When an object is burning, two atoms of oxygen (in the air) combine with one atom of carbon (from the substance burning). this produces three atoms that combine to form carbon dioxide gas. explain how the law of conservation of matter applies to this reaction.?

Chemical reaction: C + O₂ → CO₂.
Law of conservation of mass states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time.
In chemical reactions, the mass of the chemical components before the reaction (in this reaction carbon and oxygen) is equal to the mass of the components after the reaction (carbon dioxide).
If we use one mole of substances, that:
mass of reactants is: 12 g (C) + 2·16 g (O) = 44 g.
mass of product is: 12 g + 32 g = 44 g.

No. an alpha particle is a pair of protons and a pair of neutrons, i.e. a helium