Final answer:
The principal quantum number (n) plays the primary role in the screening effect of electrons by determining their average distance from the nucleus.
Step-by-step explanation:
The quantum number primarily associated with the screening (shielding) effect of electrons in an atom is the principal quantum number (n).
The principal quantum number determines the average relative distance of an electron from the nucleus, and as a result, electrons with higher values of n are on average further away and thus experience less electrostatic attraction to the nucleus due to shielding by inner electrons.
This leads to the screening effect, whereby inner layers of electrons protect outer electrons from the nucleus' full charge.