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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Solid State

NTA Abhyas 2020 · Chemistry · Solid State

An element crystallizes both in fcc and bcc lattice. If the density...

An element crystallizes both in fcc and bcc lattice. If the density of the element in the two forms is the same, the ratio of unit cell length of fcc to that of bcc lattice is

Options

  1. A(2)1/3( 2{)}^{1 / 3}
  2. B(12)1/3{\left(\dfrac{1}{2}\right)}^{1 / 3}
  3. C(4)1/3( 4{)}^{1 / 3}
  4. D(14)1/3{\left(\dfrac{1}{4}\right)}^{1 / 3}

Correct answer

A. (2)1/3( 2{)}^{1 / 3}

Step-by-step solution

Z=a3×d×NAMZ = \dfrac{a^{3} \times d \times {N}_{A}}{M}
fcc (4) =a13×d×NAM= \dfrac{{a}_{1}^{3} \times d \times {N}_{A}}{M} …(i)
bcc (2) =a23×d×NAM= \dfrac{{a}_{2}^{3} \times d \times {N}_{A}}{M} …(ii)
Dividing equation (i) by (ii)
2=(a1a2)32 = {\left(\dfrac{{a}_{1}}{{a}_{2}}\right)}^{3}
a1a2=21/3\dfrac{{a}_{1}}{{a}_{2}} = {2}^{1 / 3}
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