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 $Y_{a} B a_{b} C u_{c} O_{d}$ .

Find the value of $a + b + c + d$ .

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Solution

Lets divide the structure into three blocks from top to bottom and consider each as separate unit cell.
No. of $Y = 1$
No. of $B a = 2$
No. of $C u = 24 \times \frac{1}{8} = 3$
No. of $O = 28 \times \frac{1}{4} = 7$
The formula of mixed oxide becomes $Y_{1} B a_{2} C u_{3} O_{7}$ .
Hence value of $a + b + c + d = 13$

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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 YaBabCucOd. Find the value of a+b+c+d.

Lets divide the structure into three blocks from top to bottom and consider each as separate unit cell. No. of Y=1 No. of Ba=2 No. of Cu=24×18=3 No. of O=28×14=7 The formula of mixed oxide becomes Y1Ba2Cu3O7. Hence value of a+b+c+d=13

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 $Y_{a} B a_{b} C u_{c} O_{d}$ .

Find the value of $a + b + c + d$ .