Calculate the density of an element having molar mass $27 \ g \ mol^{-1}$ that forms $fcc$ unit cell. $[a^3 \cdot N_A = 38.5 \ cm^3 \ mol^{-1}]$ (in $g \ cm^{-3}$)

$A$ compound can crystallise in two forms $\alpha$ and $\beta$ which are $fcc$ and $bcc$, respectively. The $\alpha$-form has a side length of $2 \ pm$ and the $\beta$-form has a side length of $4 \ pm$. The ratio of their density $\frac{\rho_\alpha}{\rho_\beta}$ is

Calculate the edge length of $fcc$ unit cell if the radius of the metal atom is $139 \ pm$.

When an electron in an excited atom jumps from the $L$ shell to the $K$ shell,$X$-rays are emitted. These $X$-rays undergo first-order diffraction at an angle of $7.75^{\circ}$ by a crystal with an interplanar spacing of $2.64 \ \mathring{A}$. Calculate the energy difference between the $K$ shell and the $L$ shell. $(\sin \ 7.75^{\circ} = 0.1349)$

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.52 \ \mathring{A}$. Its atomic weight is $39$. Its density (in $kg \ m^{-3}$) will be:

Radius of cation and anion are $2.5 \ \mathring{A}$ and $2.6 \ \mathring{A}$ respectively. If a cubic crystal system is prepared by combination of above cation and anion then edge length of unit cell is ................ $\mathring{A}$ (Take $\sqrt{3} = 1.7$)