$(a)$ What is the basis of arranging the elements in the Modern Periodic Table?
$(b)$ How does this remove the problem of positioning of isotopes?

(N/A) The basis of arranging elements in the Modern Periodic Table is the increasing order of their atomic number $(Z)$. This approach allows for more precise predictions of elemental properties.
$(b)$ Isotopes are atoms of the same element that have the same atomic number $(Z)$ but different atomic masses. Since the Modern Periodic Table is organized based on increasing atomic numbers,all isotopes of a given element share the same position. Therefore,they are placed in the same group and the same period,effectively resolving the problem of their positioning.