Question

If the intercepts of crystallographic axes are 0.5a : 1b : 0.75c on a crystallographic plane {h k l}, the value of ‘l’ is _________. (In integer)

Answer 1

Correct Answer: 4

Given:
Intercepts of the plane on crystallographic axes are: 
\[ 0.5a : 1b : 0.75c \] Step 1: Convert intercepts to fractional intercepts
\[ x = 0.5,\quad y = 1,\quad z = 0.75 \] Step 2: Take reciprocals to get Miller indices
\[ h = \frac{1}{0.5} = 2,\qquad k = \frac{1}{1} = 1,\qquad l = \frac{1}{0.75} = \frac{4}{3} \] Step 3: Clear fractions by multiplying all by 3
\[ (2,\,1,\,\tfrac{4}{3}) \times 3 = (6,\,3,\,4) \] Thus the Miller index \(l = \boxed{4}\).