A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this radiation is $3 \mathrm{~V}_0$. If the same surface is illuminated with a radiation of wavelength $2 \lambda$, the stopping potential is $V_0$. The threshold wavelength of this surface for photoelectric effect is $\_\_\_\_$ $\lambda$.
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Solution
EK = hc/λ − φhc
e(3V₀) = hc/λ₀ − φ …(i)
eV₀ = hc/2λ₀ − φ …(ii)
Using (i) & (ii)
φ = hc/4λ₀ = hc/λ₁
λ₁ = 4λ₀
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