An element with molar mass $2.7 \times 10^{-2} \ kg \ mol^{-1}$ forms a cubic unit cell with edge length of $405 \ pm$. If its density is $2.7 \times 10^3 \ kg \ m^{-3}$, the number of atoms present in one unit cell of it is (Given : $N_{A}=6.023 \times 10^{23} \ mol^{-1}$)

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:

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. $(\sin \ 7.75^{\circ} = 0.1349)$

An element (molar mass $180 \ g \ mol^{-1}$) has a $BCC$ crystal structure with a density of $18 \ g \ cm^{-3}$. What is the edge length of the unit cell?

Calculate the radius of a metal atom if it forms a $bcc$ unit cell having an edge length of $530 \ pm$. (in $pm$)

Aluminium crystallises in a face-centred cubic structure, its atomic radius is $125 \text{ pm}$. What is the edge length of the unit cell (in $\text{pm}$)?