Question

In an experiment with photoelectric effect, the stopping potential:

• A. increases with increase in the wavelength of the incident light
• B. increases with increase in the intensity of the incident light
• C. is \( \frac{1}{e} \) times the maximum kinetic energy of the emitted photoelectrons
• D. decreases with increase in the intensity of the incident light

Hint:

The stopping potential \( V_s \) is a key factor in the photoelectric effect, representing the potential needed to stop the emitted electrons. It is directly related to the maximum kinetic energy of the emitted photoelectrons.

Answer 1

The Correct Option is C

In the photoelectric effect, the energy of the emitted photoelectrons is given by: \[ E = h \nu - W \] where \( h \nu \) is the energy of the incident photons and \( W \) is the work function. The stopping potential \( V_s \) is related to the kinetic energy of the emitted photoelectrons, and it is given by: \[ eV_s = K_{\text{max}} \] where \( K_{\text{max}} \) is the maximum kinetic energy of the emitted photoelectrons. Hence, the stopping potential is \( \frac{1}{e} \) times the maximum kinetic energy of the emitted photoelectrons.

Answer 2

Step 1: Understanding the concept of stopping potential
In the photoelectric effect, when light of frequency greater than the threshold frequency strikes a metal surface, electrons are emitted. These emitted electrons have a range of kinetic energies, with some possessing a maximum kinetic energy given by:
\[ K_{\text{max}} = eV_0 \] where \( V_0 \) is the stopping potential and \( e \) is the electronic charge.

Step 2: Meaning of stopping potential
The stopping potential is the minimum negative potential that must be applied to the collector plate to stop even the most energetic photoelectrons from reaching it. At this potential, the photocurrent becomes zero because all electrons are repelled before they can reach the collector.

Step 3: Relationship between stopping potential and kinetic energy
From the energy conservation relation in the photoelectric effect:
\[ K_{\text{max}} = eV_0 \] Rearranging gives: \[ V_0 = \frac{K_{\text{max}}}{e} \] Thus, the stopping potential is equal to \( \frac{1}{e} \) times the maximum kinetic energy of the emitted photoelectrons.

Step 4: Conclusion
The stopping potential directly represents the energy of the most energetic photoelectrons, expressed in volts. Therefore:

Final Answer:
is \( \frac{1}{e} \) times the maximum kinetic energy of the emitted photoelectrons