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A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?
- a)Empirical formula of the substance is BaTiO3.
- b)Titanium can be described as occupying octahedral holes in the BaO lattice.
- c)Titanium occupies one-fourth of the total octahedral holes.
- d)There is no restriction for titanium to occupy any of the octahedral holes available to it.
Correct answer is option 'A,B,C'. Can you explain this answer?
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Most Upvoted Answer
A crystalline substance composed of Ba, Ti and O crystallises in a pe...
The correct option is A, B, C.
The perovskite structure is a type of crystal structure where the cations are located at the corners of the unit cell and the anions are located at the face centers of the unit cell. In this case, the Ba ions occupy the corners of the unit cell, and the O ions occupy the face centers of the unit cell. The Ti ions are located in the octahedral holes in the BaO lattice.
The empirical formula of a compound gives the simplest whole number ratio of the elements present in the compound. In this case, since Ba is at the corners and O is at the face centers, the simplest ratio is 1:1 for Ba and O. However, there is also Ti present in the compound, so the empirical formula would be BaTiO3.
In the perovskite structure, the cations are located at the corners of the unit cell, and the anions are located at the face centers of the unit cell. The Ti ions are located in the octahedral holes formed by the O ions. This means that the Ti ions are surrounded by 6 O ions in an octahedral arrangement.
In the perovskite structure, each unit cell contains 1 Ba ion, 1 Ti ion, and 3 O ions. Since the Ti ions are located in the octahedral holes, and there are 6 octahedral holes in each unit cell, the occupancy of Ti in the octahedral holes is one-fourth. This means that each Ti ion occupies one-fourth of an octahedral hole.
In the perovskite structure, there is no restriction on the occupancy of the octahedral holes by the Ti ions. As long as the Ti ions are surrounded by 6 O ions in an octahedral arrangement, they can occupy any of the available octahedral holes.
Therefore, the correct statements are:
a) The empirical formula of the substance is BaTiO3.
b) Titanium can be described as occupying octahedral holes in the BaO lattice.
c) Titanium occupies one-fourth of the total octahedral holes.
Explanation:
The perovskite structure is a type of crystal structure where the cations are located at the corners of the unit cell and the anions are located at the face centers of the unit cell. In this case, the Ba ions occupy the corners of the unit cell, and the O ions occupy the face centers of the unit cell. The Ti ions are located in the octahedral holes in the BaO lattice.
Empirical formula:
The empirical formula of a compound gives the simplest whole number ratio of the elements present in the compound. In this case, since Ba is at the corners and O is at the face centers, the simplest ratio is 1:1 for Ba and O. However, there is also Ti present in the compound, so the empirical formula would be BaTiO3.
Titanium in octahedral holes:
In the perovskite structure, the cations are located at the corners of the unit cell, and the anions are located at the face centers of the unit cell. The Ti ions are located in the octahedral holes formed by the O ions. This means that the Ti ions are surrounded by 6 O ions in an octahedral arrangement.
Titanium occupancy in octahedral holes:
In the perovskite structure, each unit cell contains 1 Ba ion, 1 Ti ion, and 3 O ions. Since the Ti ions are located in the octahedral holes, and there are 6 octahedral holes in each unit cell, the occupancy of Ti in the octahedral holes is one-fourth. This means that each Ti ion occupies one-fourth of an octahedral hole.
Restriction on titanium occupancy:
In the perovskite structure, there is no restriction on the occupancy of the octahedral holes by the Ti ions. As long as the Ti ions are surrounded by 6 O ions in an octahedral arrangement, they can occupy any of the available octahedral holes.
Therefore, the correct statements are:
a) The empirical formula of the substance is BaTiO3.
b) Titanium can be described as occupying octahedral holes in the BaO lattice.
c) Titanium occupies one-fourth of the total octahedral holes.
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Community Answer
A crystalline substance composed of Ba, Ti and O crystallises in a pe...
1) Number of Ba ions per unit cell = 1/8 x 8 = 1
Number of Ti ions per unit cell = 1 x 1 = 1
Number of O ions per unit cell = 1/2 x 6 = 3
Hence, the empirical formula of the substance should be BaTiO3.
Thus, (a) is correct.
2) Titanium ions can be assumed to occupy a hole in the lattice formed by barium and oxide ions. The titanium ions occupy the body centres of the face centred cubic and this is one of the octahedral holes in the fcc lattice.
So, (b) is also true.
3) The octahedral holes at the centres of unit cell constitute just one-fourth of all the octahedral holes in a face centred cubic lattice. Thus, (c) is also true.
4) An octahedral hole at the centre of a unit cell, occupied by titanium ion, has 6 nearest neighbour oxide ions. The other octahedral holes located at the centres of the edges of unit cells have 6 nearest neighbours each, as in case with any octahedral hole, but 2 of the 6 neighbours are barium ions (at unit cell corners terminating the given edge) and 4 oxide ions. The proximity of two cations Ba2+ and Ti4+ would be electrostatically unfavourable. So, titanium cannot occupy all of the octahedral holes and restrictions as stated above exist.
So, (d) is wrong.
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A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer?
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A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer?.
A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer?.
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ample number of questions to practice A crystalline substance composed of Ba, Ti and O crystallises in a perovskite structure. This structure may be described as a cubic lattice, with barium ion occupying corners of the unit cell and oxide ions occupying the face centres of the unit cell. Which of the following statements is/are true?a)Empirical formula of the substance is BaTiO3.b)Titanium can be described as occupying octahedral holes in the BaO lattice.c)Titanium occupies one-fourth of the total octahedral holes.d)There is no restriction for titanium to occupy any of the octahedral holes available to it.Correct answer is option 'A,B,C'. Can you explain this answer? tests, examples and also practice JEE tests.
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