Question

3. The lattice parameters a, b, c of an orthorhombic crystal are related by a =2b =3c. What is the interplanar separation between (1 2 1) planes?

Answer 1

The interplanar separation between (1 2 1) planes in an orthorhombic crystal with lattice parameters a = 2b = 3c can be calculated using the formula d = √((h²/a²) + (k²/b²) + (l²/c²)).

Step-by-step explanation:

In an orthorhombic crystal with lattice parameters a = 2b = 3c, the interplanar separation between (1 2 1) planes can be calculated using the formula:

d = √((h²/a²) + (k²/b²) + (l²/c²))

Where h, k, and l are the Miller indices of the plane. In this case, (h k l) = (1 2 1).

Substituting the values into the formula, we get:

d = √((1²/2²) + (2²/3²) + (1²/1²))

d = √(1/4 + 4/9 + 1/1)

d = √(9/36 + 16/36 + 36/36)

d = √(61/36)

d = (√(61))/6

Therefore, the interplanar separation between (1 2 1) planes is (√(61))/6 times the unit cell parameter c.