Following is the fact about the newly discovered superconductor of `C_(60)` (fullerene). The alkali metal fulleride superconductor `M_(3)C_(60)` has a cubic closest-packed (face-centered cubic) arragement of nearly spherical `C_(60)^(3-)` anions with `M^(+)` cations in the holes between the larger `C_(60)^(3-)` ions. The holes are of two types-octahedral holes, which are surrounded octahedrally by six `C_(60)^(3-)` ions, and tetrahedral holes, which are surrounded tetrahedrally by four `C_(60)^(3-)` ions.
  Specify fractional coordinates for the tetrahedral holes (Fractional coordinates are fractions of the unit cell edge lengths. For example, a hole at the centre of the cell has fractional coordinates `(1)/(2),(1)/(2),(1)/(2)`

Options

A. `(1)/(2),(1)/(2),(1)/(2)`
B. `(1)/(3),(1)/(3),(1)/(3)`
C. `(1)/(4),(1)/(4),(1)/(4)`
D. `(1)/(2),(1)/(2),(1)/(4)`

Answer

C

Explanation

Centre of the cell has fractional co-ordinates `1/2, 1/2, 1/2` because in the X-direction, Y-direction, Zdirection at half of the edge length. Tetrahedral holes is at the `1/4 th` of the body iagonal `therefore` at `1/4` th edge length in the X, Y, Z directions `therefore 1/4, 1/4, 1/4`