A crystal of a metal oxide MO exhibits a metal deficiency defect. A detailed analysis reveals that for every 100 oxide ( O²⁻ ) ions in the crystal lattice, there are exactly 4 cation vacancies. To maintain electrical neutrality, some of the metal ions exist in the +3 oxidation state instead of the usual +2 state. The ratio of the number of M²⁺ ions to M³⁺ ions in the crystal is:

Step-by-step solution

Let the number of O²⁻ ions be 100 . Since there are 4 cation vacancies per 100 O²⁻ ions, the total number of metal ions present is 100 - 4 = 96 . Let the number of M³⁺ ions be x and the number of M²⁺ ions be y . Total number of metal ions: x + y = 96 To maintain electrical neutrality, the total positive charge must equal the total negative charge. The total negative charge from 100 O²⁻ ions is 200 . Total positive charge: 3x + 2y = 200 Substituting y = 96 - x into the charge equation: 3x + 2(96 - x) = 200 x + 192 =