A ray of light of wavelength λ is incident on three photoelectric cells 1,2,3 with threshold wavelengths λ₁,λ₂,λ₃ and stopping potentials V₁,V₂,V₃ respectively. Given λ₁<λ, λ₂>λ, λ₃λ, the correct option is:

Solution & Explanation

Principle: a photoelectron is emitted only if the incident photon energy exceeds the work function, i.e. only if the incident wavelength is shorter than the threshold wavelength (λ < λ_th). The stopping potential satisfies e·V = hc/λ − hc/λ_th. Cell 1: given λ₁ < λ, i.e. the threshold wavelength λ₁ is shorter than the incident λ. Then hc/λ < hc/λ₁, the photon energy is below the work function, no emission occurs → V₁ = 0. Cells 2 and 3: λ₂ > λ and λ₃ > λ, so the incident wavelength is shorter than both thresholds → emission occurs in both. For an emitting cell, e·V = hc/λ − hc/λ_th. A larger threshold wavelength λ_th means a smaller work function (hc/λ_th smaller), hence a larger stopping potential. With λ₃ > λ₂, cell 3 has the larger threshold (smaller work function), giving the larger stopping potential: V₃ > V₂, i.e. V₂ < V₃. So V₁ = 0 and V₂ < V₃, which is option A. Trap: 'threshold wavelength larger than incident' is the condition for emission; cell 1 fails it and gives zero stopping potential.