Questions & Answers

Question

Answers

[ Consider the atoms to be within the parallel planes if their centres are on or within the two parallel planes.]

Answer
Verified

- We will first draw the diagram:

- Here, we know that the distance given in between parallel planes is $\frac{C}{2}$$\frac{C}{2}$\[\begin{align}

& \left( OM \right)+\left( RO \right)={{\left( MR \right)}^{2}} \\

& \left( \frac{C}{2} \right)+\left( \frac{2r}{\sqrt{3}} \right)={{\left( 2r \right)}^{2}} \\

\end{align}\]

- Now, by solving this equation we get :

\[\begin{align}

& {{\left( \frac{C}{2} \right)}^{2}}=\frac{8{{r}^{2}}}{3} \\

& C=4r\sqrt{\frac{2}{3}} \\

\end{align}\]

Now, we have to find the height C,

\[H(C)=4r\sqrt{\frac{2}{3}}\]

- We can also write this equation as:

\[or,\text{ }H(C)=2a\sqrt{\frac{2}{3}}\]

- Now, the distance between two layers that is A and B= $\frac{C}{2}=\sqrt{\frac{8}{3}}(r)=\sqrt{\frac{2}{3}}(2r)$

- The given distance between two imaginary plane=$13\sqrt{\frac{2}{3}}(r)$

Now, let K number of imaginary planes=

\[\begin{align}

& K\times \frac{\sqrt{2}}{\sqrt{3}}\left( r \right) \\

& =13\sqrt{\frac{2}{3}}\left( r \right) \\

& K\approx 6.5 \\

& K=7 \\

\end{align}\]

\[\]