The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, α = 90°, β = 120°, γ = 90°. The crystal system of the substance is :

Solution

Chemistry ma’am · 3 steps

Check the edges first, then the angles: three unequal edges with only one angle off 90° is monoclinic.

1. Compare the edges. Here a = 2.5, b = 3.0 and c = 4.0, so all three edges are different: a ≠ b ≠ c. That rules out every system that needs two or three equal edges, including hexagonal.
2. Compare the angles. α = γ = 90° but β = 120°. So exactly one angle is not a right angle.

   System	Edges	Angles	Matches?
   Hexagonal	a = b ≠ c	α = β = 90°, γ = 120°	No: edges unequal, and the 120° angle is β, not γ
   Orthorhombic	a ≠ b ≠ c	all three 90°	No: β is not 90°
   Monoclinic	a ≠ b ≠ c	α = γ = 90°, β ≠ 90°	Yes
   Triclinic	a ≠ b ≠ c	none of them 90°	No: two angles are 90°

3. So. Three unequal edges with only β different from 90° is the monoclinic system, option (c).

The idea to keep. Count how many angles are not 90°. With all edges unequal: none off means orthorhombic, one off means monoclinic, all three off means triclinic.

Answer from the NTA final answer key. Solution by PrepWiser.