chemistry : class12 Frenkel Defects : Ionic solids : Solid State MCQ Questions and Answers
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Frenkel Defects
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MCQ Questions
1. In a crystal containing N formula units of an ionic solid, a fraction x of the cations leave their normal lattice sites and occupy interstitial sites, producing Frenkel defects. What are the numbers of cation vacancies and interstitial cations, respectively?
A.
xN and xN
B.
xN and (1 − x)N
C.
(1 − x)N and xN
D.
2xN and xN
Correct Answer:
xN and xN
Explanation:
Each cation displaced from its normal site creates exactly one cation vacancy and one interstitial cation. Therefore, both numbers are xN.
2. A perfect ionic crystal has mass M and volume V. If Frenkel defects are introduced without any ions leaving the crystal or any significant volume change occurring, which conclusion about its density is correct?
A.
The density increases because interstitial ions add extra particles
B.
The density decreases because normal lattice sites become vacant
C.
The density remains essentially unchanged because ions are only displaced internally
D.
The density becomes zero at sufficiently high Frenkel-defect concentration
Correct Answer:
The density remains essentially unchanged because ions are only displaced internally
Explanation:
In a Frenkel defect, an ion moves from its normal lattice position to an interstitial position within the same crystal. Since the mass and approximately the volume remain unchanged, the density remains essentially unchanged.
3. Which microscopic process represents the formation of a Frenkel defect in an ionic solid?
A.
A cation leaves the crystal completely, creating a cation vacancy
B.
An anion leaves its normal site and occupies an interstitial site
C.
A cation leaves its normal lattice site and occupies a nearby interstitial site
D.
A cation and an anion simultaneously exchange their lattice positions
Correct Answer:
A cation leaves its normal lattice site and occupies a nearby interstitial site
Explanation:
A Frenkel defect is a dislocation defect in which a usually small cation is displaced from its regular lattice site into an interstitial position, producing a vacancy-interstitial pair.
4. An ionic solid contains 4.00 × 10^22 cations, and 0.50% of them participate in Frenkel defects. Assuming each displaced cation forms one defect pair, how many cation vacancies are present?
A.
2.00 × 10^17
B.
2.00 × 10^20
C.
8.00 × 10^20
D.
4.00 × 10^22
Correct Answer:
2.00 × 10^20
Explanation:
The number of displaced cations, and hence the number of cation vacancies, is 0.005 × 4.00 × 10^22 = 2.00 × 10^20.
5. Why does formation of a Frenkel defect generally preserve the electrical neutrality of an ionic crystal?
A.
Only neutral atoms are displaced from their sites
B.
A charged cation is removed from the crystal and replaced by an electron
C.
The displaced ion remains within the crystal, so its charge is still present as an interstitial ion
D.
The vacancy automatically acquires a charge equal to that of an anion
Correct Answer:
The displaced ion remains within the crystal, so its charge is still present as an interstitial ion
Explanation:
The cation is not lost from the crystal; it merely changes position. Its original site becomes vacant, while the same positive charge appears at an interstitial site, preserving overall neutrality.
6. Which combination of structural characteristics most favors the formation of Frenkel defects?
A.
Large cations, small anions, and very compact packing
B.
Small cations, relatively large interstitial spaces, and sufficient mobility of the cation
C.
Equal-sized ions with no available interstitial positions
D.
Large anions occupying interstitial sites while cations remain fixed
Correct Answer:
Small cations, relatively large interstitial spaces, and sufficient mobility of the cation
Explanation:
Frenkel defects are favored when a comparatively small cation can leave its normal site and fit into an interstitial position without excessive lattice distortion.
7. If 1 in every 200 cations of an ionic crystal occupies an interstitial site due to Frenkel disorder, what fraction of the cation sites is vacant?
A.
1/400
B.
1/200
C.
199/200
D.
2/200
Correct Answer:
1/200
Explanation:
Every interstitial cation originates from one normal cation site. Thus, one cation vacancy accompanies every interstitial cation, making the vacant-site fraction equal to 1/200.
8. A crystal develops Frenkel defects while its anion sublattice remains undisturbed. Which change occurs in the cation distribution?
A.
The number of cations decreases, and the number of anions increases
B.
The number of normal-site cations decreases by the same amount that interstitial cations increase
C.
The number of normal-site cations and interstitial cations both increase
D.
The cations are replaced by an equal number of anion vacancies
Correct Answer:
The number of normal-site cations decreases by the same amount that interstitial cations increase
Explanation:
A Frenkel defect transfers cations from regular lattice sites to interstitial sites. Therefore, normal-site cations decrease by exactly the number of interstitial cations formed.
9. In a Frenkel-defective crystal, the concentration of interstitial cations is measured as 3.0 × 10^19 cm−3. Assuming every interstitial cation is paired with one vacancy, what is the concentration of cation vacancies?
A.
1.0 × 10^19 cm−3
B.
3.0 × 10^19 cm−3
C.
6.0 × 10^19 cm−3
D.
9.0 × 10^38 cm−6
Correct Answer:
3.0 × 10^19 cm−3
Explanation:
Each Frenkel defect produces one interstitial cation and one vacancy. Therefore, their concentrations are equal.
10. Which observation most directly supports the presence of Frenkel defects rather than the complete removal of ions from an ionic crystal?
A.
The crystal becomes electrically neutral only after external electrons are supplied
B.
The crystal shows vacant cation sites together with cations located at interstitial positions, without a change in overall composition
C.
The crystal contains an excess of anions and no cation vacancies
D.
The crystal loses mass in exact proportion to the number of vacant sites
Correct Answer:
The crystal shows vacant cation sites together with cations located at interstitial positions, without a change in overall composition
Explanation:
The defining feature of a Frenkel defect is the coupled presence of a cation vacancy and an interstitial cation, while the ions remain within the crystal and the composition is unchanged.
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