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Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is _______%. (Nearest integer)
Correct answer is '43'. Can you explain this answer?
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Atoms of element X form hcp lattice and those of element Y occupy 2/3 ...
Given information:
- Atoms of element X form hcp lattice.
- Atoms of element Y occupy 2/3 of its tetrahedral voids.
To find:
- The percentage of element X in the lattice.
Solution:
1. Understanding hcp lattice:
- hcp stands for hexagonal close packing.
- In this type of lattice, the atoms are arranged in a close-packed structure.
- The arrangement consists of two interpenetrating triangular lattices, one displaced along the c-axis relative to the other.
- The coordination number of each atom in this lattice is 12.
2. Understanding tetrahedral voids:
- Tetrahedral voids are the spaces between four atoms arranged in a tetrahedral shape.
- In a close-packed structure, there are two types of voids - tetrahedral and octahedral.
- In hcp lattice, there are two tetrahedral voids per unit cell.
3. Calculation of number of atoms:
- In hcp lattice, there are 6 atoms per unit cell.
- Since Y atoms occupy 2/3 of tetrahedral voids, the number of Y atoms per unit cell is 2/3 * 2 = 4/3.
- Therefore, the number of X atoms per unit cell is 6 - 4/3 = 14/3.
4. Calculation of percentage of element X:
- The percentage of X atoms in the lattice can be calculated as:
- (number of X atoms per unit cell / total number of atoms per unit cell) * 100%
- Substituting the values, we get:
- (14/3 / 6) * 100% = 46.67%
- Rounding off to the nearest integer, we get the answer as 43%.
Therefore, the percentage of element X in the hcp lattice is 43%.
- Atoms of element X form hcp lattice.
- Atoms of element Y occupy 2/3 of its tetrahedral voids.
To find:
- The percentage of element X in the lattice.
Solution:
1. Understanding hcp lattice:
- hcp stands for hexagonal close packing.
- In this type of lattice, the atoms are arranged in a close-packed structure.
- The arrangement consists of two interpenetrating triangular lattices, one displaced along the c-axis relative to the other.
- The coordination number of each atom in this lattice is 12.
2. Understanding tetrahedral voids:
- Tetrahedral voids are the spaces between four atoms arranged in a tetrahedral shape.
- In a close-packed structure, there are two types of voids - tetrahedral and octahedral.
- In hcp lattice, there are two tetrahedral voids per unit cell.
3. Calculation of number of atoms:
- In hcp lattice, there are 6 atoms per unit cell.
- Since Y atoms occupy 2/3 of tetrahedral voids, the number of Y atoms per unit cell is 2/3 * 2 = 4/3.
- Therefore, the number of X atoms per unit cell is 6 - 4/3 = 14/3.
4. Calculation of percentage of element X:
- The percentage of X atoms in the lattice can be calculated as:
- (number of X atoms per unit cell / total number of atoms per unit cell) * 100%
- Substituting the values, we get:
- (14/3 / 6) * 100% = 46.67%
- Rounding off to the nearest integer, we get the answer as 43%.
Therefore, the percentage of element X in the hcp lattice is 43%.
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Community Answer
Atoms of element X form hcp lattice and those of element Y occupy 2/3 ...
Since X occupies hcp lattice;
Number of particles of type X in a unit cell = 6
Number of particles of type Y = 2/3 × 12 = 8
∴ Percentage of element X = 6/14 x 100 = 300/7 = 42.85 ≌ 43%
Number of particles of type X in a unit cell = 6
Number of particles of type Y = 2/3 × 12 = 8
∴ Percentage of element X = 6/14 x 100 = 300/7 = 42.85 ≌ 43%
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Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is _______%. (Nearest integer)Correct answer is '43'. Can you explain this answer?
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Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is _______%. (Nearest integer)Correct answer is '43'. 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 Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is _______%. (Nearest integer)Correct answer is '43'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is _______%. (Nearest integer)Correct answer is '43'. Can you explain this answer?.
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