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Important Questions on Solid State
1. If the interplanar distance in the crystal is 0.200 nm and only first-order diffraction is observed (sin 8.40 ° = 0.1461), then what will be the wavelength of X-rays that give a diffraction angle (2θ) = 16.80 ° for a crystal?
A. 584 pm
B. 584 nm
C. 58.4 pm
D. 65.8 pm
2. The unit cell edge length in a metal M with BCC arrangement is 400 pm. The metal's atomic radius is:
A. 100 pm
B. 141 pm
C. 173 pm
D. 200 pm
3. Copper is discovered to make up the ccp lattice in an alloy of copper, silver, and gold. The alloy will have the following formula if silver atoms occupy the edge centres and gold is present at the body centre.:
4. An element with a molar mass of 2.7 × 10–2 kg mol–1 forms a cubic unit cell with an edge length of 405 pm. If its density is 2.7 × 103 kg m–3, what is the nature of the cubic unit cell?
D. Simple Cubic Cell
5. There are four formula units in a unit cell of sodium chloride. The unit cell's edge length is 0.564 nm. What is sodium chloride's density?
A. 1.65 g/ml
B. 1.74 g/ml
6. When heated above 916°C, iron changes its crystal structure from a body-centred cubic to a cubic closed-packed structure. First, find the ratio of the density of the bcc crystal to that of the ccp crystal, assuming that the metallic radius of the atom does not vary.
7. In an FCC unit cell, a cube is constructed by combining the centres of all the tetrahedral voids to generate a new cube. The new cube would then have voids as –
A. 1 Tetrahedral void, 1 Octahedral void
B. 1 Tetrahedral void only
C. 8 Tetrahedral voids and 1 Octahedral void
D. 1 Octahedral void only
8. In a closest packed lattice, a tetrahedral site can be created by inserting four spheres of radius ‘R' at alternate corners of the cube. What is the length of the cube's body diagonal?
9. The diameter of the largest sphere that will fit in the void at the centre of a BCC crystal's cube edge with an edge length of a?
A. 0.134 a
B. 0.76 a
C. 0.04448 a
D. 0.098 a
10. Assume you have a collection of glass marbles that are organised in a hexagonal pattern. What would the average density of matter in the collection be if the glass density was .
In a BCC lattice, an atom at the centre of the cube is in contact with atoms at the corners. Thus, the diagonal of the cube is
a3 = 4*atomic radius
Au is at the body centre so Au=1*1=1
Ag is at the edge centre so Ag=1/4*12=3
Cu is having ccp lattice so Cu=8*1/8 +1/2*6=1+3=4
The alloy will have the formula, Au:Ag: Cu=1:3:4 = Cu4Ag3Au
Z=4, M for NaCl=58.5
a=0.564 nm=0.564*10-7 cm
Putting the values, we get D=2.16g/ml
No. of octahedral void = 1 at the centre
No. of tetrahedral voids = 8 × 1/8 = 1 (as each original tetrahedral void will be shared by 8 smaller cubes).
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