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Question: If the radius of the metal atom is 1.00 angstrom and its crystal structure is simply cubic, then wha...

If the radius of the metal atom is 1.00 angstrom and its crystal structure is simply cubic, then what is the volume of one unit cell?
A. 8×10−24m38 \times {10^{ - 24}}{m^3}
B. 4×10−30cm34 \times {10^{ - 30}}c{m^3}
C. 8×10−30m38 \times {10^{ - 30}}{m^3}
D. 2×10−24cm32 \times {10^{ - 24}}c{m^3}

Explanation

Solution

The solid elements in nature occur in either the crystalline form or the amorphous form. The two of these structures differ in the arrangement of the ions and the molecules of the element . Both the amorphous form and the crystalline forms have different properties and packing of the overall structure which in turn gives them their distinct nature.

Complete step by step answer:
The solids can broadly be categorised as amorphous or crystalline based on the packing of this structure in the lattice space. The crystalline solids have a more defined structure than their amorphous counterparts. The crystals of the crystalline are distinct in arrangements and can be categorized in various categories .
All these categories contain a distinct arrangement of the atoms in the crystal lattice. All the factors like the intermolecular distance and the positions of the atoms are fixed for a specific crystal . These different arrangements are what gives rise to the different structures of crystal.
One of such crystal types is the simple cubic structure in which the atoms of the crystals take the form of a cube in which all the edges are of the same length. It has atoms only at their corners.
The distance between the ions of these crystals is given as 2r, where r is the radius of the atom or ion.
So the side of the simple cubic lattice structure is 2r as the two ions are placed one above the other along all the edges to form a cubic structure.
So the volume of the cube is (edge)3{(edge)^3} , since the edge of the structure is
2r=2×1angstorm=2angstorm2r = 2 \times 1angstorm = 2angstorm
So the volume of the unit cell is (2)3 angstorm{(2)^3}\,angstorm
8 angstorm38\,angstor{m^3}
Since 1 angstorm=10−10m1\,angstorm = {10^{ - 10}}m
So 8 angstorm3=8×10−30m38\,angstor{m^3} = 8 \times {10^{ - 30}}{m^3}

So, the correct answer is Option C.

Note: The crystals in the solids are categorised as the unit cell structure. These are seven in count and are namely cubic, tetragonal,orthorhombic, trigonal, monoclinic, triclinic, hexagonal.
All these primitive crystals are differentiated based on their size , edge and the angle which the edges subtend with each other.