In a simple cubic lattice, how many atoms are effectively present in one unit ce

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Question: In a simple cubic lattice, how many atoms are effectively present in one unit cell? (2019)

Options:

Correct Answer: 1

Exam Year: 2019

Solution:

In a simple cubic lattice, there is 1 atom effectively present in one unit cell, as each corner atom contributes 1/8th of an atom to the unit cell.

In a simple cubic lattice, how many atoms are effectively present in one unit cell? (2019)

In a simple cubic lattice, how many atoms are effectively present in one unit cell? (2019)

Step 1: Understand what a simple cubic lattice is. It is a 3D arrangement of atoms where each atom is located at the corners of a cube.
Step 2: Identify how many corners are in a cube. A cube has 8 corners.
Step 3: Know that each corner atom is shared by 8 adjacent unit cells. This means that only a fraction of each corner atom belongs to one unit cell.
Step 4: Calculate the contribution of each corner atom to the unit cell. Since each corner atom contributes 1/8th of an atom, you multiply the number of corners (8) by the contribution of each corner (1/8).
Step 5: Perform the calculation: 8 corners * (1/8) = 1 atom.
Step 6: Conclude that there is 1 atom effectively present in one unit cell of a simple cubic lattice.

Simple Cubic Lattice – A simple cubic lattice is a type of crystal structure where atoms are located at the corners of a cube.
Unit Cell – The smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal.
Atomic Contribution – In a simple cubic lattice, each corner atom contributes 1/8th of its volume to the unit cell, leading to a total of 1 atom per unit cell.