question: the radio ratio for cations and anions just touching eachother when a cation is present within an octahedral hole formed by anions is 0.414. derive the radius ratio for a cation present within a tetrahedral hole formed by anions.
I have seriously no idea how to go about solving this problem. I drew out the structure and uses pythagoreans theorem and it came down to cos45 = 2radius of anion/2 radius of cation + 2 radius of anion. I don't think I even did it right though.