In cubic ZnS, the radii of the Zn and S atoms are 0.83 mathringA and 1.74 mathringA respectively. What is the edge length of the unit cell of ZnS ?

Question

In cubic ZnS, the radii of the Zn and S atoms are 0.83 mathringA and 1.74 mathringA respectively. What is the edge length of the unit cell of ZnS ? (A) 2.57 mathringA (B) 3.64 mathringA (C) 2.97 mathringA (D) 5.935 mathringA

Tardigrade Admin · Accepted Answer

This figure shows one part of eight cubic components of a unit cell of

Z n S

.

Let edge length of the unit cell

= a

3 \times \frac{a}{2} \times \frac{1}{2} = r_{Z n^{2 +}} + r_{S^{2 -}}

or

3 \frac{a}{4} = 0.83 + 1.74 = 2.57

or

a = 2.57 \times \frac{4}{3} = 5.935 \overset{˚}{A}

Q. In cubic $Z n S$ , the radii of the $Z n$ and $S$ atoms are $0.83 \overset{˚}{A}$ and $1.74 \overset{˚}{A}$ respectively. What is the edge length of the unit cell of $Z n S$ ?

$2.57 \overset{˚}{A}$

$3.64 \overset{˚}{A}$

$2.97 \overset{˚}{A}$

$5.935 \overset{˚}{A}$

This figure shows one part of eight cubic components of a unit cell of $Z n S$ .

Let edge length of the unit cell $= a$
$3 \times \frac{a}{2} \times \frac{1}{2} = r_{Z n^{2 +}} + r_{S^{2 -}}$
or $3 \frac{a}{4} = 0.83 + 1.74 = 2.57$
or $a = 2.57 \times \frac{4}{3} = 5.935 \overset{˚}{A}$

Q. In cubic ZnS, the radii of the Zn and S atoms are 0.83A˚ and 1.74A˚ respectively. What is the edge length of the unit cell of ZnS ?

2.57A˚

3.64A˚

2.97A˚

5.935A˚