Question

The Cu metal crystallises into fcc lattice with a unit cell edge length of 361 pm. The radius of Cu atom is:

• A. 157 pm
• B. 181 pm
• C. 127 pm
• D. 108 pm

Answer 1

The Correct Option is C

For a face-centered cubic (fcc) lattice, the relationship between the edge length (a) and the atomic radius (r) is given by:

\(4r = \sqrt 2  a\)

Where:

• r = atomic radius
• a = edge length

Given that the edge length (a) is 361 pm, we can calculate the radius (r):

\(4r = \sqrt 2 \times 361\) pm

\(4r = 1.414 \times 361\) pm

\(4r = 510.454\) pm

\(r = \frac {510.454}{4}\)

\(r ≈ 127.6\) pm

Therefore, the radius of the Cu atom is approximately \(127\) pm.

The correct answer is (A}: \(127\) pm

Answer 2

To determine the radius of a copper (Cu) atom in a face-centered cubic (fcc) lattice, we begin by recognizing that in an fcc lattice, the atoms are positioned at each corner and the centers of each face of the cube. In such a lattice, the diagonal of the face of the cube is composed of four atomic radii, and this can be expressed by the equation:

\(\sqrt 2a=4r\)

Here, \(a\) is the edge length of the cube, and \(r\) is the atomic radius. Given that the unit cell edge length \(a\) is 361 pm, we can solve for \(r\) as follows:

\(r=\frac{√2a}{4}\)

Substituting the given edge length:

\(r=\frac{√2 \times 361}{4}\) pm

\(r=\frac{510.54 }{4}\) pm

\(r=127.635\) pm

Since the radius should be provided in whole numbers, we round off to 127 pm. Therefore, the radius of the Cu atom is 127 pm.