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The following figure shows the unit cell...

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

Text Solution

Verified by Experts

The correct Answer is:
13
Singal unit cell consists of thrre cubes. ltbRgt Number of `Ba^(2+)` ions `= 2` per lunit cell
Number of `Y^(4+)` ions `= 1` per unit cell
Number of `Cu^(2+)` ions `= 8` in each at corners)
`= 8 xx 3` (in three cubs)
`xx 1/8` (per corner share)
`= 3//"unit cell"`
Number of `O^(2-)` ions `= 10` (at edge centre of cube `1`)
`+ 8` (at eedge centre of cube `2`)
`+ 10` (at edge centre of cube `3`)
`= 28` (edge centre)
`xx 1/4` (per edge centre share)
`= 7//"unit cell"`
Formula: `Y_((a))^(4+)Ba_((b)^(2+))Cu_((c)^(2+))O_((d)^(2-))`
`rArr Y_(1^(4+))Ba_(2^(2+))Cu_(3^(2+))O_(7^(2-))`
`[{:("Total +ve charge (14)"),("is equal to total" -ve),("charge" (14)):}]`
`:. a + b + c + d = 1 + 2 + 3 + 7 = 13`
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