Atoms per unit cell and density: Class 12 practice
Simple cubic has 1 atom per cell, body-centred cubic 2, face-centred cubic 4. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Mole concept
The idea behind atoms per unit cell and density
Simple cubic has 1 atom per cell, body-centred cubic 2, face-centred cubic 4. Density ρ = Z × M ÷ (a³ × Nₐ), with a in cm and Nₐ = 6.022 × 10²³.
Step-by-step method
- Find Z from the lattice type.
- Convert edge length to cm (1 pm = 10⁻¹⁰ cm).
- ρ = ZM ÷ (a³Nₐ).
Worked example 1 (Basic)
How many atoms are there per unit cell of a simple cubic lattice?
- 8 corners × 1/8
- Answer: 1
Worked example 2 (Standard)
An element (M = 180 g/mol) forms a simple cubic cell with edge 331 pm. Find its density.
- Z = 1
- a³ = 3.626e-23 cm³
- ρ = 8.24 g/cm³
- Answer: 8.24 g/cm³
Worked example 3 (Challenge)
An element (M = 94 g/mol) forms a body-centred cubic cell with edge 449 pm. Find its density.
- Z = 2
- a³ = 9.052e-23 cm³
- ρ = 3.45 g/cm³
- Answer: 3.45 g/cm³
Common mistakes and misconceptions
- Using pm without converting
- Wrong Z for bcc/fcc
Practice questions
- (Basic) How many atoms are there per unit cell of a face-centred cubic lattice?
- (Basic) How many atoms are there per unit cell of a body-centred cubic lattice?
- (Standard) An element (M = 157 g/mol) forms a simple cubic cell with edge 301 pm. Find its density.
- (Standard) An element (M = 42 g/mol) forms a body-centred cubic cell with edge 376 pm. Find its density.
- (Challenge) An element (M = 141 g/mol) forms a body-centred cubic cell with edge 361 pm. Find its density.
- (Challenge) An element (M = 174 g/mol) forms a face-centred cubic cell with edge 344 pm. Find its density.
Answer key with full working
- Q1: 8 × 1/8 + 6 faces × 1/2 → Answer: 4
- Q2: 8 × 1/8 + 1 centre → Answer: 2
- Q3: Z = 1 → a³ = 2.727e-23 cm³ → ρ = 9.56 g/cm³ → Answer: 9.56 g/cm³
- Q4: Z = 2 → a³ = 5.316e-23 cm³ → ρ = 2.62 g/cm³ → Answer: 2.62 g/cm³
- Q5: Z = 2 → a³ = 4.705e-23 cm³ → ρ = 9.95 g/cm³ → Answer: 9.95 g/cm³
- Q6: Z = 4 → a³ = 4.071e-23 cm³ → ρ = 28.39 g/cm³ → Answer: 28.39 g/cm³
Syllabus note
This skill is listed under "The Solid State" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is atoms per unit cell and density in?
"The Solid State", Class 12 Chemistry (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.