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The threshold wavelength for a metal having work function W₀ is λ₀. What is the threshold wavelength for a metal whose work function is (W₀)/2?

Asked in GUJCET 2007 · Threshold frequency and wavelength

• (1) 4λ₀
• (2) 2λ₀
• (3) (λ₀)/2
• (4) (λ₀)/4

Step-by-step solution

Why the other options are wrong

• (1) 4λ₀ would need λ₀ ∝ 1/(W₀²). The threshold relation λ₀ = (hc)/(W₀) is a simple inverse, so halving W₀ only doubles it.
• (3) This treats λ₀ as proportional to W₀. A smaller work function is overcome by lower-energy, longer-wavelength photons, so the threshold wavelength grows; (λ₀)/2 belongs to a work function of 2W₀.
• (4) Both the direction and the power are wrong: (λ₀)/4 would be the threshold for a work function of 4W₀.

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