Question

A surface ejects electrons when hitted by green light but not when hitted by yellow light. Will the electrons be ejected if the surface is hitted by red light:
(A) Yes
(B) No
(C ) Yes, if the red beam is quite intense
(D) Yes, if the red beam continues to fall upon the surface for a long time.

Answer 1

Hint: Energy of red light is less than that of yellow light. If the wavelength of incident light is less than that of yellow light, photoelectric emission is possible. The energy of light waves is inversely proportional to the wavelength. Kinetic energy is directly proportional to the frequency. The stopping potential depends on two factors, the frequency of incident light and nature of emitter material. Frequency of incident light is independent of the intensity of the light. 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 step by step solution:
We know that,
$e{{V}_{0}}={{K}_{\max }}=hv-\varphi $
Energy of red light is less than that of yellow light. If the wavelength of incident light is less than that of yellow light, photoelectric emission is possible. The energy of light waves is inversely proportional to the wavelength. Here the wavelength of red is greater than that of yellow light. Hence, no electrons are ejected if the surface is hitted by red light.
When light energy falls on some metal surfaces 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.

So, the correct answer is “Option B”.

Additional Information: Some conclusions arrived from photoelectric effect are,
(1) The energy distribution of the photoelectrons doesn’t depend on the intensity of incident light.
(2) The maximum kinetic energy of the photoelectrons and frequency of the incident radiation are directly proportional.
(3) Photoelectrons are not emitted if the frequency of light is below the threshold value.
(4) There is no time lag between the onset of radiation and the resulting photoelectric current.

Note: Kinetic energy and frequency are directly proportional. The stopping potential depends on two factors, the frequency of incident light and nature of emitter material. But kinetic energy has values varying 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.