Animated Solution for Chemistry - Periodicity in Properties: According to the periodic law of elements, the variation in properties of elements is related to their

For decades, chemists wrestled with a monumental puzzle: how to organize the known elements in a way that made logical sense. Dmitri Mendeleev made a massive leap forward by arranging elements according to their atomic masses. He proposed that the physical and chemical properties of elements were periodic functions of their atomic mass.

While Mendeleev's periodic table was revolutionary and even predicted the existence of undiscovered elements, it wasn't perfect. Certain elements had to be placed out of order regarding their mass to keep elements with similar properties in the same column. For instance, Argon (mass $39.9$) had to be placed before Potassium (mass $39.1$). This anomaly hinted that atomic mass was not the ultimate fundamental property.

The true breakthrough came in 1913 with the brilliant work of Henry Moseley. Moseley conducted an elegant experiment where he bombarded various elements with high-energy electrons and analyzed the X-rays they emitted.

He discovered a striking mathematical relationship: the square root of the frequency of the emitted X-rays ($\sqrt{ u}$) was directly proportional to the atomic number ($Z$) of the element, not its atomic mass. The relationship is given by Moseley's Law:

where $a$ and $b$ are constants.

Moseley's experiment proved beyond a shadow of a doubt that the atomic number—the number of protons in an atom's nucleus—is the most fundamental property of an element. Because atoms are electrically neutral, the atomic number also dictates the number of electrons. It is the arrangement of these electrons (the electronic configuration) that ultimately determines an element's chemical behavior.

This led to the formulation of the Modern Periodic Law, which states:

> "The physical and chemical properties of elements are periodic functions of their atomic numbers."

Therefore, the variation in properties of elements is intrinsically related to their atomic numbers, making option (c) the correct answer.