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The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)
Correct answer is between '12.00,15.00'. Can you explain this answer?
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The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays ...
Given:
Lattice constant of NaCl crystal, a = 0.563 nm
Wavelength of X-rays, λ = 0.141 nm
To find:
Angle at which the first order maximum occurs
Formula used:
Bragg's law: nλ = 2d sinθ
where n is the order of diffraction, λ is the wavelength of the incident X-ray, d is the distance between the planes of atoms, and θ is the angle of incidence.
Steps to solve the problem:
1. Find the distance between the planes of atoms:
In a NaCl crystal, the (1 1 1) plane is the most closely packed and has the greatest number of atoms. Therefore, we can use this plane to calculate the distance between planes.
d = a/√(h² + k² + l²) where h, k, and l are the Miller indices of the plane
For the (1 1 1) plane, h = k = l = 1
d = a/√3 = 0.325 nm
2. Substitute the values in Bragg's law:
nλ = 2d sinθ
For first order maximum, n = 1
1 × 0.141 nm = 2 × 0.325 nm × sinθ
sinθ = 0.217
θ = sin⁻¹(0.217) = 12.83°
3. Round off the answer to two decimal places:
The angle at which the first order maximum occurs is 12.83°, which is between 12.00° and 15.00°.
Therefore, the correct answer is between 12.00° and 15.00°.
Lattice constant of NaCl crystal, a = 0.563 nm
Wavelength of X-rays, λ = 0.141 nm
To find:
Angle at which the first order maximum occurs
Formula used:
Bragg's law: nλ = 2d sinθ
where n is the order of diffraction, λ is the wavelength of the incident X-ray, d is the distance between the planes of atoms, and θ is the angle of incidence.
Steps to solve the problem:
1. Find the distance between the planes of atoms:
In a NaCl crystal, the (1 1 1) plane is the most closely packed and has the greatest number of atoms. Therefore, we can use this plane to calculate the distance between planes.
d = a/√(h² + k² + l²) where h, k, and l are the Miller indices of the plane
For the (1 1 1) plane, h = k = l = 1
d = a/√3 = 0.325 nm
2. Substitute the values in Bragg's law:
nλ = 2d sinθ
For first order maximum, n = 1
1 × 0.141 nm = 2 × 0.325 nm × sinθ
sinθ = 0.217
θ = sin⁻¹(0.217) = 12.83°
3. Round off the answer to two decimal places:
The angle at which the first order maximum occurs is 12.83°, which is between 12.00° and 15.00°.
Therefore, the correct answer is between 12.00° and 15.00°.
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The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer?
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The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer? 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 The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer?.
The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer? 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 The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lattice constant of unit cell of NaCl crystal is 0.563 nm. X-rays of wavelength 0.141 nm are diffracted by this crystal. The angle at which the first order maximum occurs is ________degrees. (Specify your answer in degrees upto two digits after the decimal point.)Correct answer is between '12.00,15.00'. Can you explain this answer?.
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