Crystals – MSQ - Physics MCQ

→ Miller indices give us an idea of the direction of the plane i.e. it tells us about the direction of normal to the plane and thus, it remains same for planes which are parallel.
→ [8 4 4] and [4 2 2] are equivalent.
→ If a plane is parallel to one of the coordinate axes, its miller indices for that particular direction is zero which indicates infinite intercept.
The correct answers are: All the parallel equidistant planes have the same miller indices., If the miller indices of two planes are [8 4 4] and [4 2 2], the planes are parallel to each other., A plane parallel to one of the co-ordinate axes has an intercept of infinity.

Packing fraction for simple cubic is 52% and packing fraction for bcc is 68%
The correct answers are: packing fraction for simple cubic structure is 52%, packing fraction for bcc cubic structure is 68%

For simple cubic lattice, volume of unit cell = a³


⇒ lattice constant is  for reciprocal of simple cubic lattice
⇒ volume of unit cell in reciprocal lattice is

The correct answers are: The volume of unit cell of simple cubic lattice is a³ (where a is the edge), The lattice constant is for reciprocal of simple cubic lattice.,
Volume of unit cell in reciprocal lattice is

Total number of atoms/unit cell =

Co-ordinate number = 6 + 3 + 3 = 12 Packing fraction for hep = 74%
The correct answers are: total number of atoms in unit cell are 6, co-ordination number is 12, packing fraction is 74%

packing fraction for fcc is 74% and atoms / unit cell.
The correct answers are: number of atoms in unit cell are 4, packing factor is 74%

whereas  are reciprocal lattice vectors.
Now, 

hence, putting these values, we get

The correct answers are: reciprocal lattice vectors are

For atom at A, there are 4 adjacent neighbours in the x-y plain and 2 neighbours along z-axis, one above and the other below the plane.
Hence, coordination number is 6.
Now  
⇒ lattice point is equal to one.
The correct answers are: Co-ordination number are 6, Number of lattice point is equal to one

By Bragg's law:

The correct answers are:  

The correct answers are: Any diffraction pattern of a crystal is a map of the reciprocal lattice of the crystal, When a crystal is made to rotate both the direct lattice and reciprocal lattice and reciprocaj lattice rotates, The dimension of vectors in a reciprocal lattice is of (length)^-1

Reciprocal lattice of simple cubic is always simple cubic whereas reciprocal lattice of bcc is fee and that of fee is bcc.
The correct answers are: Reciprocal lattice of simple cubic lattice is simple cubic lattice, Reciprocal lattice of bcc is fcc