A photo-emissive substance is illuminated by radiation of wavelength λᵢ and emits electrons with de Broglie wavelength λₑ. The longest wavelength that can cause photoemission is λ₀. Which expression for λₑ is correct?
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Question

A photo-emissive substance is illuminated by radiation of wavelength λᵢ and emits electrons with de Broglie wavelength λₑ. The longest wavelength that can cause photoemission is λ₀. Which expression for λₑ is correct?

Options

G1 Physics · Accepted Answer

Einstein's photoelectric equation gives K = hc/λᵢ - hc/λ₀ = hc(1/λᵢ - 1/λ₀). For an electron, de Broglie wavelength is λₑ = h/p, and K = p²/(2m). Therefore, p = √(2mK), so λₑ = h/√(2mK). Substitute K: λₑ = h/√[2mhc(1/λᵢ - 1/λ₀)]. Cancel one factor h inside the square root: λₑ = √{h/[2mc(1/λᵢ - 1/λ₀)]}. Correct option: A.