The correct answer is 0.21 nm ; 0.11 nm respectively
Concept:-
- Crystallography: The study of the arrangement of atoms, molecules, or ions in crystalline solids.
- Bragg's law: A law that describes the diffraction of X-rays from a crystal lattice.
- Miller indices: A set of three numbers that describe the orientation of a plane in a crystal lattice.
- Unit cell: The smallest repeating unit of a crystal lattice.
Explanation:-
Calculation of the separation between the {123} planes:
sinθ({123}) = λ / (2d({123})) \times √(1^2 + 2^2 + 3^2)\ = λ / (2d({123})) \times √14 d({123}) \= λ \times √14 / (4 \times sinθ({123}))
Substituting the values of λ, a, b, and c into the formula, we get:
d(123)=0.154nm×√14/(4×sinθ(123))=0.21nm
To find sinθ({123}), we use Bragg's law:
2d(123)∗sinθ(123)=nλ sinθ(123)=nλ/(2d(123))
For the first-order reflection (n = 1), we get:
sinθ(123)=λ/(2d(123))
Substituting this into the formula for d({123}), we get:
d(123)=λ∗√14/(4∗λ/(2d(123))) d(123)=λ∗√14∗d(123)/(8λ) d(123)=λ∗√14/8
d(246)=0.154nm×√56/(4×sinθ(246))
To find sinθ({246}), we use Bragg's law:
2d(246)×sinθ(246)=nλ sinθ(246)=nλ/(2d(246))
For the first order reflection (n = 1), we get:
sinθ(246)=λ/(2d(246))
Substituting this into the formula for d({246}), we get:
d(246)=λ∗√56/(4∗λ/(2d(246))) d(246)=λ∗√56∗d(246)/(8λ) d(246)=λ∗√56/8
Substituting the value of λ, we get:
d(246)=0.154nm×√56/8 d(246)=0.11nm
Therefore, the separation between the {123} and {246} planes of an orthorhombic unit cell with a = 0.82 nm, b = 0.94 nm, and c = 0.75 nm are 0.21 nm and 0.11 nm, respectively.
Conclusion:-
So, Separation of {123} and {246} planes of an orthorhombic unit cell with a = 0.82 nm, b = 0.94 nm and c = 0.75 nm are 0.21 nm ; 0.11 nm respectively