Question

Copper crystallises in a face-centered cubic lattice with a edge length of unit cell a Ä. The diameter of copper atom in Ä is a/2 a/√3 a/√2 √(3a/2)

Answer 1

Given:

The given unit cell of copper is FCC.

The edge length of the unit cell = a

To Find:

The diameter of the given copper atom.

Calculation:

- We know that for FCC unit cell, the radius is given as:

r = a/2√2

- Putting the value of radius in the formula for diameter:

Diameter = 2 r

⇒ D = 2 × a/2√2

⇒ D = a/√2

- So, the correct answer is option (c) a/√2.

Answer 2

Answer:

D = a / $\sqrt{2}$

Explanation:

Given the length of a pure cubic lattice is a. In face centered cubic, the atoms are placed on the corners of the cube which means that the atoms on the face diagonal will be touching each other.

Consider the radius of the atom be r, the length of cube diagonal will be $\sqrt{2a}$

Then we can write equation as;

r + 2r + r = $\sqrt{2a}$

r = a / 2$\sqrt{2}$

Diameter = 2 r

D = a / $\sqrt{2}$

Hence option C is correct