ atoms of carbon are arranged side by side. Calculate the radius of the carbon atom if the length of this arrangement is 2.4 cm.

Answer 1

Hint: The elements in the periodic table show periodicity in their properties. The elements in the periodic table are arranged in the order of their atomic numbers. All of the elements in the periodic table formation to predict their chemical, physical, and atomic properties.

Complete step by step solution:
Trends in the periodic table are atomic radius, ionic radius, ionization energies, electronegativity, electron affinity, metallic and non-metallic properties.
-Atomic radius: The atomic radius is defined as “the distance from the center of the nucleus to the outermost shell of electrons.” The determination of the radius of an atom is not possible due to the very small size of the atom. Atomic radius can be divided into the following types based on the nature of combining atoms:
(a) Covalent radius
(b) Metallic radius
(C) Van der Waals radius
(D) Ionic radius
-Covalent radius: One-half of the distance between the internuclear distance of two covalently bonded atoms in a homo-diatomic molecule is called covalent radius atom.
${{r}_{\operatorname{cov}alent}}=\dfrac{1}{2}[bond length]$
-Metallic radius: this is defined as the half of the internuclear distance separating metal cores in a metallic crystal
-Van der Wall radius: this is the half of the distance between two similar atoms in different molecules that are separated in a solid.
-Ionic radius: a cation by the loss of one or more electrons from a neutral atom and an anion by the gain of electrons of one or more electrons from a neutral atom. The ionic radii of ions depend on the internuclear distance between the two ions in an ionic crystal.
The diameter of carbon corresponds to its length covered by one carbon atom.
The length of the carbon arrangement given = 2.4cm
The number of carbon atom arranged side by side = $2X{{10}^{8}}$ atoms
The diameter of the carbon atom = $\dfrac{2.4}{2X{{10}^{8}}}=1.2X{{10}^{-8}}cm$
The radius of the carbon atom = half of the diameter of the carbon atom = $\dfrac{1.2X{{10}^{-8}}}{2}=0.6X{{10}^{-8}}cm$

Hence, the radius of the carbon atom = 0.06nm

Note: Knowing the periodic properties of elements useful to predict the greater or smaller atomic size and also radial distribution in neutral atoms and ions. We will predict redox potential, comparing metallic character with other elements, and also predict the feasibility of chemical reactions.