Question

Lithium forms body-centered cubic structure. The length of the side of its unit cell is 351 pm. The atomic radius of lithium will be:
A) 75 pm
B) 300 pm
C) 240 pm
D) 152 pm

Answer 1

The answer for this question is dependent on the concept of crystal structures in the inorganic chemistry part where the atomic radius of the element according to body-centered cubic structure is calculated by the formula$r=\dfrac{\sqrt{3}\times a}{4}$

Complete step by step answer:
The concept of crystal lattice and also the assigned sides and angles for a particular type of crystal structure is familiar to us. These concepts come under the chapters of crystallography in inorganic chemistry.
Now, let us see in detail about the crystal lattice and also the types in it which also includes the body centered cubic structure.
- In crystallography, the cubic structure refers to the crystal system where the unit cell is in the shape of a cube.
- Unit cells are nothing but the smallest repeating unit which is having the full symmetry of the crystal structure.
- According to Bravais lattices, there are three forms of cubic lattices that are, primitive cubic, body centered cubic and face centred cubic.
Body centred cubic has one lattice point in the centre of the unit call and to calculate the radius of that element will be given by,
$r=\dfrac{\sqrt{3}\times a}{4}$
where a = edge length and according to the data given a = 351 pm.
Now, substituting this value in the above equation, we get
$r=\dfrac{\sqrt{3}\times 351}{4}=152pm$

Therefore, the correct answer is option D) 152 pm.

Note: Geometry of the unit cell is defined as parallelepiped where it describes about the six lattice parameters considered and those are the lengths of the three cell edges denoted by a, b, c and also the angles between these edges that are $\alpha ,\beta ,\gamma$ and questions relating to this may be asked and this fact may help you to solve the questions.