Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Solid State

NTA Abhyas 2020 · Chemistry · Solid State

A metal crystallizes into two cubic systems-face centred cubic...

A metal crystallizes into two cubic systems-face centred cubic (fcc) and simple cubic (SC), whose unit cell lengths are 4.5\text{4}\text{.5} and 1.5Ao\text{1}\text{.5}\overset{o}{A} respectively. Calculate the ratio of densities of face centred cubic and Simple cubic.

Options

  1. A0.15
  2. B1.44
  3. C2.25
  4. D3.25

Correct answer

A. 0.15

Step-by-step solution

face centred cubic unit cell length =4.5Ao\text{=}\text{4}\text{.5}\overset{o}{A}
Simple cubic unit cell length =1.5Ao\text{=}\text{1}\text{.5}\overset{o}{A}
Density in face centred cubic =n1×atomicweightV1×Avogadronumber= \dfrac{{n}_{1} \times atomicweight}{{V}_{1} \times Avogadronumber}
Density simple cubic (SC) =n2×atomicmassV2×Avogardronumber= \dfrac{{n}_{2} \times atomicmass}{{V}_{2} \times Avogardronumber}
DfccDbcc=n1n2×V2V1\dfrac{{D}_{fcc}}{{D}_{bcc}} = \dfrac{{n}_{1}}{{n}_{2}} \times \dfrac{{V}_{2}}{{V}_{1}}
n1{n}_{1} for face centred cubic = 4; Also V1=a3=(4.5×10−8)3{V}_{1} = a^{3} = {\left(4.5 \times {10}^{- 8}\right)}^{3}
n2{n}_{2} for simple cubic = 1; Also V2=a3=(1.5×10−8)3{V}_{2} = a^{3} = {\left(1.5 \times {10}^{- 8}\right)}^{3}
DfccDsc=4×(1.5×10−8)31×(4.5×10−8)3=0.15\dfrac{{D}_{fcc}}{{D}_{sc}} = \dfrac{4 \times ( 1.5 \times 1{0}^{- 8}{)}^{3}}{1 \times ( 4.5 \times 1{0}^{- 8}{)}^{3}} = 0.15
Practice Solid State on Quantrex Academy →

More from Solid State

The density (in g cm^ -3 ) of the metal which forms a cubic close packed (ccp) lattice… JEE Advanced 2025Atoms of metals x, y and z form face-centred cubic (fcc) unit cell of edge length L _ x… JEE Advanced 2023Which of the following expressions is correct in case of a CsCl unit cell (edge length… JEE Main 2023Sodium metal crystallises in a body centred cubic lattice with unit cell edge length of… JEE Main 2023An atomic substance A of molar mass 12g mol ^ – 1 has a cubic crystal structure with edge… JEE Main 2023The correct relationships between unit cell edge length ‘ a ’ and radius of… JEE Main 2023Number of crystal systems from the following where body centred unit cell can be found… JEE Main 2023A compound is formed by two elements X and Y . The element Y forms cubic close packed… JEE Main 2023 Full Solid State list All NTA Abhyas JEE Main PYQs