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Sometimes a question will ask you to find the longest possible wavelength, and sometimes you just have to find the wavelength. Either way you use the formula wavelength=CxH/work function. Is this right? If so what's the difference in finding the longest possible wavelength, or just the wavelength?
When you find the longest possible wavelength, you will use 0 for the kinetic energy and then figure out the wavelength normally. For finding a wavelength, it's similar but there is usually other information, such as the velocity of the ejected electron, which would give you the kinetic energy. So it's just different kinetic energies for the types of problems.
When they say "longest wavelength" they're referring to the longest wavelength that would have the threshold energy, or the minimum energy needed to remove an electron from a metal. That means that the kinetic energy would be 0, because there would be no excess energy as the incoming energy of the photon would equal the energy of the work function. So basically you're going to solve the (Kinetic energy= h(frequency) - work function) equation by setting the h(frequency) equal to the work function as kinetic energy would equal 0. Then solve for the frequency and then using that, the wavelength. This would give you the longest wavelength. If you're just trying to figure out the wavelength, you use either this equation, the de Broglie equation you mentioned, or another one. Basically just look at what variables you have and see which equation(s) allows you to use them!
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