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

Explanation

To solve the question, we need to fill in the blank in the statement: "In the long form of the periodic table, physical and chemical properties of the elements are a periodic function of their '_______'."

### Step-by-Step Solution:

1. **Understanding the Question**: The question asks for the factor in the periodic table that relates to the physical and chemical properties of elements.

2. **Identifying the Key Concept**: In the long form of the periodic table, elements are arranged in order of increasing atomic number. The atomic number is defined as the number of protons in the nucleus of an atom.

3. **Historical Context**: Initially, elements were arranged based on their atomic mass, as proposed by Mendeleev. However, Moseley later established that the properties of elements are more accurately periodic functions of their atomic number rather than atomic mass.

4. **Conclusion**: Therefore, the correct answer to fill in the blank is "atomic number."

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

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