Physics  >  Solid State Physics, Devices & Electronics  >  Crystal Structure: Assignment

Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics

Document Description: Crystal Structure: Assignment for Physics 2022 is part of Solid State Physics, Devices & Electronics preparation. The notes and questions for Crystal Structure: Assignment have been prepared according to the Physics exam syllabus. Information about Crystal Structure: Assignment covers topics like and Crystal Structure: Assignment Example, for Physics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Crystal Structure: Assignment.

Introduction of Crystal Structure: Assignment in English is available as part of our Solid State Physics, Devices & Electronics for Physics & Crystal Structure: Assignment in Hindi for Solid State Physics, Devices & Electronics course. Download more important topics related with notes, lectures and mock test series for Physics Exam by signing up for free. Physics: Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
1 Crore+ students have signed up on EduRev. Have you?

Q.1. The lattice constant of an Al is 04.05 Å and atomic mass is 26.9 a.m.u. The unit cell structure of Al is face centered cubic (fcc).
(a) How many unit cells are there in an Al foil of 0.1 mm thick and side 20 cm2 ?
(b) If the foil weighs 10 g , than how many atoms are present?

(a) Volume of the foil = 20 x 20 x 0.01 = 4 cm3
Volume of the unit cell = a3
∴ Number of unit cell = Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(b) Number of atoms Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.2. Find the Miller indices of a plane that makes intercept of 4Å,5Å,2Å on the crystallographic axes of an orthorhombic crystal with a : b : c = 2 : 3 : 4.

The lattice parameters are a = 2 Å, b= 3 Å, and c = 4Å
Following the standard procedure of finding the miller indices we have
(i)  intercepts are : 4Å,5Å, 2Å
(ii) Divide by lattice constant : 4/2(=2) (5/3) 2/4(=1/2)
(iii) Reciprocal : (1/2) (3/5) 2
(iv) Clear fraction : 5 6 20
Therefore, the required miller indices of the plane is (5 6 20)


Q.3. A plane makes intercept of 2Å, 3Å, 4Å on the co-ordinate axes of a tetragonal crystal with b : c = 1 : 1.5 . Find the Miller indices.

For tetragonal lattice, a = b¹ c
Therefore, lattice parameters are a =b= 1 and c = 3/2
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.4. Miller indices of a plane is (4 2 1) . If the plane makes intercept of 4Å along the z -axis of an orthorhombic crystal with a : b : c = 4 : 3 : 2 , find the intercept along the x and y-axis.

 Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Given a = 4 Å,  b = 3Å,  c = 2 Å and (h k l) = (4 2 1)
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Now, Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
And Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Therefore, intercept along x - and y- axes are 2 Å and 3 Å


Q.5. Draw the planes Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics and Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics Find the indices of lines common to these two planes.

The planes Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics are drawn together as shown in the figure.
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - PhysicsThe line common to this plane have indices Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.6. In a tetragonal crystal, the lattice parameters are a = b = 2.4Å and c = 1.5Å. Calculate the interplanar spacing between (a) (1 0 0) planes (ii) (1 1 0) planes and (iii) (1 1 1) planes

 Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics 

Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.7. Diamond crystal structure has the cube edge of 3.56Å, calculate
(a) the distance between the nearest neighbours and
(b) the number of atoms per unit volume
(c) density of the diamond (where atomic mass of carbon is 12 a.m.u.)
(d) packing fraction of the crystal

(a) The nearest neighbour distance = 1/4 x ( diagonal length)
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(b) Effective number of atoms in diamond crystal is
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Therefore, number of atoms / unit volume Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics

Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(c) Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(d) Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.8. Calculate the planar density of the plane (1 0 0) in a simple cubic lattice having lattice constant of 2.5Å.

Planer density of the (100 ) plane is
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.9. An element crystallizes into an fcc structure where, 208 gms of the substance contain 4.28 x 1024 atoms. Calculate the length of the unit cell if its density is 7200 kg /m3

Given Crystal structure is fcc, so that neff = 4,
Mass of the one mole of the substance = 208 gm= 0.208 kg,
The number of atoms  = 4.28 x 1024, ρ = 7200kg /m3, a = ?
We know that the number of atoms in 2.208 kg of materials are (= number of atoms/unit cell ) x number of unit cells
or 4.28 x 1024 = 4 x number of unit cell
or Number of unit cells Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Further, Volume of 0.208 kg of materials is
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Therefore, volume of the unit cell (a3) = Volume of 0.208 of materials/Number of unit cells in 0.208kg
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
a = (27 x 10-30)1/3 = 3 x 10-10m = 3Å


Q.10. A unit cell of a NaCl has four formula units. Calculate its density if the side of the unit cell is 5.64 Å. 

Given neff = 4, a = 5.64Å = 5.64 x 10-10m,
Molecular Weight of NaCl = 23 + 35.5 = 58.5 amu, ρ = ?
We know that the density of the crystal material is given by
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.11. Sodium chloride has a fcc structure. Its density is 2.18 x 103 k /m3. The atomic weights of sodium and chlorine are 23amu and 35.5 amu, respectively. Calculate the interatomic separation. 

Given, Molecular Weight of  is NaCl = 23 + 35.5 = 58.5 amu, and density ρ = 2.18x103 kg/m, neff = 8
Since; Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Where, a is the side of the unit cell
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Therefore, the interatomic distance
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.12. The nearest neighbour distance in a silver crystal is 2.87Å. Silver crystallizes in fcc form, determine its density. 

Given; Crystal structure is fcc , so that neff = 4,
Nearest neighbour distance = 2.87Å = 2.87 x 10.-10m,
Atomic Weight. of silver = 107.68 amu, ρ= ?
We know that the nearest neighbour distance in fcc crystal is Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Now the density of crystal material is given by
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.13. Calculate the radius of an atom in a -iron belonging to a bcc structure. The density of the α -iron is 7860 kg/m3 and the atomic weight is 55.85 amu. 

Given ρ = 7860kg/m3, atomic weight= 55.85 amu,
Structure bcc, so that 2, neff n = r = ?
We know that the density of crystal material is given by Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
or Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
a = 2.86 x 10-10m = 2.86Å
Further, in a bcc structure, we have 4r = √3a
Where, r is the radius of the atom
Therefore, Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.14. Calculate the density of atoms in the (1 0 0) , (1 1 0) and (1 1 1) planes of an fcc aluminum whose lattice parameter is 4.05Å.

Given; Planes are (100) , (110) and (111) , crystal structure is fcc, and lattice constant is a = 4.05Å = 4.05x10-10m
We know that the number density of atoms in a crystal plane is given by
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(a) In fcc structure, for plane (100) : neff = 2, A = a2
Therefore, Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(b) In fcc structure, for plane (110) : neff = 2, A = √2a2
Therefore, Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
(c) In fcc structure, for plane (100): Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Therefore, Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.15. Determine the nearest neighbour distance in a bcc and fcc structures when the atomic radius is given as 10Å.

Given Radius of the atom, R = 10Å nearest neighbour distance, say dbcc = ?, dfcc = ?
The nearest neighbour distance in a bcc structure is Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Where, a is the side of the cube and √3a = 4R
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
Similarly, the nearest neighbour distance in an fcc structure is Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics
where a is the side of the cube and √2a = 4R

Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics


Q.16. Calculate the packing factor of a sodium chloride structure. The ionic radii of Naand Clare 0.98Å and 1.81Å, respectively. 

Given the ionic radius of Na+ = 0.98Å, Cl- = 1.81Å, (PF)Nacl = ?
The structure of NaCl is shown in the figure.
The Na+ and Cl- ions touch each other, so that a = 2 (radius of Na+ + radius of Cl-)
= 2 (0.98+ 1.81) = 5.58Å
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics

Therefore, the unit cell volume is V = a3 = (5.58)3(Å)3
Further in the figure, we observe that there are 4 NaCl molecules in the unit cell.
Therefore, according to the definition
Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics 

The document Crystal Structure: Assignment Notes | Study Solid State Physics, Devices & Electronics - Physics is a part of the Physics Course Solid State Physics, Devices & Electronics.
All you need of Physics at this link: Physics
Download as PDF

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!

Related Searches

mock tests for examination

,

Devices & Electronics - Physics

,

Devices & Electronics - Physics

,

Previous Year Questions with Solutions

,

Summary

,

MCQs

,

shortcuts and tricks

,

pdf

,

practice quizzes

,

ppt

,

Objective type Questions

,

Sample Paper

,

Crystal Structure: Assignment Notes | Study Solid State Physics

,

video lectures

,

study material

,

Viva Questions

,

Crystal Structure: Assignment Notes | Study Solid State Physics

,

Crystal Structure: Assignment Notes | Study Solid State Physics

,

Free

,

past year papers

,

Devices & Electronics - Physics

,

Extra Questions

,

Semester Notes

,

Exam

,

Important questions

;