Modern periodic law was given after the periodic law and table by Mendeleev as it has some limitations and when Mendeleev made his periodic table. Scientists did not know about the internal structure of the atom.
Later scientists discovered that atomic number is the most basic property of a chemical element so this leads to the modern periodic law.
Thus modern periodic law states that “The physical and chemical properties of the elements are periodic functions of their atomic numbers”.
The atomic number is equal to the number of protons in an atom and a new periodic table was developed based on the modern periodic law.