chemistry : class12 Miller Indices : Crystalline solids : Solid State MCQ Questions and Answers
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Miller Indices
MCQ questions and answers.
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MCQ Questions
1. A crystal plane cuts the crystallographic axes at 2a, 3b, and remains parallel to the c-axis. What are its Miller indices?
A.
(2 3 0)
B.
(3 2 0)
C.
(1 2 0)
D.
(2 1 0)
Correct Answer:
(3 2 0)
Explanation:
The reciprocals of the intercepts in units of a, b, and c are 1/2, 1/3, and 0. Multiplying by 6 gives the smallest integers 3, 2, and 0; hence the Miller indices are (3 2 0).
2. A plane has Miller indices (2 -1 3). Which set of intercepts, expressed in terms of the unit-cell parameters, corresponds to this plane?
A.
a/2, -b, c/3
B.
2a, -b, 3c
C.
a/2, b, c/3
D.
2a, -b, c/3
Correct Answer:
a/2, -b, c/3
Explanation:
For a plane with Miller indices (h k l), the intercepts are a/h, b/k, and c/l. Therefore, (2 -1 3) gives intercepts a/2, -b, and c/3.
3. A plane is parallel to the b-axis and intersects the a- and c-axes at 3a and 2c, respectively. What are its Miller indices?
A.
(2 0 3)
B.
(3 0 2)
C.
(1 0 2)
D.
(2 1 3)
Correct Answer:
(2 0 3)
Explanation:
The intercepts in unit-cell units are 3, infinity, and 2. Their reciprocals are 1/3, 0, and 1/2. Multiplication by 6 gives (2 0 3).
4. A plane passes through the points (2a, 0, 0), (0, 3b, 0), and (0, 0, 6c). What are the Miller indices of the plane?
A.
(1 2 3)
B.
(3 2 1)
C.
(6 3 2)
D.
(2 3 6)
Correct Answer:
(3 2 1)
Explanation:
The intercepts are 2a, 3b, and 6c, giving reciprocal values 1/2, 1/3, and 1/6. Clearing denominators by multiplying by 6 yields (3 2 1).
5. Which plane has an intercept of a along the a-axis, b/2 along the b-axis, and is parallel to the c-axis?
A.
(1 2 0)
B.
(2 1 0)
C.
(1 1 0)
D.
(2 2 1)
Correct Answer:
(1 2 0)
Explanation:
The intercepts in normalized units are 1, 1/2, and infinity. Taking reciprocals gives 1, 2, and 0, so the Miller indices are (1 2 0).
6. A plane cuts the a- and b-axes at -2a and 3b, respectively, and is parallel to the c-axis. What are its Miller indices?
A.
(3 2 0)
B.
(-3 2 0)
C.
(3 -2 0)
D.
(-2 3 0)
Correct Answer:
(-3 2 0)
Explanation:
The normalized intercepts are -2, 3, and infinity. Their reciprocals are -1/2, 1/3, and 0. Multiplication by 6 gives (-3 2 0), with the negative index conventionally represented by an overbar over 3.
7. A plane intersects the axes at 2a, -3b, and 6c. Which Miller indices represent this plane?
A.
(3 -2 1)
B.
(-3 2 1)
C.
(2 -3 6)
D.
(6 -3 2)
Correct Answer:
(3 -2 1)
Explanation:
Taking reciprocals of the normalized intercepts 2, -3, and 6 gives 1/2, -1/3, and 1/6. Multiplying by 6 produces (3 -2 1).
8. In a cubic crystal, which plane belongs to the same family as the plane (2 1 0), considering permutations of the indices?
A.
(1 2 0)
B.
(2 0 1)
C.
(1 0 2)
D.
All three listed planes
Correct Answer:
All three listed planes
Explanation:
In a cubic crystal, planes related by permutations of the indices have equivalent crystallographic characteristics. The planes (1 2 0), (2 0 1), and (1 0 2) are permutations of (2 1 0), so all belong to the same family.
9. For the plane (3 2 1), which point lies on the plane when coordinates are expressed relative to the crystallographic axes?
A.
(a/6, b/4, 0)
B.
(a/3, b/2, 0)
C.
(a/6, b/2, 0)
D.
(a/3, b/4, c/2)
Correct Answer:
(a/6, b/4, 0)
Explanation:
The equation of the plane (3 2 1) is 3x/a + 2y/b + z/c = 1. For (a/6, b/4, 0), the left side is 3(1/6) + 2(1/4) + 0 = 1/2 + 1/2 = 1, so the point lies on the plane.
10. A plane has intercepts -a, b/2, and c/3 along the three crystallographic axes. What are its Miller indices?
A.
(-1 2 3)
B.
(1 -2 3)
C.
(-3 2 1)
D.
(1 2 -3)
Correct Answer:
(-1 2 3)
Explanation:
The normalized intercepts are -1, 1/2, and 1/3. Their reciprocals are -1, 2, and 3, already in the smallest integer ratio. Thus, the Miller indices are (-1 2 3).
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