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 of density 7.5 × 1 0 ^ 3 kg m^ - 3 has an fcc crystal...

A metal of density 7.5×1037.5 \times 1{0}^{3} kg m−3m^{- 3} has an fcc crystal structure with lattice parameter a = 400 pm. Calculate the number of unit cells present in 0.015 kg of the metal.

Options

  1. A6.250×10226.250 \times 1{0}^{22}
  2. B3.125×10233.125 \times 1{0}^{23}
  3. C3.125×10223.125 \times 1{0}^{22}
  4. D1.563×10221.563 \times 1{0}^{22}

Correct answer

C. 3.125×10223.125 \times 1{0}^{22}

Step-by-step solution

V1=a3=(400×10−12m)3=64×10−30m3{V}_{1} = a^{3} = ( 400 \times 1{0}^{- 12}m{)}^{3} = 64 \times 1{0}^{- 30}m^{3}
V2=massdensity=0.015kg7.5×10−3m−3{V}_{2} = \dfrac{mass}{density} = \dfrac{0.015kg}{7.5 \times 1{0}^{- 3}m^{- 3}}
=2×10−6m3= 2 \times 1{0}^{- 6}m^{3}
where V1{V}_{1} is the volume of the unit cell and V2{V}_{2} that of the metal sample.
So number of unit cell =TotalvolumeVolumeofunitcell=2×10−6m364×10−30m3= \dfrac{Total\text{volume}}{\text{Volumeofunitcell}} = \dfrac{2 \times 1{0}^{- 6}m^{3}}{64 \times 1{0}^{- 30}m^{3}}
=3.125×1022= 3.125 \times 1{0}^{22}
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