Question

The interplanar spacing for cubic materials is given by the equation

• A. \( d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}} \)
• B. \( d_{hkl} = \frac{200}{\sqrt{h^2 + k^2 + l^2}} \)
• C. \( d_{hkl} = \frac{3a}{\sqrt{h^2 + k^2 + l^2}} \)
• D. \( d_{hkl} = \frac{4a}{\sqrt{h^2 + k^2 + l^2}} \)

Hint:

Interplanar spacing formulas vary by crystal structure but follow the same principle of inverse relation to Miller indices. Proper substitution of indices ensures correctness, crucial for applications in X-ray diffraction and material characterization.

Answer 1

The Correct Option is A

The formula for interplanar spacing in cubic systems is:
\[d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}\]
This relationship holds for all cubic materials, where \(h, k, l\) are Miller indices, and \(a\) is the lattice constant.