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Q)

A molecule $A_2B$(mol.weight = 166.4) occupies triclinic lattice with a = 5A , b = 8A and C = 4A . If density of $AB_2$ is $5.2g cm^{-3}$. Calculate the number of molecules present in one unit cell.

$(a)\;1\qquad(b)\;2\qquad(c)\;3\qquad(d)\;4$

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A)
Volume of unit cell = $a\times b\times c$
$=5\times10^{-8}\times8\times10^{-8}\times4\times10^{-8}$
$= 1.6\times10^{-22}cm^3$
Mass of unit cell = $1.6\times10^{-22}\times5.2$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = 8.32\times10^{-22}g$
No of molecules in one unit cell = $\large\frac{8.32\times10^{-22}\times6\times10^{23}}{166.4}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=3$
Hence answer is (c)
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