The stopping potential in the photoelectric effect is related to the energy of the incident photons and the work function of the material. The work function represents the minimum energy required to release an electron from the surface of the material.
The energy of a photon can be calculated using the formula:
E = hc/λ
Where:
E = energy of the photon
h = Planck's constant
c = speed of light
λ = wavelength of the light
Now, let's consider two cases:
When the surface is illuminated with monochromatic light of wavelength λ, the stopping potential is 3V₀. The energy of these photons is E₁ = hc/λ.
When the same surface is illuminated with light of wavelength 2λ, the stopping potential is V₀. The energy of these photons is E₂ = hc/(2λ).
The stopping potential is given by the difference in energy between the incident photons and the work function (W) of the material:
V₀ = E₁ - W
V₀ = E₂ - W
Now, let's subtract the second equation from the first to eliminate the work function:
3V₀ - V₀ = (hc/λ) - (hc/(2λ))
2V₀ = (hc/λ) - (hc/(2λ))
2V₀ = (2hc/λ) - (hc/λ)
2V₀ = (2hc - hc) / λ
2V₀ = hc / λ
Now, let's solve for λ:
λ = (hc) / (2V₀)
Now, we can substitute the given value of V₀, which is 3V₀:
λ = (hc) / (2 * 3V₀)
λ = (hc) / (6V₀)
So, the threshold wavelength (λₜ) is:
λₜ = (hc) / (6V₀)
Now, let's look at the answer choices and see which one matches this expression:
A) 6λ - This is not the correct answer.
B) (4/3)λ - This is not the correct answer.
C) 4λ - This is not the correct answer.
D) 8λ - This is not the correct answer.
None of the given answer choices match the expression for the threshold wavelength. It's possible that there is an error in the answer choices or in the problem statement. Please double-check the problem or provide additional information if needed.
