If electrons are in orbits for metals, then, collision are more likely when the orbital radius and the radius of circular motion of the photons are about equal. Too big or too small and they miss each other. At low frequency, \(r\) is too big. As frequency increases, \(r\) decreases and is able to interact with the outer most electrons when they are of about the same radius. This could be the reason for the threshold frequency. At higher frequencies, \(r\) is small enough to interact with electrons in the inner shells of comparable radius.
