Question

A plane in a cubic lattice makes intercepts of \( a, a/2 \) and \( 2a/3 \) with the three crystallographic axes, respectively. The Miller indices for this plane are:

• A. (2 4 3)
• B. (3 4 2)
• C. (6 3 4)
• D. (1 2 3)

Hint:

When calculating Miller indices, remember to take the reciprocals of the intercepts and clear fractions to get the correct form.

Answer 1

The Correct Option is A

Step 1: Understanding Miller indices.
The Miller indices are derived from the intercepts of a plane with the crystallographic axes. For intercepts of \( a, a/2, 2a/3 \), the Miller indices are calculated by taking the reciprocals of the intercepts and clearing any fractions. The final result is (2 4 3), which corresponds to option (A).
Step 2: Conclusion.
Therefore, the correct answer is option (A) because the Miller indices for this plane are (2 4 3).