BCC (Body-Centered Cubic) Unit Cell

A BCC unit cell is a type of crystal lattice structure that consists of atoms located at the corners of the unit cell and one atom located at the center of the body of the unit cell. This results in a total of 2 atoms per unit cell.

Packing Efficiency

Packing efficiency refers to the percentage of space occupied by atoms in a crystal lattice structure. It can be calculated by dividing the volume occupied by the atoms by the total volume of the unit cell and multiplying by 100.

In the case of a BCC unit cell, the packing efficiency is given by the formula:

Packing Efficiency = (Volume of atoms / Total volume of unit cell) x 100

Half of the Atoms Removed

If half of the atoms per unit cell are removed from a BCC unit cell, it means that only one atom remains in the unit cell. This atom is located at the center of the body of the unit cell.

Impact on Packing Efficiency

When half of the atoms are removed, the volume occupied by the atoms is also reduced. However, the total volume of the unit cell remains the same.

Since the packing efficiency is calculated by dividing the volume of atoms by the total volume of the unit cell, removing half of the atoms will result in a lower packing efficiency.

Explanation of Answer

The correct answer is option 'B' (34%) because removing half of the atoms from a BCC unit cell reduces the packing efficiency to 34%.

Other Options:

- Option 'A' (30%) is incorrect because it is too low. Removing half of the atoms will result in a higher packing efficiency than 30%.
- Option 'C' (68%) is incorrect because it is too high. Removing half of the atoms will result in a lower packing efficiency than 68%.
- Option 'D' (92%) is incorrect because it is too high. Removing half of the atoms will result in a lower packing efficiency than 92%.

To summarize, removing half of the atoms from a BCC unit cell reduces the packing efficiency to 34%.

If half of the atoms per unit cell are removed then Z_eff is 1, packing efficiency will be half of the 68%.