The number of periods in the modern periodic table is:
The modern periodic table has 7 periods, each corresponding to the highest principal quantum number (n=1 to 7). This follows from NCERT principle where relation explains outcome clearly for students.
Ref: NCERT Chemistry Textbook for Class XI and XII, Chapter: Some Basic Concepts, Structure of Atom, Periodicity and relevant Chemistry topic, Topic: Mole concept and periodic trends.