Aluminum crystallizes in a cubic close-packed structure. If its metallic radius is $125 \ pm$, what is the side length of the unit cell?

Solid $AB$ has $NaCl$ type structure. If the radius of $A^{+}$ and $B^{-}$ are $0.5 \ \mathring{A}$ and $1.5 \ \mathring{A}$ respectively and the formula mass of $AB$ is $48 \ g/mol$,what is the density of $AB$ solid? $(N_A = 6 \times 10^{23})$

An $X^{+}Y^{-}$ ionic compound has a $bcc$ structure. The distance between two nearest ions is $1.73 \ \mathring{A}$. What is the edge length of the unit cell?

Find the radius of a metal atom in a $bcc$ unit cell having an edge length of $450 \ pm$. (in $pm$)

Calculate the density of a metal having a molar mass of $210 \ g \ mol^{-1}$ that forms a simple cubic unit cell. $(a^3 \cdot N_{A} = 21.5 \ cm^3 \ mol^{-1})$ (in $g \ cm^{-3}$)

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