A certain metallic surface is illuminated by monochromatic radiation of wavelength λ. The stopping potential for photoelectric current for this radiation is 3V₀. If the same surface is illuminated with a radiation of wavelength 2λ, the stopping potential is V₀. The threshold wavelength of this surface for photoelectric effect is ____________ λ.

Solution

Physics sir · 4 steps

Write Einstein's equation for both wavelengths and subtract: the work function drops out first.

1. Two equations. Einstein's equation says photon energy = work function + eVₛ. For wavelength λ: hc/λ = φ + 3eV₀. For wavelength 2λ: hc/2λ = φ + eV₀.
2. Subtract them. Subtracting removes φ and leaves hc/2λ = 2eV₀, so eV₀ = hc/4λ.
3. Find the work function. Put this into the second equation: φ = hc/2λ - hc/4λ = hc/4λ.

   φ = hc/λ₀ = hc/4λ ⇒ λ₀ = 4λ

4. So. The threshold wavelength is 4λ, so the answer is 4.

The idea to keep. Two stopping potentials for the same metal means two Einstein equations. Subtract to kill φ, then use φ = hc/λ₀ to get the threshold wavelength.

Answer from the NTA final answer key. Solution by PrepWiser.