Question

When green light is incident on a metal, photo electrons are emitted by it but no photoelectrons are obtained by yellow light. If red light is incident on that metal then:
(A) No electron will be emitted
(B) Less electrons will be emitted
(c ) More electrons will be emitted
(D) We cannot predict

Answer 1

Hint: Kinetic energy is directly proportional to the frequency. The stopping potential depends on the frequency of incident light and nature of emitter material. Frequency of incident light is independent of its intensity. The stopping potential is directly associated with the maximum kinetic energy of electrons emitted.

Formula used:
$e{{V}_{0}}={{K}_{\max }}=hv-\varphi $
 where, $\varphi $ is the work function.
$e$ is the charge of electron
${{V}_{0}}$ is the stopping potential
$h$ is the Planck’s constant
$v$ is the frequency of light

Complete answer:
When green light is made incident on a metal, photoelectrons are emitted by it, this means the frequency of green light is the threshold frequency. This is the minimum frequency due to which electron is able to knock out of the surface of metal.
The frequency of light is inversely proportional to the wavelength of light.
Since, the wavelengths of yellow and red light are more than green light, their frequencies are lesser than green light hence, no photoelectrons will be emitted when yellow or red light makes an incident on metal.
We know that,
$e{{V}_{0}}={{K}_{\max }}=hv-\varphi $
When light energy falls on a metal surface electrons are emitted from it. The emitted electrons are called photoelectrons. This process is called the photoelectric effect. Einstein got the Nobel prize for the discovery of the photoelectric effect.
But KE ranges from zero to ${{K}_{\max }}$ due to the loss of energy due to subsequent collisions before getting ejected and not due to range of frequencies within the incident light.

So, the correct answer is “Option A”.

Additional Information:
Some important conclusions arrived from photoelectric effect are,
(1) The energy distribution of the photoelectrons is independent of the intensity of incident light.
(2) The maximum kinetic energy of the photoelectrons from a given metal is found to be proportional to the frequency of the incident radiation.
(3) Photoelectrons are not emitted if the frequency of light is below the threshold value.
(4) For a given frequency, the number of photoelectrons emitted is directly proportional to the intensity of incident light.
(5) There seems to be no time lag between the onset of radiation and the resulting photoelectric current.

Note:
Kinetic energy is directly proportional to the frequency. The stopping potential depends on the frequency of incident light and nature of emitter material. When the ultraviolet light is replaced by X-rays, both ${{V}_{0}}$ and ${{K}_{\max }}$ increase. But kinetic energy ranges from zero to ${{K}_{\max }}$ because of the loss of energy due to subsequent collisions before getting ejected and not due to range of frequencies in the incident light.