Question

$ C_{60} $ (bucky ball) is cubic closest packed (face centred cubic) in its crystalline form. If you insert potassium atoms into all the tetrahedral and octahedral holes of the $ C_{60} $ structure, the formula would become $ K_{x}C_{60} $ . What is the value of $x$?

• A. 1
• B. 2
• C. 3
• D. None of these

Answer 1

Answer: (C)

$C _{60}$ forms fcc unit cell. If $N$ represents the number of $C _{60}$ present in one unit cell, then the number of octahedral voids in one unit cell will be $N$ and the number of tetrahedral voids in one unit cell will be $2\, N$. Total number of voids in one unit cell will be $N +2\, N =3\, N$.
This is equal to the number of $K$ atoms.
Thus, for $NC _{60}$ units in one unit cell, there will be $3 \,N K$ atoms.
For $1 C _{60}$ unit, there will be $3 \,K$ atoms.
The formula will be $K _{3} C _{60}= K _{ x } C _{60}$ or $x =3$.