Question

When a surface 1 cm thick is illuminated by light of wavelength \( \lambda \), the stopping potential is \( V_0 \). When the same surface is illuminated by light of wavelength \( 3\lambda \), the stopping potential is \( \frac{V_0}{6} \). The threshold wavelength for the metallic surface is

• A. \( 5\lambda \)
• B. \( 2\lambda \)
• C. \( 3\lambda \)
• D. \( 4\lambda \)

Hint:

In photoelectric effect problems, use the energy of photons and the stopping potential to find the threshold wavelength.

Answer 1

The Correct Option is A

Step 1: Understanding the photoelectric effect.
The stopping potential is related to the energy of the incident photons. The energy of a photon is given by: \[ E = \frac{hc}{\lambda} \] where \( h \) is Planck's constant and \( c \) is the speed of light. The stopping potential depends on the energy of the incident photons compared to the work function \( \phi \) of the material. The equation for the stopping potential is: \[ eV = \frac{hc}{\lambda} - \phi \] Step 2: Using the given conditions.
From the problem, we know: For \( \lambda \), the stopping potential is \( V_0 \): \[ eV_0 = \frac{hc}{\lambda} - \phi \] For \( 3\lambda \), the stopping potential is \( \frac{V_0}{6} \): \[ e \times \frac{V_0}{6} = \frac{hc}{3\lambda} - \phi \] Step 3: Solving the equations.
By solving the equations, we find that the threshold wavelength \( \lambda_0 \) is \( 5\lambda \).
Step 4: Conclusion.
Thus, the threshold wavelength for the metallic surface is \( 5\lambda \), corresponding to option (A).