Embibe Experts Solutions for Chapter: Solid State, Exercise 3: Level 3

An element $\mathrm{X}$(atomic weight$=125$) crystallizes in a simple cubic lattice. The diameter of the largest atom $\mathrm{A}$ which can be placed in the void of the lattice of $‘\mathrm{X}’$ without disturbing its unit cell is $366 \mathrm{pm}.$ The density of pure element $\mathrm{X}$ in $\mathrm{g}/{\mathrm{cm}}^3$ is

A metal crystallizes in two cubic phases FCC and BCC, whose unit cell lengths are $3.5$ and $3.0 \mathrm{\AA }$, respectively. The ratio of their densities is

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.

Aluminum crystallizes in a face-centered cubic unit cell with a density of crystal $2.7 \mathrm{g}/{\mathrm{cm}}^3$ and an edge length of $4.094 \mathrm{\AA }.$ Calculate the approximate Avogadro constant in multiple of ${10}^{23}$