1.020g of metallic oxide contains 0.540g of metal taking the symbol for metal as M find the molecular formula of the oxide. The specific heat of metal is 0.216cal deg/per gram

Given data:
- Mass of metallic oxide = 1.020g
- Mass of metal (M) in the oxide = 0.540g
- Specific heat of metal (M) = 0.216 cal deg/g

Finding the atomic mass of metal (M):
1. Calculate the number of moles of metal (M) in 0.540g using the formula:
Moles = Mass / Molar mass
Moles of metal (M) = 0.540g / Molar mass of metal (M)
2. Since the mass of the oxide is 1.020g and the mass of the metal (M) in the oxide is 0.540g, the mass of oxygen in the oxide can be calculated as:
Mass of oxygen = Mass of oxide - Mass of metal (M) = 1.020g - 0.540g
3. Determine the number of moles of oxygen in the oxide using the formula:
Moles of oxygen = Mass of oxygen / Molar mass of oxygen
4. Calculate the atomic mass of the metal (M) using the specific heat capacity formula:
Specific heat = (Moles of metal (M) x Atomic mass of metal (M) + Moles of oxygen x Atomic mass of oxygen) x Specific heat capacity

Finding the molecular formula of the oxide:
1. Determine the molar ratio of metal (M) to oxygen in the oxide by comparing the moles of metal (M) and oxygen calculated earlier.
2. Use the molar ratio to write the empirical formula of the oxide.
3. Calculate the molar mass of the empirical formula.
4. Divide the molar mass of the oxide by the molar mass of the empirical formula to find the molecular formula of the oxide.
By following these steps, you can determine the molecular formula of the metallic oxide based on the given data and specific heat capacity of the metal.