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The effective number of lattice points in the unit celi of simple cubic, body centered cubic and face centered cubic space lattices respectively are
  • a)
    1, 2, 2
  • b)
    1, 2, 4
  • c)
    2, 3, 4
  • d)
    2, 4, 4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The effective number of lattice points in the unit celi of simple cubi...
For simple cubic effective number of lattice point = 1
For B.C.C. effective number of lattice point = 2
For F.C.C. effective number of lattice point = 4
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The effective number of lattice points in the unit celi of simple cubi...
Introduction:
In crystallography, lattices are used to study the arrangement of atoms or molecules in a crystal structure. The three most common types of lattices are simple cubic, body-centered cubic (bcc), and face-centered cubic (fcc). Each of these lattices has a specific number of lattice points within its unit cell.

Simple Cubic Lattice:
A simple cubic lattice is the most basic type of lattice, where each lattice point represents a single atom or molecule. In this lattice, the unit cell consists of eight corners, with each corner representing one lattice point. Therefore, the effective number of lattice points in the unit cell of a simple cubic lattice is 1.

Body-Centered Cubic Lattice:
In a body-centered cubic lattice, in addition to the eight corner lattice points, there is an additional lattice point at the center of the unit cell. This central point is shared by eight neighboring unit cells. Therefore, the effective number of lattice points in the unit cell of a body-centered cubic lattice is 2.

Face-Centered Cubic Lattice:
In a face-centered cubic lattice, there are lattice points not only at the eight corners but also at the center of each face of the unit cell. Each corner lattice point is shared by eight neighboring unit cells, while each face-centered lattice point is shared by two neighboring unit cells. Therefore, the effective number of lattice points in the unit cell of a face-centered cubic lattice is 4.

Summary:
To summarize, the effective number of lattice points in the unit cell of a simple cubic lattice is 1, in a body-centered cubic lattice is 2, and in a face-centered cubic lattice is 4. Therefore, the correct answer is option B, which states that the effective number of lattice points in the unit cell of simple cubic, body-centered cubic, and face-centered cubic space lattices respectively is 1, 2, 4.
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