When light of wavelength λ is incident on a photosensitive surface the stopping potential is ' V '. When light of wavelength 3λ is incident on same surface the stopping potential is V/6. Then the threshold wavelength for the surface is (a) 2λ (b) 3λ (c) 4λ (d) 5λ

Answer: (d). Einstein: (hc)/(λ) = φ + eVs; write A = (hc)/(λ). A - φ = eV and A/3 - φ = eV/6 A - φ = 6(A/3 - φ) = 2A - 6φ ⇒ φ = A/5 λ₀ = (hc)/(φ) = 5λ So the answer is (d) 5λ.

When light of wavelength λ is incident on a photosensitive surface… | MHT CET 2023 (12 May, Shift 1)

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Photoelectric Effect: Einstein's Equation

When light of wavelength $\lambda$ is incident on a photosensitive surface the stopping potential is ' $V$ '. When light of wavelength $3\lambda$ is incident on same surface the stopping potential is $\frac{V}{6}$ . Then the threshold wavelength for the surface is

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Answer: (d)

Einstein: $\frac{hc}{\lambda} = \phi + eV_s$ ; write $A = \frac{hc}{\lambda}$ .
$A - \phi = eV$ and $\frac{A}{3} - \phi = \frac{eV}{6}$
$A - \phi = 6\left(\frac{A}{3} - \phi\right) = 2A - 6\phi \Rightarrow \phi = \frac{A}{5}$
$\lambda_0 = \frac{hc}{\phi} = 5\lambda$
So the answer is (d) $5\lambda$ .

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