Dual Nature of Matter

JEE Main level, numerical answer, medium

157 of 200

Question 157 of 200

A certain metallic surface is illuminated by monochromatic radiation of wavelength λ\lambda. The stopping potential for photoelectric current for this radiation is 3V0.3{V}_{0}. If the same surface is illuminated with a radiation of wavelength 2λ,2\lambda , the stopping potential is V0.{V}_{0}. The threshold wavelength of this surface for photoelectric effect is___________λ.\lambda .

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Answer: 4

KE=hcλ−ϕhcKE=\dfrac{hc}{\lambda }-\phi hc
e(3V0)=hcλ0−ϕ…(i)e\left(3{V}_{0}\right)=\dfrac{hc}{{\lambda }_{0}}-\phi \ldots \left(i\right)
eV0=hc2λ0−ϕ…(ii)e{V}_{0}=\dfrac{hc}{2{\lambda }_{0}}-\phi \ldots \left(ii\right)
Using (i)and(ii)\left(i\right)\text{and}\left(ii\right),
ϕ=hc4λ0=hcλt\phi =\dfrac{hc}{4{\lambda }_{0}}=\dfrac{hc}{{\lambda }_{t}}
λt=4λ0{\lambda }_{t}=4{\lambda }_{0}

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