Question

Given below are two statements :
Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source
Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.
In the light of above statements, choose the most appropriate answer from the options given below

• A. Both Statement I and Statement II are incorrect
• B. Statement I is correct but statement II is incorrect
• C. Both Statement I and statement II are correct
• D. Statement I is incorrect but statement II is correct

Answer 1

The Correct Option is C

To solve this question, we need to examine each statement regarding the photoelectric effect and determine whether it is correct or incorrect.

Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source.

The stopping potential is the voltage needed to stop the most energetic photoelectrons emitted from a metal surface during the photoelectric effect. According to the photoelectric effect theory, the stopping potential is related to the maximum kinetic energy of the photoelectrons. The kinetic energy of a photoelectron is given by the equation:

\(K_{\text{max}} = hf - \phi\),

where \(hf\) is the energy of the incoming photon and \(\phi\) is the work function of the metal. The stopping potential \(V_0\) is then related to the maximum kinetic energy by:

\(eV_0 = K_{\text{max}}\).

It is important to note that the stopping potential, and hence the maximum kinetic energy of the electrons, does not depend on the intensity or power of the light. Higher power means more photons are incident per unit time, increasing the number of emitted electrons but not their maximum kinetic energy. Therefore, Statement I is correct.

Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.

The energy of a photon is related to its wavelength by the equation:

\(E = \frac{hc}{\lambda}\),

where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.

Thus, the energy of the photon, and therefore the maximum kinetic energy of the emitted photoelectrons, depends directly on the wavelength of the incident light. A shorter wavelength means higher energy photons, resulting in greater maximum kinetic energy for the photoelectrons. Hence, Statement II is correct.

Conclusion: Both Statement I and Statement II are correct.