Assertion: Only T-voids are present in CCP lattice structure.

Reason: Packing efficiency in CCP lattice structure is 74%.

Assertion is wrong statement, but reason is correct statement.

The correct answer is option 4. Assertion is wrong statement, but reason is correct statement.

Two types of voids are present in a CCP lattice

Tetrahedral voids (T-voids) are located at the body diagonals, two in each body diagonal, at one-fourth distance from each end.

Total number of tetrahedral voids per unit cell = 8

Octahedral voids (O-voids) are located at body-center and at edge centers of cubit unit cell.

Total number of octahedral voids per unit cell = \(\frac{1}{4}\) x 12 + 1 = 4

Thus, in CCP, total number of voids per unit cell = 8 + 4 = 12

Face centered cubic unit cell (FCC) is present in CCP Lattice structure

let the unit cell edge length be ‘a’ and face diagonal AC = b.

In ∆ ABC

AC² = b² = BC² + AB² = a² + a² = 2a² or b = \(\sqrt{2}\)a

If r is the radius of the sphere, we find b = 4r = \(\sqrt{2}\)a or a = \(\frac{4r}{\sqrt{2}}\) 

a = 2\(\sqrt{2}\)r

we can also write, r = \(\frac{a}{2\sqrt{2}}\)

We know that each unit cell in ccp structure i.e., FCC unit cell has effectively 4 spheres.

Total volume of four spheres is equal to 4 x \(\frac{4}{3}\)πr³ and volume of the cube is a³ or (2\(\sqrt{2}\)r)³.

Therefore,

Packing efficiency = \(\frac{\text{Volume occupied by four spheres in the unit cell}}{\text{Total volume of the unit cell}}\) x 100%

Packing efficiency = \(\frac{4 × \frac{4}{3}πr^3}{(2\sqrt{2}r)^3}\) x 100% = 74%