In the modern periodic table, the period indicates the value of:

The correct option is Principal Quantum Number.

In the modern periodic table, elements are arranged in horizontal rows called periods and vertical columns called groups. There are seven periods in the periodic table, numbered from 1 to 7.

The period number to which an element belongs corresponds directly to the highest energy level (or shell) that is occupied by electrons in its ground-state electronic configuration. In quantum mechanics, this principal energy level of an atom is represented by the principal quantum number, denoted by the symbol $n$.

For example:
- Elements in Period 1 (such as Hydrogen and Helium) have their valence electrons in the first shell ($n$ = 1).
- Elements in Period 2 (such as Lithium and Neon) have their valence electrons in the second shell ($n$ = 2).
- Elements in Period 3 (such as Sodium and Argon) have their valence electrons in the third shell ($n$ = 3).

Therefore, the period number in the periodic table indicates the maximum value of the principal quantum number ($n$) for the electrons in the elements of that period.