The periodic law was not explained by the Dalton's atomic theory.
The periodic law was first postulated by Dimitry Mendeleef and Lothar Meyer around 1869 where they independently arrived at the periodic table or chart.
The table was based on the periodic law which states that "chemical properties of elements are a periodic function of their atomic weights".
The modern periodic law was restated by Henry Moseley in the early 1900s. He changed the basis of the law to atomic number.
The present periodic law is stated as "the properties of elements are a periodic function of their atomic number".
The laws of conservation of mass, multiple proportions and definite proportions are all explained by the Dalton's atomic theory.
An Atom would be considered to be the smallest unit that would make up matter. If were to ever see a picture of an atom, they would consists of a proton, neutron, electron, and a nucleus. And all this would be called a Atom.
