Number of atom per unit cell in B.C.C. - DASH

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Question

Number of atom per unit cell in B.C.C.

9

4

2

1

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Step-by-Step Explanation Step 1: Recognize the type of lattice The question specifies a body-centered cubic (BCC) lattice. In such a lattice, atoms are located at each corner of the cube and one atom is located at the center of the cube. Step 2: Count corner atoms contribution Each corner of the cube is shared by 8 adjacent cubes. Hence, each corner atom contributes $ \frac{1}{8} $ of an atom to one unit cell. Since there are 8 corners, the total contribution from the corners to one unit cell is: $$ \frac{1}{8} \times 8 = 1 $$ Step 3: Count the center atom contribution There is one atom at the center of the cube, and this atom belongs entirely to that single unit cell. So it contributes 1 atom. Step 4: Add up the total By adding contributions from corners and the center atom, the total number of atoms present in one BCC unit cell is: $$ 1 + 1 = 2 $$ Step 5: Conclusion Therefore, the number of atoms per unit cell in a body-centered cubic (BCC) lattice is 2.

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