Question

The frequency of incident light falling on a photosensitive metal plate is doubled, the K.E of the emitted photoelectron is
(A). Double the earlier value
(B). Unchanged
(C). More than doubled
(D). Less than doubled

Answer 1

Hint- This question is based on Einstein's equation of photoelectric effect which is nothing but the relation between the energy of electrons ejected and the energy of electromagnetic radiation. Which is discussed in more details as?

Complete step-by-step solution -
Photoelectric effect, a phenomenon where electrically charged ions are emitted or emitted into a substance where electromagnetic radiation is absorbed; the effect is also described as the ejection of electrons when light falls on it from a metal plate.
Mathematically,
\[{E_k} = h\nu - \omega \] where ${E_k}$ is the kinetic energy of the photoelectron, h is the Planck constant, ν is the frequency associated with the radiation quantum, and ω the work function of the photon.
Now from the Einstein’s equation for photoelectric effect, the maximum kinetic energy
\[{E_k} = h\nu - \omega \]
When the frequency of incident light is made double
\[
  {E_k} = h\nu - \omega \\
  E{'_k} = 2\nu h - \omega \\
  E{'_k} = 2\left( {h\nu - \omega } \right) + \omega \\
  E{'_k} = 2{E_k} + \omega \\
\]
From the above equations it is clear that the kinetic energy of the photoelectrons will be more than double when incident frequency is double.
Hence, the correct option is “C”.

Additional Information-
Electromagnetic radiation will release electrons from the solid surface. The photoelectric effect is called this method. Photo emissive is said to be a substance with the photoelectric effect. Photoelectrons are called electrons thrown by the photoelectric effect.

Note- The photoelectric research resulted in important steps in the realization of light's and electrons' quantum existence and inspired the development of the wave-particle duality principle. Often commonly used to analyze the electron energy level in matter are the photoelectric effects.