Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths is nearest to (a) 1: 2 (b) 4: 1 (c) 2: 1 (d) 1: 4

Answer: (c). Threshold wavelength λ₀ = (hc)/(φ), so λ₀ ∝ 1/φ. λNaλCu = φCuφNa = (4.5)/(2.3) ≈ 1.96 ≈ 2 So the answer is (c) 2: 1.

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively… | JEE Main 2002 (AIEEE)

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Photoelectric Effect: Einstein's Equation

Sodium and copper have work functions $2.3\text{ eV}$ and $4.5\text{ eV}$ respectively. Then the ratio of the wavelengths is nearest to

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Answer: (c)

Threshold wavelength $\lambda_0 = \frac{hc}{\phi}$ , so $\lambda_0 \propto \frac{1}{\phi}$ .
$\frac{\lambda_{Na}}{\lambda_{Cu}} = \frac{\phi_{Cu}}{\phi_{Na}} = \frac{4.5}{2.3} \approx 1.96 \approx 2$
So the answer is (c) $2 : 1$ .