Question
Chemistry Question on The solid state
How many number of atoms are there in a cube based unit cell, having one atom on each corner and two atoms on each body diagonal of cube?
4
8
9
6
9
Solution
In a cube-based unit cell, there is one atom located at each corner and two atoms located on each body diagonal.
The number of corners in a cube is 8, and each corner is shared by 8 unit cells. Therefore, the contribution of atoms at the corners is:
8 corners * 1/8 atom per corner = 1 atom
The number of body diagonals in a cube is 4, and each body diagonal is shared by 2 unit cells. Therefore, the contribution of atoms on the body diagonals is:
4 body diagonals * 2 atoms per diagonal = 8 atoms
Adding the contributions from the corners and body diagonals, we get:
1 atom (corners) + 8 atoms (body diagonals) = 9 atoms
So, the correct answer is (C) 9.