An atom forms face centred cubic crystal with density d=8.92 ~g / mL and edge length a=3.6 × 10^ -8 ~cm . The molecular mass of atom in amu is

JIPMER 2018

JIPMER 2018 · Chemistry · Solid State

An atom forms face centred cubic crystal with density d=8.92 ~g /...

An atom forms face centred cubic crystal with density

\mathrm{d}=8.92 \mathrm{~g} / \mathrm{mL}

and edge length

\mathrm{a}=3.6 \times 10^{-8} \mathrm{~cm}

. The molecular mass of atom in amu is

B. $63 amu$

Given, Density

(\mathrm{d})=8.92 \mathrm{~g} / \mathrm{mL}

Edge length

(\mathrm{a})=3.6 \times 10^{-8} \mathrm{~cm} \mathrm{Z}=4

(fcc) The molecular mass of atom in a lattice can be calculated by using the formula

\begin{aligned} & \mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{N}_0 \mathrm{a}^3} \\ & \therefore \quad \mathrm{M}=\frac{\mathrm{dN}_0 \mathrm{a}^3}{\mathrm{Z}} \\ & M=\frac{8.92 \times 6.023 \times 10^{23} \times(3.6)^3 \times\left(10^{-8}\right)^3}{4} \\ & M=62.6 \approx 63 \mathrm{amu} \\ & \end{aligned}