In the long form of the perodic table, physical and chemical properties of the elements are a periodic function of their `"_______"` .

Explanation

To answer the question, we need to understand the relationship between the properties of elements and their position in the periodic table.

### Step-by-Step Solution:

1. **Understanding the Periodic Table**: The periodic table organizes elements based on their properties. Elements in the same group (column) typically exhibit similar physical and chemical properties.

2. **Modern Periodic Law**: According to the modern periodic law, the properties of elements are periodic functions of their atomic numbers. This means that as we move across the periodic table, the properties of elements change in a predictable manner based on their atomic number.

3. **Atomic Number and Electronic Configuration**: The atomic number of an element is the number of protons in its nucleus. It also determines the number of electrons in a neutral atom. The arrangement of these electrons (electronic configuration) influences the element's chemical behavior and properties.

4. **Conclusion**: Therefore, in the long form of the periodic table, the physical and chemical properties of the elements are a periodic function of their **atomic numbers**.

### Final Answer:
In the long form of the periodic table, physical and chemical properties of the elements are a periodic function of their **atomic numbers**.

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