Calculate the number of atoms present in a unit cell of an element having molar mass $190 \ g \ mol^{-1}$ and density $20 \ g \ cm^{-3}$. Given that $[a^3 \cdot N_A = 38 \ cm^3 \ mol^{-1}]$.

The diffraction pattern of a crystalline solid gave a peak at $2 \theta = 60^{\circ}$. What is the distance (in $cm$) between the layers which gave this peak? ($\lambda$ of $X$-rays is $1.54 \mathring{A}$) ($\sin 30^{\circ} = 0.5$,$\sin 60^{\circ} = 0.866$; $n = 1$)

At $100\, ^\circ C$,copper $(Cu)$ has $FCC$ unit cell structure with cell edge length $x\, \mathring{A}$. What is the approximate density of $Cu$ (in $g\, cm^{-3}$) at this temperature? [Atomic mass of $Cu = 63.55\, u$]

Calculate the volume of the unit cell for an element having a molar mass of $56 \ g \ mol^{-1}$ that forms $bcc$ unit cells. $\left[\rho \cdot N_{A} = 4.8 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$

Sodium metal crystallises in a body-centred cubic $(BCC)$ lattice with an edge length of $x \ \mathring{A}$. If the radius of the sodium atom is $1.86 \ \mathring{A}$,the value of $x$ is:

$A$ diatomic molecule $X_2$ has a body-centred cubic (bcc) structure with a cell edge of $300 \ pm$. The density of the molecule is $6.17 \ g \ cm^{-3}$. The number of molecules present in $200 \ g$ of $X_2$ is (Avogadro constant $N_A = 6 \times 10^{23} \ mol^{-1}$) (in $N_A$)