How many atoms surround the central atom present in a unit cell with the least free space available?a)4b)6c)8d)12Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Explanation:

To determine the number of atoms surrounding the central atom in a unit cell with the least free space available, we need to consider the arrangement of atoms in the unit cell.

In a unit cell, the central atom is surrounded by other atoms, which are usually referred to as the coordination number of the central atom. The coordination number determines the number of atoms that directly contact the central atom.

In the case of a unit cell with the least free space available, we can consider a close-packed structure, such as a face-centered cubic (FCC) or a body-centered cubic (BCC) arrangement.

Face-Centered Cubic (FCC) Structure:
In an FCC structure, each corner of the unit cell is occupied by an atom, and there is an additional atom at the center of each face of the unit cell. This arrangement results in a coordination number of 12 for the central atom.

Body-Centered Cubic (BCC) Structure:
In a BCC structure, each corner of the unit cell is occupied by an atom, and there is an additional atom at the center of the unit cell. This arrangement results in a coordination number of 8 for the central atom.

Conclusion:
Therefore, in a unit cell with the least free space available, the central atom is surrounded by 12 atoms in an FCC structure and 8 atoms in a BCC structure. Among the given options, the correct answer is option 'D' with 12 atoms surrounding the central atom.

Answer

FCC, CCP and HCP are unit cells with least free space available i.e. highest packing efficiency. The coordination number of given cells are 12.

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