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I would guess the question is asking you what the maximum charge on the sphere is. Suppose the photon energy ($hc/\lambda$) is $E$, then the kinetic energy of the electron leaving the surface (in electron volts) is $E$ - 4.47. As you increase the positive charge on the sphere you increase the work needed to remove an electron to infinity, and for some ...

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You're not doing this wrong. As you know energy of each photon is $E = hf = 2.27eV$ so they can't produce any photoelectrons on a metal with work function greater than that.

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The "color" of a photon can be ultraviolet. Visible light is just a small part of the electromagnetic spectrum. Ultraviolet is the part of the spectrum with slightly shorter wavelengths than blue and purple. Many materials have a threshold wavelength in the ultraviolet. And for any material with a threshold wavelength in the visible, ultraviolet light will ...

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The metal's threshold wavelength is a wavelength of light. So yes, you would use a chart converting wavelengths of light to the color to identify it. For some metals, the threshold wavelength is not visible light; it might be ultraviolet. But whatever chart you're using would identify the wavelength you have as either ultraviolet or visible, and which color ...

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I think you should re-read the question, because "frequency of the metal" doesn't make much sense in this context. And the color of photon is dependant only on it's frequency which is given. Do you need some further explanations on that? Photoeffect's main equation is one of energy balance. The only energy source in this event is the photon whose energy is ...

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