Paramagnetic substances are those in which the individual atoms, ions or molecules possess a permanent magnetic dipole moment. In the absence of an external magnetic field, the atomic dipoles of paramagnetic substances are as

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.]

The density of a pure substance '$\mathrm{A}$' whose atoms are packed in a cubic-close packed arrangement is $1 \mathrm{g} {\mathrm{cc}}^{-1}$. If $\mathrm{B}$ atoms can occupy tetrahedral void and all the tetrahedral voids are occupied by '$\mathrm{B}$' atoms, what is the density of resulting solid in $\mathrm{g} {\mathrm{cc}}^{-1}?$ $[$Atomic mass $\left(\mathrm{A}\right)=30 \mathrm{g} {\mathrm{mol}}^{-1}$ and atomic mass $\left(\mathrm{B}\right)=50 \mathrm{g} {\mathrm{mol}}^{-1}]$.

A metal cystallises into two cubic phases, f.c.c and b.c.c. whose unit-cell lengths are $3.5 {\mathrm{A}}^{°}$ and $3.0 \mathrm{A}°$. Calculate the ratio of densities of f.c.c. and b.c.c.

Give answer after multiplying with 100 and rounding off to the nearest integer value.