PROBLEMS

Copper has a face-centred cubic structure with a unit-cell edge length of $3.61 \mathrm{\AA }$. What is the size of the largest atom (in pm), which could fit into the interstices of the copper lattice without distorting it?

[Hint: Calculate the radius of the smallest circle in the figure.]

A face-centred cubic solid of an element (atomic mass $60$) has a cube edge of $4.0 \mathrm{\AA }$ Calculate its density.

A metallic element has a simple cubic lattice. Each edge of the unit cell is $3.0 \mathrm{\AA }.$ The density of the metal is $8.5 \mathrm{g}/\mathrm{cc}.$ How many unit cells will be present in $50 \mathrm{g}$ of the metal?

(Give your answer in multiples of ${10}^{23}$.)

Two capillary tubes of radius $0.2$ and $0.1 \mathrm{mm}$ were placed into a sample of liquid ${\mathrm{H}}_2{\mathrm{O}}_2.$ The difference between the heights of the liquid in the tubes is $5.50 \mathrm{cm}$. Given that density $\left({\mathrm{H}}_2{\mathrm{O}}_2\right)=1.41 \mathrm{g} {\mathrm{cm}}^{-3},$ If $\mathrm{\gamma }$$=\mathrm{A}\times {10}^{-3} \mathrm{N}/\mathrm{m}$, then find $\mathrm{A}$.

$50$ drops each of water and ether, weigh $3.64 \mathrm{g}$ and $0.852 \mathrm{g}$, respectively. Determine the surface tension of ether, if the surface tension of water is $72.75 \mathrm{dyne} {\mathrm{cm}}^{-1}$.

Give an answer to the nearest integer value.

The number of drops of water, counted in the falling-drop method using a stalagmometer is $100,$ whereas the number of drops of an organic liquid is $280$. The surface tension of an organic liquid is $\mathrm{Z}\times {10}^{-2} \mathrm{N} {\mathrm{m}}^{-1}$, if the surface tension of water is $0.07275 \mathrm{N} {\mathrm{m}}^{-1}$ and the densities of water and the organic liquid are $0.998\times {10}^3\mathrm{kg} {\mathrm{m}}^{-3}$ and $0.755\times {10}^3\mathrm{kg} {\mathrm{m}}^{-3}$, respectively. Find the value of $\mathrm{Z}$.

Round-off and give your answer to the nearest integer value.

The viscosity of olive oil at $293 \mathrm{K}$ is $0.084 \mathrm{N} {\mathrm{m}}^{-2} \mathrm{s}$ and density is $1.1\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. How long will it take to pass through a viscometer, if water under the same conditions takes $30$ seconds ? $\left({\mathrm{\eta }}_{{\mathrm{H}}_2\mathrm{O}}=0.00101 \mathrm{N} {\mathrm{m}}^{-2} \mathrm{s}, {\mathrm{d}}_{{\mathrm{H}}_2\mathrm{O}}=0.998\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}\right)$

An organic liquid rises $1.0 \mathrm{cm}$ in a capillary tube of radius $\mathrm{r}.$ How much will it rise if, the cross-sectional area of the tube is halved?