Question

The following figure shows the unit cell of a compound, i.e., a mixed oxide of yttrium, barium , and copper. The formula of mixed oxide is `Y_(a)Ba_(b)Cu_(c)O_(d)` . Find the value of `(c+d)-(a-b)`.

Answer 1

Correct Answer - 7
Single unit cell consists of three cubes.
Number of `Ba^(2+)` ions =2 per unit cell
Number of `Y^(4+)` ion=1 per unit cell
Number of `Cu^(2+)` ions=8 in each cube at corners)
`=8xx3` (in three cubes) `xx(1)/(8)` (per corner share)=3/unit cell.
Number of `O^(2-)` ions=10(at edge center of cube 1)+8 (at edge center of cube2)
+10 (at edge center of cube3)=28 (edge center)
`xx(1)/(4)` (per edge center share)=7//unit cell
Formula `^(4+)Ba^(2+)Cu^(2+)O^(2-)`
`Y_(1)^(4+)Ba_(2)^(2+)Cu_(3)^(2+)O_(7)^(2-)` [Total +ve charge (14) is equal to total -ve charge (14)]
`therefore (c+d)-(a+b)=7+3-(1+2)=7`