Final answer:
The photoelectric effect determines that increasing the frequency of incident light above the threshold frequency, while keeping intensity constant, leads to electrons with greater kinetic energy being ejected, but does not change the rate of electron ejection.
Step-by-step explanation:
The photoelectric effect is the phenomenon where light causes electrons to be ejected from a metal surface. According to the equation E = hv, where E is the energy of the photon, h is Planck's constant, and v is the frequency of the light, the energy of a photon is directly proportional to its frequency. If the frequency of the incident light on the metal is increased while keeping the intensity constant, then, according to quantum theory, the kinetic energy of the ejected electrons will increase as long as the frequency is above the threshold frequency for that particular metal. However, the rate at which electrons are ejected (the number of electrons per unit time) does not change with frequency alone; it is influenced by changes in intensity.
If the frequency is below the threshold frequency, no electrons are ejected regardless of the intensity. Thus, with increased frequency above the threshold, the correct answer is that the rate of ejected electrons will remain the same, but their speed - or equivalently, their kinetic energy - will increase. Hence, the correct choice is B: the rate of ejected electrons will remain the same but their speed will increase.