Question

Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of lithium will be:
A.175 pm
B.300 pm
C.240 pm
D.152 pm

Answer 1

Hint: A body centred cubic structure is a type of crystal structure in metals. Since the edge length of the unit cell (a) is given in the question. So, for finding the atomic radius of the lithium, we will use the formula, radius $ = \dfrac{{\sqrt 3 }}{4}a$ (where a = edge length of a unit cell)

Complete step by step answer:
A body centred cubic structure is a type of crystal structure in metals. This structure can be seen as a gathering of cubes with atoms at the edges and an atom in the centre of every cube. It is a type of atomic arrangement and is a loosely packed structure.
Given in the question is,
In a body centred cubic (bcc) structure,
Edge length = 351 pm
We know,
radius $ = \dfrac{{\sqrt 3 }}{4}a$
Where, a = edge length of a unit cell
Radius,
 \[
  r = \dfrac{{\sqrt 3 }}{4} \times 351 \\
   \Rightarrow r = \sqrt 3 \times 87.75 \\
   \Rightarrow r = 152pm \\
 \]
So, the atomic radius of lithium will be 152 pm.

Therefore, the correct answer is option (D).

Note: In the Body-Centered cubic (BCC) unit cell, each atom has eight neighbours arranged at the corners of a cube plus one atom in the centre of the cube. Because each of the corner atoms is the corner of another cube, the corner atoms in each unit cell will be shared among eight unit cells. The BCC unit cell consists of a net total of two atoms, the one in the centre and eight eighths from the corners. Some examples of metals that possess this crystalline structure include the α phase of iron, chromium, tungsten, tantalum, and molybdenum.