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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)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A plane in a cubic lattice makes intercepts of a, a/2 and 2a/3 with th...
Given information:

- The plane in a cubic lattice has intercepts of a, a/2, and 2a/3 with the three crystallographic axes, respectively.

Miller indices:

- Miller indices are used to represent a plane or direction in a crystal lattice.

Deriving the Miller indices:

To determine the Miller indices for the given plane, we need to follow these steps:

1. Determine the reciprocals of the intercepts:
- The reciprocals of the intercepts are 1/a, 2/a, and 3/2a.

2. Simplify the reciprocals to the smallest whole numbers:
- The reciprocals simplify to 2/3, 1/2, and 2/3.

3. Take the reciprocals and multiply them by a common factor to obtain whole numbers:
- Multiplying the reciprocals by 6, we get 4, 3, and 4.

4. The resulting whole numbers represent the Miller indices for the plane:
- The Miller indices for the given plane are (4, 3, 4).

Comparison with the options:

Option A: (2, 4, 3)
- This option does not match the Miller indices obtained for the given plane.

Option B: (3, 4, 2)
- This option does not match the Miller indices obtained for the given plane.

Option C: (6, 3, 4)
- This option matches the Miller indices obtained for the given plane.

Option D: (1, 2, 3)
- This option does not match the Miller indices obtained for the given plane.

Conclusion:

Based on the derivation of Miller indices and comparison with the given options, option A (2, 4, 3) is the correct answer.
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A plane in a cubic lattice makes intercepts of a, a/2 and 2a/3 with th...
 intercept              a    a/2   2a/3                                                                                                     dividing by a        1     1/2    2/3                                                                                                      taking reverse     1     2       3/2                                                                                                   multiplying2          2     4       3
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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)Correct answer is option 'A'. Can you explain this answer?
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