Number of crystal systems from the following where body centred unit cell can be found, is ____________.
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic

Solution

Chemistry ma’am · 3 steps

Go through the 14 Bravais lattices and tick the systems that have a body-centred cell.

1. What to check. There are 7 crystal systems but only 14 Bravais lattices. Not every system allows every centring (primitive, body-centred, face-centred, end-centred), so look up the allowed centrings for each system.

   Crystal system	Allowed unit cells	Body-centred?
   Cubic	primitive, body-centred, face-centred	yes
   Tetragonal	primitive, body-centred	yes
   Orthorhombic	primitive, body-centred, face-centred, end-centred	yes
   Hexagonal	primitive only	no
   Rhombohedral	primitive only	no
   Monoclinic	primitive, end-centred	no
   Triclinic	primitive only	no

2. Check the count. The cell counts add up to 3 + 2 + 4 + 1 + 1 + 2 + 1 = 14, which matches the 14 Bravais lattices.
3. So. Only cubic, tetragonal and orthorhombic have a body-centred unit cell, so the answer is 3.

The common slip: 4. Counting monoclinic as body-centred gives 4. Monoclinic has only primitive and end-centred cells.

The idea to keep. Remember the 14 Bravais lattices as 3, 2, 4, 1, 1, 2, 1 across cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic. Orthorhombic is the only one with all four centrings.

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