Question:
Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):
Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):
Updated On: Jul 27, 2022
- $\frac{20}{3} \pi r^{3}$
- $\frac{24}{3}\pi r^{3}$
- $\frac{12}{3}\pi r^{3}$
- $\frac{16}{3}\pi r^{3}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Total number of atoms in face centred cubic unit cell = 4
At corner $=8\times\frac{1}{8}=1$
On faces $=6\times\frac{1}{2}=3$
Total = 4
Total volume $=4\times\frac{4\pi r^{3}}{3}$
$=\frac{16}{3} \pi r^{3}$
Was this answer helpful?
0
0
Top Questions on Unit Cells
- Which of the following statements is incorrect for antibiotics?
- JEE Main - 2023
- Chemistry
- Unit Cells
- Which of the following expressions is correct in case of a CSCl unit cell (edge length, a) ?
- JEE Main - 2023
- Chemistry
- Unit Cells
- The correct option for the number of body centred unit cells in all $14$ types of Bravais lattice unit cells is :
- NEET (UG) - 2021
- Chemistry
- Unit Cells
- Right option for the number of tetrahedral and octahedral voids in hexagonal primitive unit cell are:
- NEET (UG) - 2021
- Chemistry
- Unit Cells
- The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively :
- JEE Main - 2019
- Chemistry
- Unit Cells
View More Questions
Questions Asked in AIEEE exam
- This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. It is not possible to make a sphere of capacity $1$ farad using a conducting material. It is possible for earth as its radius is $6.4 \times 10^6\,m$.
- AIEEE - 2012
- electrostatic potential and capacitance
- A steel wire can sustain $100\, kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
- AIEEE - 2012
- mechanical properties of solids
- The limiting line in Balmer series will have a frequency of (Rydberg constant, $R_{\infty}=3.29\times10^{15}$ cycles/s)
- AIEEE - 2012
- Electromagnetic Spectrum
- Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?
- The ratio of number of oxygen atoms (O) in 16.0 g ozone $(O_3), \,28.0\, g$ carbon monoxide $(CO)$ and $16.0$ oxygen $(O_2)$ is (Atomic mass: $C = 12,0 = 16$ and Avogadro?? constant $N_A = 6.0 x 10^{23}\, mol^{-1}$)
- AIEEE - 2012
- Mole concept and Molar Masses
View More Questions
Concepts Used:
Unit Cells
The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.
The characteristics of a unit cell are:
- The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
- The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).
Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.
Types of Unit Cell:
Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.
- Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
- Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
- Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
- Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
- End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.