Question

Light of a single frequency falls on a photo-electric material but no electrons are emitted . Electrons may be emitted if the _____________

Answer 1

Correct answer is "frequency of the light is increased".

The light that hits the photo-electric material consists of several photons, each one carrying an energy of
$E=hf$
where h is the Planck constant while f is the light frequency. Part of this energy is used to extract the photo-electrons from the material, and part it is converted into kinetic energy K of the electron:
$hf= \phi + K$
where $\phi$ is the work function of the material, which is the amount of energy needed to extract the photo-electron.

If no photo-electrons are emitted, it means that the energy given by the photon is not enough to extract the photo-electron. But we see that the energy of the photon is directly proportional to the frequency of the light f, so in order to increase the energy, we should increase the frequency of the light.