Metal $M$ crystallizes in $fcc$ lattice. If the edge length of the unit cell is $4.077 \times 10^{-8} \ cm$ and the density is $10.5 \ g \ cm^{-3}$,the atomic mass of the metal is:

Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

The distance between two parallel $(111)$ planes in a crystal with an edge length of $300 \, pm$ is ................ $pm$.

How many unit cells are present in $39 \ g$ of potassium that crystallizes in a body-centred cubic structure? $[At. \ wt. \ of \ K = 39]$

$A$ metal crystallises in two phases,one as $fcc$ and other as $bcc$ with unit cell edge lengths of $3.5 \ \mathring{A}$ and $3.0 \ \mathring{A}$ respectively. The ratio of density of $fcc$ and $bcc$ phases approximately is

In a $NaCl$ crystal,the distance between $Na^+$ and $Cl^-$ ions is $2.814 \ \overset{\circ}{A}$ and the density of the crystal is $2.167 \ g/cm^3$. Calculate the value of Avogadro's number $(N_A)$.