sodium metal crystallizes in BCC structure . Its unit cell edge length is 420pm calculate density. (Atomic mass is 23u and NA= 6.022 x 1023 mol -1.)

Number of atoms present in an unit shell, Z = (1/8 X 8 + 1) = 2
Number of mole = Z/N
Mass is then given by (Z/N)XM = ZM/N, where M is molar mass.
Mass = 2X23 g/mol = 46 X 10-3 kg/mol
Volume of the unit shell, V = (420 X 10-12 m)3 = 7.41X10-29 m3
 
Density = mass/volume = (ZM/N)/V = ZM/NV
 
                                       = (46 X 10-3 kg/mol) / (6.022X1023 mol-1)X(7.41X10-29 m3)
                                       = 1.03 X 103 kg/m3
 

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