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For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:
- a)51/2
- b)71/2
- c)111/2
- d)131/2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
For a simple cubic lattice, the ratio between the unit cell length and...
Explanation:
The separation between two adjacent parallel crystal planes is given by the Miller indices of the crystal planes. For a simple cubic lattice, the Miller indices of the crystal planes are (hkl), where h, k, and l are integers. The separation distance between two adjacent parallel crystal planes is given by the formula:
d = a / sqrt(h^2 + k^2 + l^2)
where a is the length of the unit cell.
To find the ratio between the unit cell length and the separation of two adjacent parallel crystal planes, we can divide both sides of the equation by a:
d/a = 1 / sqrt(h^2 + k^2 + l^2)
Therefore, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes depends only on the Miller indices of the crystal planes.
Now, let's consider the options given in the question:
a) 5^(1/2)/2 = 1.118: This ratio can be obtained for the (111) crystal plane.
b) 7^(1/2)/2 = 1.322: This ratio can be obtained for the (110) crystal plane.
c) 11^(1/2)/2 = 1.658: This ratio can be obtained for the (100) crystal plane.
d) 13^(1/2)/2 = 1.826: This ratio cannot be obtained for any of the crystal planes in a simple cubic lattice.
Therefore, the correct answer is option 'D'.
The separation between two adjacent parallel crystal planes is given by the Miller indices of the crystal planes. For a simple cubic lattice, the Miller indices of the crystal planes are (hkl), where h, k, and l are integers. The separation distance between two adjacent parallel crystal planes is given by the formula:
d = a / sqrt(h^2 + k^2 + l^2)
where a is the length of the unit cell.
To find the ratio between the unit cell length and the separation of two adjacent parallel crystal planes, we can divide both sides of the equation by a:
d/a = 1 / sqrt(h^2 + k^2 + l^2)
Therefore, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes depends only on the Miller indices of the crystal planes.
Now, let's consider the options given in the question:
a) 5^(1/2)/2 = 1.118: This ratio can be obtained for the (111) crystal plane.
b) 7^(1/2)/2 = 1.322: This ratio can be obtained for the (110) crystal plane.
c) 11^(1/2)/2 = 1.658: This ratio can be obtained for the (100) crystal plane.
d) 13^(1/2)/2 = 1.826: This ratio cannot be obtained for any of the crystal planes in a simple cubic lattice.
Therefore, the correct answer is option 'D'.
Community Answer
For a simple cubic lattice, the ratio between the unit cell length and...
The answer should be B because we cannot express 7 as the sum of the squares of three coordinates
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For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:a)51/2b)71/2c)111/2d)131/2Correct answer is option 'D'. Can you explain this answer? for Chemistry 2025 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:a)51/2b)71/2c)111/2d)131/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemistry 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:a)51/2b)71/2c)111/2d)131/2Correct answer is option 'D'. Can you explain this answer?.
For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:a)51/2b)71/2c)111/2d)131/2Correct answer is option 'D'. Can you explain this answer? for Chemistry 2025 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:a)51/2b)71/2c)111/2d)131/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemistry 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a simple cubic lattice, the ratio between the unit cell length and the separation of two adjacent parallel crystal planes can NOT have a value of:a)51/2b)71/2c)111/2d)131/2Correct answer is option 'D'. Can you explain this answer?.
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