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Chemistry Question on The solid state

A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass is about 50 g mol−150\, g\, mol^{-1}. What would be the density of the metal (in g cm−3g\, cm^{-3})?

A

3.1

B

6.2

C

9.3

D

12.4

Answer

6.2

Explanation

Solution

a=300 pm, Z=2a = 300\, pm,\, Z = 2 (for bcc unit cell) M=50 g mol−1M = 50 \,g\,mol^{-1} Density, ρ=Z×MNA×a3×10−30g cm−3\rho = \frac{Z\times M}{N_{A} \times a^{3}\times 10^{-30}} g \,cm^{-3} =2×50NA×1023×(300)3×10−30=1006.02×27×10−1= \frac{2\times 50}{N_{A}\times 10^{23}\times \left(300\right)^{3}\times 10^{-30}} =\frac{100}{6.02\times 27\times 10^{-1}} =10006.02×27=6.15 g cm−3≈6.2 g cm−3= \frac{1000}{6.02\times 27} = 6.15\,g\,cm^{-3} \approx 6.2\,g \,cm^{-3}