Q.Define modern periodic law.

Henry Moseley (1913) studied the characteristic X-rays emitted by elements bombarded with high-energy electrons and found a strict linear relationship between the square root of the emitted X-ray frequency $\nu$ and the element's atomic number $Z$:

with $a$ and $b$ constants common to all elements. This let atomic number be measured directly and unambiguously, and it is atomic number -- not atomic weight -- that Moseley's results showed the elements' properties are truly periodic functions of. This is the modern periodic law: the physical and chemical properties of the elements are periodic functions of their atomic numbers. Elements are arranged in the periodic table by increasing atomic number, and this ordering is what resolves the anomalies (such as cobalt/nickel and tellurium/iodine) that plagued Mendeleev's atomic-weight-based table. The regular recurrence of similar properties as atomic number increases is called periodicity, and it is a direct consequence of the regular, repeating way electron shells fill (the Aufbau principle) as atomic number increases.