NEET Chemistry The Solid State Questions Solved

A rhombohedral unit cell is shown. What is its volume ?
Side length = a Å.

(A) $\frac{{a}^{3}}{\sqrt{3}}$

(B) ${a}^{3}\frac{\sqrt{3}}{2}$

(C) $\frac{{a}^{3}}{\sqrt{2}}$

(D)

(C). The volume is Take $\stackrel{\to }{a}=a.\stackrel{\to }{i}$

Now $\stackrel{\to }{b}=\left(a\mathrm{cos}\theta \right)\stackrel{\to }{i}+\left(a\mathrm{sin}\theta \right)\stackrel{\to }{j}=\frac{a}{2}\stackrel{\to }{i}+\frac{a\sqrt{3}}{2}\stackrel{\to }{j}$

$\stackrel{\to }{c}=\frac{a}{2}\stackrel{\to }{i}+\frac{a}{2\sqrt{3}}\stackrel{\to }{j}+\frac{a\sqrt{2}}{\sqrt{3}}\stackrel{\to }{k}$

$\left|\begin{array}{ccc}a& 0& 0\\ \frac{a}{2}& \frac{a\sqrt{3}}{2}& 0\\ \frac{a}{2}& \frac{a}{2\sqrt{3}}& \frac{a\sqrt{2}}{\sqrt{3}}\end{array}\right|={a}^{3}×\frac{\sqrt{3}}{2}×\frac{\sqrt{2}}{\sqrt{3}}=\frac{{a}^{3}}{\sqrt{2}}$

Difficulty Level:

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