Question

The crystalline solids have definite orderly arrangement of their constituent particles in three dimensions known as lattice. The smallest repeating part in the lattice is known as unit cell. The unit cell are described as simple cubic face centred and body centred unit cell.
For the stable ionic crystalline structures, there is definite radius ratio limit for a cation to fit perfectly in the lattice of anions called radius ratio rule. This also defines the coordination number of an ion.
(iii) Gold crystallises in a face centred unit cell. Its edge length is $0.410\text{nm}$. The radius of gold atom is:

• A. $0.205\text{nm}$
• B. $0.290\text{nm}$
• C. $0.145\text{nm}$
• D. $0.578\text{nm}$

Answer 1

The correct option is C $0.145\text{nm}$

Given: $a=0.410\text{nm}$
As we know, in face centered unit cell,
$r=\frac{a}{2\sqrt{2}}=\frac{0.410}{2\times 1.414}=0.145\text{nm}$