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Question

Chemistry Question on The solid state

A metal has a fccfcc lattice. The edge length of the unit cell is 404 pm404\, pm. The density of the metal is 2.72 g2.72\,g cm−3cm^{-3}. The molar mass of the metal is :

A

20g mol−120 g \, mol^{-1}

B

40g mol−140 g \, mol^{-1}

C

30g mol−130 g \, mol^{-1}

D

28g mol−128 g \, mol^{-1}

Answer

28g mol−128 g \, mol^{-1}

Explanation

Solution

ρ=Z×MNA×a3\rho = \frac{Z \times M}{N_{A } \times a^{3}} for FCC, Z = 4
a = 404 pm = 404×10−10404 \times 10^{-10} cm.
2.72=4×M6.02×1023×(404×10−10)32.72 = \frac{ 4\times M}{6.02 \times10^{23} \times\left(404 \times10^{-10}\right)^{3}}