Q24 / 77 · NTA Abhyas (JEE Main) 2020 · Chemistry · Solid State

A metal crystallizes into two cubic systems-face centred cubic (fcc) and simple cubic (SC), whose unit cell lengths are 4.5 and 1.5  A o respectively. Calculate the ratio of densities of face centred cubic and Simple cubic.

  • Correct answer
    A
    0.15
  • B
    1.44
  • C
    2.25
  • D
    3.25

Solution

face centred cubic unit cell length = 4.5  A o
Simple cubic unit cell length = 1.5  A o
Density in face centred cubic =n1×atomic   weightV1×Avogadro   number
Density simple cubic (SC) =n2×atomic    massV2×Avogardro   number
DfccDbcc=n1n2×V2V1
n1 for face centred cubic = 4; Also V1=a3=4.5×10-83
n2 for simple cubic = 1; Also V2=a3=1.5×10-83
DfccDsc=4×(1.5×10-8)31×(4.5×10-8)3=0.15

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

More Solid State Questions