Mumbai University > First Year Engineering > Sem 1 > Applied Physics 1

Marks: 5M

Year: May 2016

Ligancy

Ligancy is defined as the number of nearest anions surrounding the central cation.

Value of critical radius ratio for ligancy

As Ligancy is 6, configuration s Octahedral.

![enter image description here][1]

The figure shows the cation with center at E and 4 anions surrounding it. Two other anions are also in contact which is placed at the front and the back of the given plane.

In ΔEBF, $m \lt EPB = 90^0 and \hspace{0.2cm} rest \hspace{0.2cm} are 45^0$

$cos B = cos 45 = \frac{BF}{BE} \frac{r_a}{r_c+ r_a}$

Applying Invertendo and Dividendo, we get;

$\frac{r_c}{r_a} = \frac{1-cos45}{cos45} = 0.414$

$r_c = 0.414r_a$

Given that, $r_a 2.02 A^0$

$r_c= 0.414 x 2.02$

$r_c = 0.836 A^0$