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

Answer: (C)

5.19 x 1022

Answer 2

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.