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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)131/2
- c)111/2
- d)71/2
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 ratio between the unit cell length and the separation of two adjacent parallel crystal planes is known as the Miller indices of the plane. For a simple cubic lattice, the Miller indices of the planes are expressed as (hkl), where h, k, and l are integers representing the intercepts of the planes on the three axes.
The distance between two adjacent parallel crystal planes of a simple cubic lattice can be calculated using the formula:
d = a/√(h^2 + k^2 + l^2)
where a is the length of the unit cell.
To find the value of d/a, we can simplify the above formula as:
d/a = 1/√(h^2 + k^2 + l^2)
Therefore, the value of d/a depends on the values of h, k, and l.
Now, let's consider the given options:
a) d/a = 5^(1/2)/1 = 5^(1/2)
b) d/a = 13^(1/2)/1 = 13^(1/2)
c) d/a = 11^(1/2)/2 = 5.5
d) d/a = 7^(1/2)/1 = 7^(1/2)
We can see that option D has a value of d/a that is not expressible as a simple radical or a rational number. Therefore, option D is the correct answer.
In summary, the Miller indices of a simple cubic lattice can be used to calculate the distance between adjacent parallel crystal planes. The value of d/a depends on the values of h, k, and l, and not all values are expressible as simple radicals or rational numbers.
The ratio between the unit cell length and the separation of two adjacent parallel crystal planes is known as the Miller indices of the plane. For a simple cubic lattice, the Miller indices of the planes are expressed as (hkl), where h, k, and l are integers representing the intercepts of the planes on the three axes.
The distance between two adjacent parallel crystal planes of a simple cubic lattice can be calculated using the formula:
d = a/√(h^2 + k^2 + l^2)
where a is the length of the unit cell.
To find the value of d/a, we can simplify the above formula as:
d/a = 1/√(h^2 + k^2 + l^2)
Therefore, the value of d/a depends on the values of h, k, and l.
Now, let's consider the given options:
a) d/a = 5^(1/2)/1 = 5^(1/2)
b) d/a = 13^(1/2)/1 = 13^(1/2)
c) d/a = 11^(1/2)/2 = 5.5
d) d/a = 7^(1/2)/1 = 7^(1/2)
We can see that option D has a value of d/a that is not expressible as a simple radical or a rational number. Therefore, option D is the correct answer.
In summary, the Miller indices of a simple cubic lattice can be used to calculate the distance between adjacent parallel crystal planes. The value of d/a depends on the values of h, k, and l, and not all values are expressible as simple radicals or rational numbers.
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Community Answer
For a simple cubic lattice, the ratio between the unit cell length and...
We know that
d=a/(h^2+k^2+l^2)
for scc any (hkl) can be taken
let MI (210)
a/d(hkl)=5^(1/2)
MI (311)
a/d= 11^(1/2)
MI(320)
a/d=13^(1/2)
Therefore option d is not possible
d=a/(h^2+k^2+l^2)
for scc any (hkl) can be taken
let MI (210)
a/d(hkl)=5^(1/2)
MI (311)
a/d= 11^(1/2)
MI(320)
a/d=13^(1/2)
Therefore option d is not possible
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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)131/2c)111/2d)71/2Correct 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)131/2c)111/2d)71/2Correct 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)131/2c)111/2d)71/2Correct answer is option 'D'. Can you explain this answer?.
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