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A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom?
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A first order reflection from (111)plane is observed forLiX with 2 thi...
Calculation of the length of the side of the unit cell for LiX Crystal
To calculate the length of the side of the unit cell for LiX crystal, we need to use the formula for the Bragg's law:
nλ = 2dsinθ
Where:
- n is the order of reflection (in this case, n = 1 for first order reflection)
- λ is the wavelength of the X-ray (given as 1.54 Å)
- d is the interplanar spacing
- θ is the angle of incidence (given as 24.6°)
Step 1: Calculating the interplanar spacing (d)
To calculate the interplanar spacing, we need to use the formula for cubic crystal systems:
d = a / √(h² + k² + l²)
Where:
- a is the length of the side of the unit cell
- h, k, and l are the Miller indices of the plane (in this case, h = 1, k = 1, l = 1 for (111) plane)
Substituting the given values, we have:
d = a / √(1² + 1² + 1²)
Step 2: Substituting the values in Bragg's law
Substituting the values of n, λ, d, and θ in the Bragg's law equation, we have:
1.54 Å = 2(a / √3)sin(24.6°)
Simplifying the equation further:
1.54 Å = (2√3 / 3)a * 0.4067
Step 3: Solving for a
To find the value of a, we can rearrange the equation:
a = (1.54 Å * 3) / (2 * √3 * 0.4067)
Simplifying the equation further:
a = 2.66 Å
Therefore, the length of the side of the unit cell for LiX crystal is 2.66 Å.
To calculate the length of the side of the unit cell for LiX crystal, we need to use the formula for the Bragg's law:
nλ = 2dsinθ
Where:
- n is the order of reflection (in this case, n = 1 for first order reflection)
- λ is the wavelength of the X-ray (given as 1.54 Å)
- d is the interplanar spacing
- θ is the angle of incidence (given as 24.6°)
Step 1: Calculating the interplanar spacing (d)
To calculate the interplanar spacing, we need to use the formula for cubic crystal systems:
d = a / √(h² + k² + l²)
Where:
- a is the length of the side of the unit cell
- h, k, and l are the Miller indices of the plane (in this case, h = 1, k = 1, l = 1 for (111) plane)
Substituting the given values, we have:
d = a / √(1² + 1² + 1²)
Step 2: Substituting the values in Bragg's law
Substituting the values of n, λ, d, and θ in the Bragg's law equation, we have:
1.54 Å = 2(a / √3)sin(24.6°)
Simplifying the equation further:
1.54 Å = (2√3 / 3)a * 0.4067
Step 3: Solving for a
To find the value of a, we can rearrange the equation:
a = (1.54 Å * 3) / (2 * √3 * 0.4067)
Simplifying the equation further:
a = 2.66 Å
Therefore, the length of the side of the unit cell for LiX crystal is 2.66 Å.
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A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom?
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A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom?.
A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order reflection from (111)plane is observed forLiX with 2 thita=24.6(X ray of wave length 1.54 angstrom). Assuming LiX to be a cubic Crystal system, calculate the length of the side of the unit cell in angstrom?.
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