Question
A compound forms hexagonal close-packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?
✓
Answer
Number of closed packed particles $= 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$
$0.5 \times 6.022 \times 1023 = 3.011 \times 1023$
Therefore number of octhahedral voids $= 3.011 \times 10^{23}\times 1023$
and number of tetrahedral voids $= 2 \times 3.011 \times 10^{23}$
$= 6.022 \times 10^{23}2 \times 3.011 \times 1023$
$= 6.022 \times 1023$
Therefore total number of voids $= 3.011 \times 10^{23} + 6.022\times 10^{23}$
$ = 9.033 \times 10^{23}3.011 \times 1023 + 6.022 \times 1023$
$= 9.033 \times 1023.$
$0.5 \times 6.022 \times 1023 = 3.011 \times 1023$
Therefore number of octhahedral voids $= 3.011 \times 10^{23}\times 1023$
and number of tetrahedral voids $= 2 \times 3.011 \times 10^{23}$
$= 6.022 \times 10^{23}2 \times 3.011 \times 1023$
$= 6.022 \times 1023$
Therefore total number of voids $= 3.011 \times 10^{23} + 6.022\times 10^{23}$
$ = 9.033 \times 10^{23}3.011 \times 1023 + 6.022 \times 1023$
$= 9.033 \times 1023.$
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