Question

Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius (in pm) of copper atoms?
A.109
B.127
C.157
D.181

Answer 1

There are eight atoms at the corners of the unit cell and one atom centred on each of the faces of the FCC arrangement. The face atom is shared with the cell next to it. Four atoms make up FCC unit cells, with eight eighths at the corners and six halves on the faces.

Complete answer: The cubic (or isometric) crystal structure is a crystal system with a cube-shaped unit cell in crystallography. This is one of the most basic and straightforward crystal and mineral forms.
These crystals come in three different types:
Cubic primitive (abbreviated cP and alternatively called simple cubic)
Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated cI or bcc) (abbreviated cF or fcc, and alternatively called cubic close-packed or ccp). Each is further subdivided into the following variants. Although the unit cell of these crystals is usually assumed to be a square, the primitive unit cell is not always.
For the FCC lattice, the relationship between edge length (a) and atom radius (r) is$\sqrt {2a} = 4r$.
The volume of a cube is equal to the sum of its length, width, and height. However, since it's a cube, the length, width, and height are all equal and equal to the length of one of the cube's edges.
Given a = 361 pm
$\sqrt {2a} = 4r$
$r = \dfrac{{\sqrt 2 a}}{4}$
$r = \dfrac{{\sqrt 2 \times 361}}{4}$
r = 127.6 pm
Hence option B is correct.

Note:
Each electron, molecule, or ion (constituent particle) in a crystal lattice is described by a single point.
The term "lattice site" or "lattice point" refers to these points.
In a crystal lattice, a straight line connects the lattice sites or points.
We can get a three-dimensional image of the system by connecting these straight lines. The Crystal Lattice, also known as Bravais Lattices, is a three-dimensional structure.