Why do electrons eject only if the frequency of incident ray is greater than the threshold frequency?

Question

Why do the electrons start moving even if the dim light (less intense) of a specific frequency falls on the material ?

Answer 1

Because the light is absorbed mostly as single photons. Two-photon absorption is also possible, but it is a much rarer event.

A single photon carries energy $\hbar\omega$. If it is not sufficient to "lift" the electron to higher allowed energy, such a photon is scattered elastically, without absorption.

The problem is that the electron is not alone, it is attracted to the nucleus. And it is not a classical particle, but a standing wave. Standing waves have distinct frequencies( energies). Thus, there is an energy threshold for promoting an electron to higher levels.