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 $2N$. Total number of voids in one unit cell will be $N+2N=3N$.
This is equal to the number of $K$ atoms.
Thus, for $N{C}_{60}$ units in one unit cell, there will be $3NK$ atoms.
For $1C_{60}$ unit, there will be $3K$ atoms.
The formula will be $K_3{C}_{60}=K_x{C}_{60}$ or $x=3$.