chemistry : class12 NaCl Crystal Structure : Ionic solids : Solid State MCQ Questions and Answers
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NaCl Crystal Structure
MCQ questions and answers.
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MCQ Questions
1. In the ideal NaCl crystal structure, chloride ions form a face-centred cubic lattice. If the unit-cell edge length is a, what is the shortest Na+–Cl− distance?
A.
a/4
B.
a/2
C.
a/√2
D.
a
Correct Answer:
a/2
Explanation:
In the NaCl structure, Na+ ions occupy all octahedral holes of the fcc chloride-ion lattice. A chloride ion at a corner is nearest to a sodium ion at the edge centre, giving a separation of a/2.
2. A conventional unit cell of NaCl contains chloride ions at the face-centred cubic positions and sodium ions at all octahedral sites. What is the number of NaCl formula units per unit cell?
A.
1
B.
2
C.
4
D.
8
Correct Answer:
4
Explanation:
The fcc arrangement contributes 4 chloride ions per unit cell, while the four octahedral sites occupied by Na+ also give 4 sodium ions. Therefore, the unit cell contains 4 NaCl formula units.
3. Which set of fractional coordinates represents the four Na+ ions in one conventional NaCl unit cell when Cl− ions occupy the fcc lattice points?
A.
(0,0,0), (1/2,1/2,0), (1/2,0,1/2), (0,1/2,1/2)
B.
(1/2,1/2,1/2), (1/2,0,0), (0,1/2,0), (0,0,1/2)
C.
(0,0,0), (1/2,1/2,1/2), (1/4,1/4,1/4), (3/4,3/4,3/4)
D.
(1/4,1/4,1/4), (1/4,3/4,3/4), (3/4,1/4,3/4), (3/4,3/4,1/4)
Explanation:
For an fcc lattice of Cl− ions at corners and face centres, the octahedral sites are the body centre and the six edge centres. The edge-centre sites are shared between cells, giving four Na+ ions in total.
4. For an NaCl-type crystal, the ionic radii are r+ and r−. Assuming the ions are in contact along the cube edge, which relation gives the unit-cell edge length a?
A.
a = r+ + r−
B.
a = 2(r+ + r−)
C.
a = √2(r+ + r−)
D.
a = 4(r+ + r−)
Correct Answer:
a = 2(r+ + r−)
Explanation:
Along a cube edge in the NaCl structure, a cation and an anion touch through a sequence of two cation–anion contacts. Thus, half the edge equals r+ + r−, so a = 2(r+ + r−).
5. The radius-ratio condition for a cation to occupy an octahedral site without causing anion overlap in the ideal NaCl structure is best represented by which limiting value?
A.
r+/r− = 0.155
B.
r+/r− = 0.225
C.
r+/r− = 0.414
D.
r+/r− = 0.732
Correct Answer:
r+/r− = 0.414
Explanation:
Na+ in the NaCl structure has octahedral coordination. The minimum radius ratio for octahedral coordination is √2 − 1, approximately 0.414.
6. In the NaCl structure, each Na+ ion is surrounded by how many nearest-neighbour Cl− ions, and what is the corresponding coordination number of Cl−?
A.
4 and 4
B.
4 and 6
C.
6 and 4
D.
6 and 6
Correct Answer:
6 and 6
Explanation:
Each Na+ occupies an octahedral hole and is surrounded by six Cl− ions along the positive and negative directions of the three coordinate axes. The structure is reciprocal, so each Cl− is likewise coordinated by six Na+ ions.
7. If the lattice parameter of NaCl is 5.64 Å, what is the nearest-neighbour Na+–Cl− separation?
A.
1.41 Å
B.
2.82 Å
C.
3.99 Å
D.
5.64 Å
Correct Answer:
2.82 Å
Explanation:
The nearest Na+–Cl− distance in the NaCl structure is a/2. Substituting a = 5.64 Å gives 5.64/2 = 2.82 Å.
8. In an NaCl-type unit cell, the shortest distance between two Cl− ions is related to the edge length a by which expression?
A.
a/2
B.
a/√2
C.
√2a
D.
a
Correct Answer:
a/√2
Explanation:
The Cl− ions occupy an fcc lattice. The nearest chloride ions lie along a face diagonal, with separation equal to half the face diagonal: (a√2)/2 = a/√2.
9. A hypothetical NaCl crystal has molar mass M and cubic lattice parameter a. Using Z = 4 for the NaCl structure, which expression gives its theoretical density?
A.
M/(N_Aa^3)
B.
2M/(N_Aa^3)
C.
4M/(N_Aa^3)
D.
N_Aa^3/(4M)
Correct Answer:
4M/(N_Aa^3)
Explanation:
The NaCl unit cell contains four formula units. Its mass is 4M/N_A and its volume is a^3, so the density is 4M/(N_Aa^3), with consistent units.
10. Which statement correctly describes the relationship between the NaCl structure and the octahedral holes of an fcc anion lattice?
A.
Na+ occupies one-half of the tetrahedral holes, giving four-coordinate ions
B.
Na+ occupies all octahedral holes, giving six-coordinate ions
C.
Na+ occupies all tetrahedral holes, giving eight-coordinate ions
D.
Na+ occupies only the cubic hole at the body centre, giving one-coordinate ions
Correct Answer:
Na+ occupies all octahedral holes, giving six-coordinate ions
Explanation:
An fcc array of Cl− ions contains four octahedral holes per unit cell: one body-centre site and twelve edge-centre sites counted as four. Na+ fills all of them, producing the six-six coordination characteristic of NaCl.
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