Q1. A metal is in the form of a cubic crystal lattice. The lattice constant of its unit cell is 2.88 Å and the density of the metal is 7.20 g/cm3. What is the number of unit cells in 100 g of the metal?
A 6 × 10^23 Correct
B 5 × 10^28
C 2 × 10^21
D 3 × 10^25
Explanation
For a cubic unit cell, volume is a3. Here a = 2.88 × 10^-8 cm, so the cell volume is about 2.39 × 10^-23 cm3. Its mass is density × volume = 7.20 × 2.39 × 10^-23, nearly 1.72 × 10^-22 g. Therefore 100 g contains 100/(1.72 × 10^-22), about 5.8 × 10^23 unit cells, which rounds to 6 × 10^23. The values 5 × 10^28 and 3 × 10^25 are far too large, while 2 × 10^21 is much too small.