Question

The lattice parameter of GaAs (radius of $Ga=1.22\mathring{A},As=1.25\mathring{A}$ ) is

• A. $5.635\mathring{A}$
• B. $2.852\mathring{A}$
• C. $5.774\mathring{A}$
• D. $4.94\mathring{A}$

Answer 1

Answer: (B)

$\frac{r_{\oplus }}{r_{\ominus }}\left(\text{ i. e. },\frac{r_{G{a}^{\oplus }}}{r_{A{s}^{3-}}}\right)=\frac{1.22\mathring{A}}{1.25\mathring{A}}=0.976$
From radius ratio, it is clear that cation( $G{a}^{3+}$ ion) lies in body centered or cubic void, where
$2\left(r_{\oplus }+r_{\ominus }\right)=\sqrt{3}a$
$2(1.22+1.25)\mathring{A}=\sqrt{3}a\Rightarrow a=2.852$