Solid State - Result Question 40
40. The crystal $A B$ (rock salt structure) has molecular weight $6.023 $ $y $ $u$. Where, $y$ is an arbitrary number in $u$. If the minimum distance between cation and anion is $y^{1 / 3} $ $nm$ and the observed density is $20$ $ kg / m^{3}$. Find the (i) density in $kg / m^{3}$ and (ii) type of defect.
$(2004,2 M)$
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Solution:
- (i) In rock salt like crystal $A B$, there are four $A B$ units per unit cell. Therefore, density $(d)$ is
$ \begin{aligned} d & =\dfrac{4 \times 6.023 y}{6.023 \times 10^{23} \times 8 y \times 10^{-27}} \\ & \quad\left[\because a=2 y^{1 / 3} \hspace{2mm}nm=2 y^{1 / 3} \times 10^{-9} m\right] \\ & =5 \times 10^{3} \hspace{2mm}g / m^{3}=5 \hspace{2mm}kg / m^{3} \end{aligned} $
(ii) Since, observed density is greater than expected, theoretical density, there must be some excess metal occupying interstitial spaces. This type of defect is known as metal excess defect.
BETA
