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For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :
- a)[1 1 0]
- b)[2 0 0]
- c)[1 0 0]
- d)[1 1 1]
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at ...
The correct answer is Option 4: [1 1 1]. The smallest angle at which Bragg reflection can occur corresponds to a set of planes with indices [1 1 1]. This is because the interplanar spacing d of the crystal planes is equal to the unit cell dimension ao for NaCl crystals. Thus, for Bragg's law to be satisfied, the path length difference between waves effectively reflected by two adjacent planes must be equal to 2d sin 8, or mA, where m is an integer. For m = 1, the Bragg angle 8 is equal to arcsin (1/2a) which is equal to arcsin (1/2 x 0.563) = 54.7°. The Miller indices of the planes satisfying this condition are [1 1 1].
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For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at ...
The Bragg reflection is a phenomenon that occurs when X-rays or neutrons are incident on a crystal and reflected at specific angles. The condition for Bragg reflection is given by the Bragg's law:
nλ = 2dsinθ
- Where n is the order of the reflection, λ is the wavelength of the incident radiation, d is the distance between the crystal planes, and θ is the angle of incidence.
In this case, we are given the cell edge of a NaCI crystal, which is a = 0.563 nm. We need to find the set of planes whose indices correspond to the smallest angle at which Bragg reflection can occur.
To solve this problem, we can use the formula for the distance between crystal planes:
d = a/√(h^2 + k^2 + l^2)
- Where h, k, and l are the Miller indices of the crystal planes.
We need to find the set of planes that gives the smallest value of d, as this will correspond to the smallest angle of incidence θ.
Let's consider the options one by one:
a) [1 1 0]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(1^2 + 1^2 + 0^2) = 0.563 nm / √2 ≈ 0.398 nm
b) [2 0 0]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(2^2 + 0^2 + 0^2) = 0.563 nm / 2 ≈ 0.2815 nm
c) [1 0 0]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(1^2 + 0^2 + 0^2) = 0.563 nm / 1 = 0.563 nm
d) [1 1 1]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(1^2 + 1^2 + 1^2) = 0.563 nm / √3 ≈ 0.325 nm
Since we are looking for the smallest value of d, the set of planes with indices [1 1 1] corresponds to the smallest angle at which Bragg reflection can occur. Therefore, the correct answer is option 'D'.
nλ = 2dsinθ
- Where n is the order of the reflection, λ is the wavelength of the incident radiation, d is the distance between the crystal planes, and θ is the angle of incidence.
In this case, we are given the cell edge of a NaCI crystal, which is a = 0.563 nm. We need to find the set of planes whose indices correspond to the smallest angle at which Bragg reflection can occur.
To solve this problem, we can use the formula for the distance between crystal planes:
d = a/√(h^2 + k^2 + l^2)
- Where h, k, and l are the Miller indices of the crystal planes.
We need to find the set of planes that gives the smallest value of d, as this will correspond to the smallest angle of incidence θ.
Let's consider the options one by one:
a) [1 1 0]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(1^2 + 1^2 + 0^2) = 0.563 nm / √2 ≈ 0.398 nm
b) [2 0 0]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(2^2 + 0^2 + 0^2) = 0.563 nm / 2 ≈ 0.2815 nm
c) [1 0 0]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(1^2 + 0^2 + 0^2) = 0.563 nm / 1 = 0.563 nm
d) [1 1 1]
- Using the formula for d, we can calculate the value for this set of planes: d = 0.563 nm / √(1^2 + 1^2 + 1^2) = 0.563 nm / √3 ≈ 0.325 nm
Since we are looking for the smallest value of d, the set of planes with indices [1 1 1] corresponds to the smallest angle at which Bragg reflection can occur. Therefore, the correct answer is option 'D'.
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For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer?
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For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer?.
For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer?.
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For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer?, a detailed solution for For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of For a NaCI crystal, the cell edge a = 0.563 nm. The smallest angle at which Bragg reflection can occur corresponds to a set of planes whose indices are :a)[1 1 0]b)[2 0 0]c)[1 0 0]d)[1 1 1]Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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