# An element with molar mass 27 g/mol forms cubic unit cell with edge length of 405 pm

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An element with molar mass 27 g/mol forms cubic unit cell with edge length of 405 pm. If density of the element is 2.7 g/cm3. What is the nature of cubic unit cell?

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Given : Molar mass = M= 27 g m0l_‘

Nature of crystal = cubic unit cell

Edge length = a = 405 pm = 4.05 x 10-8 cm

Density = ρ = 2.7 g cm-3

Nature of unit cell = ?

ρ = $$\frac{m×n}{a^3×N_A}$$

∴ n = $$\frac{ρa^3×N_A}{m}$$ = $$\frac{2.7(4.05×10^{-8})^3×6.022x10^{23}}{27}$$

= 3.997 ≅ 4

Hence the nature of unit cell is face-centred cubic, unit cell

Ans. The nature of cubic unit cell is fcc.