Identifying the Mistake
1. Valency of a Metal: The valency of an element is a whole number that represents the combining power of an element. It cannot be a fraction like 0.5. Valency is determined by the number of electrons that an atom loses, gains, or shares to achieve a stable electron configuration.
2. Formula of the Oxide: The formula of an ionic compound like an oxide is determined by the balance of positive and negative charges. In the case of metal oxide, the metal cation and oxide anion combine in a way that the overall charge is neutral.
3. Correct Formula: The correct formula for the oxide of metal M should be M2O based on the principle of charge balance in ionic compounds. The valency of the metal M is usually determined by the charge it takes when it forms an ionic compound with other elements.
4. Explanation: The formula M2O0.5 implies that there is half of an oxygen atom in the compound, which is not possible in a stable ionic compound. The valency of the metal M should be a whole number, and the formula of its oxide should reflect the complete transfer of electrons between the metal and oxygen.

Correcting the Mistake
To correct the mistake, Radhika should reconsider the valency of the metal M and write it as a whole number. She should then determine the formula of the metal oxide based on the known valency of the metal and the oxygen. The correct formula should reflect the complete transfer of electrons and the neutral charge of the compound.
By understanding the concept of valency and the formation of ionic compounds, Radhika can correct her mistake and arrive at the accurate formula for the metal oxide.