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The Solid State — Chemistry STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceChemistryThe Solid State5 Marks
Question
Chromium crystallises in bcc structure. If its atomic diameter is $245\ pm$, find its density. Atomic mass of $Cr = 52$ amu and $N_A = 6.02 \times 10^{23}\ mol^{–1}.$
✓

Answer

Deameter =$ 245pm$
$\therefore\text{Radius}=\frac{245}{2}\text{pm}=122.5\text{pm}$
In a bcc structure, $\text{r}=\frac{\sqrt{3}}{4}\text{a}\text{ or }\text{a}=\frac{4\text{r}}{\sqrt{3}}$
$\text{a}=\frac{4\times122.5}{\sqrt{3}}=\frac{490}{1.732}=282.91\text{pm}$
$\text{d}=\frac{\text{z}\times\text{M}}{\text{a}^3\times\text{N}_{\text{A}}}=\frac{2\times52}{(282.91\times10^{-10}\text{cm})^3\times6.02\times10^{23}}$
$=\frac{104}{2.264\times10^{-23}\times6.02\times10^{23}}=\frac{104}{2.264\times6.02}$
$=7.63\text{g/cm}^{-3}$

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