Question

A compound formed by elements $X$ and $Y$ crystallizes in the cubic structure where $X$ is at the corner of a cube and $Y$ is at the face centre.

If side length is $5\mathring{A}$, the density (in g cm${}^{-3}$) of the solid will be:
(Atomic mass of $X$ and $Y$ are $60$ amu and $90$ amu respectively.)

• A. $4.28$
• B. $4.38$
• C. $3.38$
• D. $3.28$

Answer 1

The correct option is B $4.38$

$Z_{effect}$ of $X$= $8\times \frac{1}{8}=1$

$Z_{effective}$ of $Y$= $6\times \frac{1}{2}=3$

$\rho$= $\frac{Z_A\times M_A+Z_B\times M_B}{N_A\times a^3}$

$\rho$= $\frac{1\times 60+3\times 90}{6.023\times {10}^{-8}\times 125\times {10}^{-24}}$

$\rho$= $4.38$ $gm/c{m}^3$

Hence, the correct option is $B$