Q6 / 77 · NTA Abhyas (JEE Main) 2020 · Chemistry · Solid State

Calcium crystallizes in a face centred cubic unit cell with a = 0.560 nm.  The density of the metal if it contains 0.1% schottky defects would be:

  • Correct answer
    A
    1 .51 gcm -3
  • B
    2 .51 gcm -3
  • C
    15 .1 gcm -3
  • D
    0 .151 gcm -3

Solution

A face centred cubic unit cell contains four atoms. Schottky defect is basically a vacancy defect in ionic solids. Due to Schottky defects, the vacant spaces will increase, resulting in decrease in number of atoms per unit cell.
Thus, number of atoms will reduce to:
Z= 4− 4×0.1 100 =3.996
The density of the metal can be calculated by:
ρ =  Z × M N 0  ×  a 3
Where, M is the molecular mass of calcium = 40 g mol -1
N 0 is the Avogadro number =6.022× 10 23 mol - 1
a is the edge length = 0.560 nm  =  0.56 ×  10 −7 cm
Putting the values in the formula above:
=  3.996 × (40 g  mol −1 ) (0.560 ×  10 −7  cm) 3  × (6.022 ×  10 23   mol −1 )
=1.51 g  cm −3

Hence, the correct answer is option: 'A'.

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