Density of crystals

The density (in $\mathrm{g\,cm^{-3}}$) of the metal which forms a cubic close packed (ccp) lattice with an axial distance (edge length) equal to 400 pm is _____.

Use: Atomic mass of metal $= 105.6$ amu and Avogadro's constant $= 6\times10^{23}\ \mathrm{mol^{-1}}$

Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length $L_x$, body-centred cubic (bcc) unit cell of edge length $L_y$, and simple cubic unit cell of edge length $L_z$, respectively.

If $r_z = \dfrac{\sqrt3}{2}r_y$; $r_y = \dfrac{8}{\sqrt3}r_x$; $M_z = \dfrac32 M_y$ and $M_z = 3M_x$, then the correct statement(s) is(are)

[Given: $M_x$, $M_y$, and $M_z$ are molar masses of metals x, y, and z, respectively. $r_x$, $r_y$, and $r_z$ are atomic radii of metals x, y, and z, respectively.]

The distance between $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ ions in solid NaCl of density 43.1 g cm$^{-3}$ is ______ $\times10^{-10}$ m. (Nearest Integer)

(Given : $N_A=6.02\times10^{23}\ \mathrm{mol^{-1}}$)

An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm$^{-3}$. The number of atoms present in 300 g of the element X is ______.

Given : Avogadro constant, $N_A=6.0\times10^{23}$ mol$^{-1}$.

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm$^{-3}$. The number of atoms present in 180 g of the element is ______ $\times10^{23}$. (Nearest integer)

Metal M crystallizes into a fcc lattice with the edge length of $4.0\times10^{-8}$ cm. The atomic mass of the metal is ______ g/mol. (Nearest integer)

(Use : $N_A=6.02\times10^{23}$ mol$^{-1}$, density of metal, M = 9.03 g cm$^{-3}$)

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is $8\ \mathrm{g\,cm^{-3}}$, then the number of atoms present in 256 g of the crystal is $N \times 10^{24}$. The value of $N$ is