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A hydrogen like atom has the energy (En) in its nth allowed orbit, given by En\((\frac{a}{n^2})\) where α is a constant. The atom is in its mth excited state. It emits rediations in coming to ground state directly from the excited state. The emitted radiations are incident on a photosensitive material of threshold wavelength λ0 . The maximum K.E, of the emitted photoelectrons, equals twice the photoelectric work function of the material. The quantum number m equals.

(1) \((\frac{λ_0a}{λ_0a-2hc})^{1/2}+1\) 

(2) \((\frac{λ_0a}{λ_0a-2hc})^{1/2}-1\)

(3) \((\frac{λ_0a}{λ_0a-hc})^{1/2}+1\)

(4) \((\frac{λ_0a}{λ_0a-3hc})^{1/2}-1\)

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 (4) \((\frac{λ_0a}{λ_0a-3hc})^{1/2}-1\)

We have w0 = work function of photosensitive material = hc/λ0. Let E = hv , be the energy of photon incident on the photosensitive material. From Einstein’s equation of photoelectric effect, we have

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