Calculate the molar mass of an element having density $21 \ g \ cm^{-3}$ that forms $fcc$ unit cell $[a^3 \cdot N_{A} = 36 \ cm^3 \ mol^{-1}]$

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 $............ \times 10^{23}$ (Nearest integer).

Calculate the number of atoms in $0.3 \ g$ of a metal if it forms a $bcc$ structure,given that $[\rho \times a^3 = 3 \times 10^{-22} \ g]$.

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centred cubic,and face-centred cubic,then the ratio of radii of the spheres in these systems will be respectively:

Niobium crystallizes in a body-centered cubic $(BCC)$ structure. If the density is $8.55 \ g \ cm^{-3}$,calculate the atomic radius of niobium. (Atomic mass of niobium $M_w = 93 \ g \ mol^{-1}$)

An element crystallizes in an $fcc$ structure with an edge length of $200 \, pm$. If $200 \, g$ of this element contains $24 \times 10^{23}$ atoms,calculate its density in $g \, cm^{-3}$.