1. If N is the number of tetrahedral voids in a close-packed structure, then the number of octahedral voids is:
a) N/4
b) 4N
c) 2N
d) N/2
Explanation: Tetrahedral voids are formed when triangular voids of one close-packed layer do not overlap while octahedral ones when they overlap. The above relation is valid for both ABAB type(HCP) and ABCABC type(FCC) packing.
2. An octahedral void is present at each edge of the FCC lattice. How much of each of these voids belong to each unit cell?
a) One-eighth
b) One-sixth
c) One-fourth
d) Half
Explanation: In a cubic lattice, each edge is shared by four adjacent cubes. Hence, the octahedral voids present at these edges are equally divided among the four cells.
3. The edge length of an FCC lattice is X times the atomic radius. Value of X is:
a) 2
b) 2√2
c) 4/√3
d) 3/√2
Explanation: In FCC unit cell, the atoms at face diagonal touch each other; thus diagonal is four times the atomic radius(r). Diagonal of the square faces is also equal to √ times of the edge length(a). Hence, √2a = 4r.
4. Density is the ratio of the mass of crystal to its volume. For a perfect FCC metallic crystal, the mass of a unit cell is 4 times M0. M0 is:
a) specific mass
b) molar mass
c) atomic mass
d) none of the mentioned
Explanation: Mass of an ideal FCC metallic crystal unit cell is four times the atomic mass of the metal since there are four atoms per unit cell.
5. A maximum of 74% packing efficiency can be achieved for crystalline solids.
a) True
b) False
Explanation: 74% is the maximum packing efficiency for pure metallic crystals. However, if there are particles of two or more different sizes, greater packing efficiency is possible by filling the tetrahedral and octahedral voids.
6. Which of the following quantities is larger in HCP as compared to FCC if the constituting atoms are similar?
a) Number of particles per unit cell
b) Volume per unit cell
c) Mass per unit cell
d) All of the mentioned
Explanation: An HCP unit cell contains 6 atoms rather than only 4 present in FCC. Also, both structures are assumed to be comprised of similar atoms thus HCP being heavier. However, the HCP unit cell is also larger in volume than an FCC one such that both have same packing efficiency.
7. X-rays have larger wavelengths than which of the following?
a) Gamma rays
b) Beta rays
c) Microwave
d) Visible light
Explanation: Larger wavelengths mean less energy. Only gamma rays have higher energy (or shorter wavelengths) than x-rays. Beta rays are actually streaming of particles and have much less energy than x-rays.
8. X-ray diffraction patterns are used for studying crystal structure of solids because
a) They have very high energy, hence they can penetrate through solids
b) They are electromagnetic radiation, and hence do not interact with matter (crystals)
c) Their wavelengths are comparable to inter-atomic distances
d) Their high frequency enables rapid analysis
Explanation: For diffraction to occur, the obstacle size should be comparable to the wavelength of the incident radiation.
9. For destructive interference to take place, the path difference between the two waves should be:
a) nλ
b) 2nλ
c) (n + 1/2)λ
d) (2n + 1)λ
Explanation: Constructive interference occurs when the phase difference between two interfering waves is an integral multiple of 2π. Also, the ratio of path difference to wavelength equals that of phase difference to 2π.
10. Bragg’s law is not a sufficient condition for diffraction by crystalline solids.
a) True
b) False
Explanation: Atoms present at non-corner positions may result in out-of-phase scattering at Bragg angles.