Question

Calculate the number of atoms in 20 gram metal which crystallises to simple cubic structure having unit cell edge length 340 pm. (density of metal = 9.8 gcm^–3)

• A. 4.95 x 10²²
• B. 5.81 x10²²
• C. 5.19 x 10²²
• D. 5.42 x 10²²

Answer 1

The Correct Option is C

Mass of the metal = 20 g 
Density of the metal = 9.8 g/cm³ 
Unit cell edge length (a) = 340 pm = 340 × 10^-10 m 
Volume of a cubic unit cell = a³ 
Number of unit cells = \(\frac {mass}{(density × volume) }\)
Convert the mass to kilograms: 
Mass = 20 g = 20 × 10^-3 kg 
Number of unit cells = \(\frac {(20 × 10^{-3} kg}{(9.8\  g/cm³ × volume) }\)
Now, we need to calculate the number of atoms per unit cell in a simple cubic structure, which is 1. 
Number of atoms = Number of unit cells × Number of atoms per unit cell 
Solving the calculations: 
Volume = (340 × 10^-10 m)³ = 39.304 × 10^-27 m³ 
Number of unit cells = \(\frac {(20 × 10^{-3} kg}{(9.8\  g/cm³ × 39.304 \times 10^{-27} m^3) }\)
Number of unit cells = 5.194 × 10²²
Number of atoms = (5.194 × 10²²) × 1 
Therefore, the correct option is (C) 5.19 × 10²² atoms.