Solveeit Logo
Login

Question

Question: Salt AB has a zinc blende structure. The radius of \({A^{2 + }}\)and \({B^{2 - }}\)ions are \(0.7\) ...

Salt AB has a zinc blende structure. The radius of A2+{A^{2 + }}and B2−{B^{2 - }}ions are 0.70.7 ​A​o \overset{​o}{​A}\, and 1.81.8 ​A​o \overset{​o}{​A}\, respectively. The edge length of AB unit cell is :
(A) 2.52.5 ​A​o \overset{​o}{​A}\,
(B) 5.095.09 ​A​o \overset{​o}{​A}\,
(C) 55 ​A​o \overset{​o}{​A}\,
(D) 5.775.77 ​A​o \overset{​o}{​A}\,

Explanation

Solution

The edge length can be defined as the length of the side of the cubic unit cell which is made up of atoms of constituent elements. The edge length of the Zinc blende unit cell can be found out by -
rA++rB−=a34r_A^ + + r_B^ - = \dfrac{{a\sqrt 3 }}{4}
Where rA+r_A^ + is the radius of cation
rB−r_B^ - is the radius of the anion
And ‘a’ is the edge length of the unit cell.

Complete step by step solution:
Given :
Salt AB has structure = zinc blende structure
Radius of A2+{A^{2 + }}ion = 0.70.7 ​A​o \overset{​o}{​A}\,
Radius of B2−{B^{2 - }}ion = 1.81.8 ​A​o \overset{​o}{​A}\,
To find :
Edge length of AB unit cell
As the structure is a zinc blende structure. We know the zinc blende structure is made of Zinc atoms and Sulphur atoms. The structure consists of a cubic lattice in which Sulphur atoms occupy corners and face centre sites while the Zinc atoms occupy half of the tetrahedral sites.
Further, we know that for zinc blende structure, the relation between radius and edge length is given by -
rA++rB−=a34r_A^ + + r_B^ - = \dfrac{{a\sqrt 3 }}{4}
Where rA+r_A^ + is the radius of cation
rB−r_B^ - is the radius of anion
And ‘a’ is the edge length of a unit cell.
By putting the values in the formula, we can find the edge length as -
0.7+1.8=a340.7 + 1.8 = \dfrac{{a\sqrt 3 }}{4}
a34\dfrac{{a\sqrt 3 }}{4} = 2.52.5
a3a\sqrt 3 = 10
And aa = 101.732\dfrac{{10}}{{1.732}}
‘a’ = 5.775.77 ​A​o \overset{​o}{​A}\,

So, the option (D) is the correct option.

Note: It must be noted that Zinc blende structure has atoms at the face centre of the unit cell also. So, it is different from a simple unit cell. The edge length of a simple unit cell can find out as- ‘a’ = rA++rB−r_A^ + + r_B^ -
Similarly, the edge length of different types of unit cells is different. It should not be mixed.