When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3 λ, the stopping potential is V/4. If the threshold wavelength for the metallic surface is n λ then value of n will be __________. Numerical answer type. Work it out, then open the answer.

Answer: 9. Einstein: (hc)/(λ) = φ + eVs; write A = (hc)/(λ). A - φ = eV and A/3 - φ = eV/4 A - φ = 4A/3 - 4φ ⇒ 3φ = A/3 ⇒ φ = A/9 λ₀ = 9λ So n = 9.

When radiation of wavelength λ is used to illuminate a metallic… | JEE Main 2020 (2 Sep, Shift 1)

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Photoelectric Effect: Einstein's Equation

When radiation of wavelength $\lambda$ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3 $\lambda$ , the stopping potential is $\frac{V}{4}$ . If the threshold wavelength for the metallic surface is n $\lambda$ then value of n will be __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 9

Einstein: $\frac{hc}{\lambda} = \phi + eV_s$ ; write $A = \frac{hc}{\lambda}$ .
$A - \phi = eV$ and $\frac{A}{3} - \phi = \frac{eV}{4}$
$A - \phi = \frac{4A}{3} - 4\phi \Rightarrow 3\phi = \frac{A}{3} \Rightarrow \phi = \frac{A}{9}$
$\lambda_0 = 9\lambda$
So $n = 9$ .

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