Question

When a photosensitive surface is irradiated by lights of wavelengths \( \lambda_1 \) and \( \lambda_2 \), kinetic energies of emitted photoelectrons are \( E_1 \) and \( E_2 \) respectively. The work function of the photosensitive surface is

• A. \( \frac{\lambda_2 E_2 - \lambda_1 E_1}{\lambda_2 - \lambda_1} \)
• B. \( \lambda_1 E_1 + \lambda_2 E_2 \)
• C. \( \frac{\lambda_1 E_1 - \lambda_2 E_2}{\lambda_2 - \lambda_1} \)
• D. \( \frac{\lambda_2 E_1 + \lambda_2 E_2}{\lambda_2 - \lambda_1} \)

Hint:

In the photoelectric effect, the work function \( \phi \) is related to the energies and wavelengths of the incident light by the equation \( \phi = \frac{\lambda_1 E_1 - \lambda_2 E_2}{\lambda_2 - \lambda_1} \).

Answer 1

The Correct Option is C

Step 1: Applying the photoelectric equation.
The work function \( \phi \) of the photosensitive surface is given by the equation: \[ \phi = \frac{\lambda_1 E_1 - \lambda_2 E_2}{\lambda_2 - \lambda_1} \] which is derived from the energy conservation in the photoelectric effect.
Step 2: Analyzing the options.
- (A) \( \frac{\lambda_2 E_2 - \lambda_1 E_1}{\lambda_2 - \lambda_1} \): Incorrect as it does not match the derived equation. - (B) \( \lambda_1 E_1 + \lambda_2 E_2 \): Incorrect, this does not correspond to the work function equation. - (C) \( \frac{\lambda_1 E_1 - \lambda_2 E_2}{\lambda_2 - \lambda_1} \): Correct, this matches the derived work function equation. - (D) \( \frac{\lambda_2 E_1 + \lambda_2 E_2}{\lambda_2 - \lambda_1} \): Incorrect, this does not match the work function equation.
Step 3: Conclusion.
The correct option is (C) because it represents the correct expression for the work function.