When a certain metal surface is illuminated with light of frequency ν, the stopping potential for photoelectric current is V₀. When the same surface is illuminated by light of frequency ν/2, the stopping potential is V₀/4, the threshold frequency of photoelectric emission is (a) ν/6 (b) ν/3 (c) 2ν/3 (d) 4ν/3

Answer: (b). Einstein: hν = φ + eV₀ hν - φ = eV₀ and hν/2 - φ = eV₀/4 hν - φ = 2hν - 4φ ⇒ φ = hν/3 ν₀ = φ/h = ν/3 So the answer is (b) ν/3.

When a certain metal surface is illuminated with light of frequency… | MHT CET 2023 (9 May, Shift 2)

Q82MHT CET 2023 · 9 MAY · SHIFT 2Medium

Photoelectric Effect: Einstein's Equation

When a certain metal surface is illuminated with light of frequency $\nu$ , the stopping potential for photoelectric current is $V_0$ . When the same surface is illuminated by light of frequency $\frac{\nu}{2}$ , the stopping potential is $\frac{V_0}{4}$ , the threshold frequency of photoelectric emission is

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Answer: (b)

Einstein: $h\nu = \phi + eV_0$
$h\nu - \phi = eV_0$ and $\frac{h\nu}{2} - \phi = \frac{eV_0}{4}$
$h\nu - \phi = 2h\nu - 4\phi \Rightarrow \phi = \frac{h\nu}{3}$
$\nu_0 = \frac{\phi}{h} = \frac{\nu}{3}$
So the answer is (b) $\frac{\nu}{3}$ .

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