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Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.
Correct answer is '8'. Can you explain this answer?
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Diamond has a three dimensional structure of C atoms formed by covalen...
The diamond is a three-dimensional structure of carbon atoms which is formed by covalent bonds. It has a face-centred cubic lattice where 50% of the tetrahedral voids are occupied by carbon atoms.
Determining the number of carbon atoms present per unit cell of diamond involves the following steps:
Step 1: Identify the components of a unit cell
A unit cell is the smallest repeating unit of a crystal lattice. In the case of diamond, a unit cell consists of eight carbon atoms arranged in a three-dimensional lattice.
Step 2: Calculate the volume of the unit cell
The volume of a unit cell can be determined by measuring the length of its sides or by using the formula:
Volume = a^3, where a is the length of the side of the unit cell.
In the case of a face-centred cubic lattice, the length of the side of the unit cell can be calculated using the formula:
a = 2 x r, where r is the radius of the atom.
Since the diamond lattice is made up of carbon atoms, the radius of each atom is 0.071 nm.
Therefore, a = 2 x 0.071 nm = 0.142 nm
Volume of the unit cell = a^3 = (0.142 nm)^3 = 0.00243 nm^3
Step 3: Calculate the number of carbon atoms per unit cell
Since a unit cell of diamond consists of eight carbon atoms, the number of carbon atoms per unit cell can be calculated by dividing the volume of the unit cell by the volume occupied by each carbon atom.
The volume occupied by each carbon atom can be calculated using the formula for the volume of a sphere:
Volume of a sphere = (4/3) x π x r^3
Volume of a carbon atom = (4/3) x π x (0.071 nm)^3 = 0.0000822 nm^3
Number of carbon atoms per unit cell = Volume of unit cell / Volume of a carbon atom
Number of carbon atoms per unit cell = 0.00243 nm^3 / 0.0000822 nm^3 = 29.6
However, since only 50% of the tetrahedral voids in the diamond lattice are occupied by carbon atoms, the number of carbon atoms per unit cell is half of the calculated value.
Therefore, the number of carbon atoms present per unit cell of diamond is 8.
Determining the number of carbon atoms present per unit cell of diamond involves the following steps:
Step 1: Identify the components of a unit cell
A unit cell is the smallest repeating unit of a crystal lattice. In the case of diamond, a unit cell consists of eight carbon atoms arranged in a three-dimensional lattice.
Step 2: Calculate the volume of the unit cell
The volume of a unit cell can be determined by measuring the length of its sides or by using the formula:
Volume = a^3, where a is the length of the side of the unit cell.
In the case of a face-centred cubic lattice, the length of the side of the unit cell can be calculated using the formula:
a = 2 x r, where r is the radius of the atom.
Since the diamond lattice is made up of carbon atoms, the radius of each atom is 0.071 nm.
Therefore, a = 2 x 0.071 nm = 0.142 nm
Volume of the unit cell = a^3 = (0.142 nm)^3 = 0.00243 nm^3
Step 3: Calculate the number of carbon atoms per unit cell
Since a unit cell of diamond consists of eight carbon atoms, the number of carbon atoms per unit cell can be calculated by dividing the volume of the unit cell by the volume occupied by each carbon atom.
The volume occupied by each carbon atom can be calculated using the formula for the volume of a sphere:
Volume of a sphere = (4/3) x π x r^3
Volume of a carbon atom = (4/3) x π x (0.071 nm)^3 = 0.0000822 nm^3
Number of carbon atoms per unit cell = Volume of unit cell / Volume of a carbon atom
Number of carbon atoms per unit cell = 0.00243 nm^3 / 0.0000822 nm^3 = 29.6
However, since only 50% of the tetrahedral voids in the diamond lattice are occupied by carbon atoms, the number of carbon atoms per unit cell is half of the calculated value.
Therefore, the number of carbon atoms present per unit cell of diamond is 8.
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Community Answer
Diamond has a three dimensional structure of C atoms formed by covalen...
Carbon atoms occupy FCC lattice points as well as half of the tetrahedral voids.
Z = 8
Z = 8
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Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer?.
Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer?.
Solutions for Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer?, a detailed solution for Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? has been provided alongside types of Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is ______.Correct answer is '8'. Can you explain this answer? theory, EduRev gives you an
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