Is it true that scientists can break atoms to get still smaller particles and a broken atom of say gold, will have the same properties as that of gold?

The above statement is false.

An element is a pure substance made up of only one kind of atom. A pure substance cannot be broken down further into simpler particles without losing its properties. Atom is the smallest unit and it cannot be broken into simpler particles with the same properties.

The correct statement will be, a broken atom of say gold will not have the same properties as that of gold.