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So using the standard equation: E = hf, we can find the relationship between light intensity and wavelength as follows: c = lambda x f Therefore, f = c/lambda substitute this in the standard equation to get: E = (h c)/lambda Where h = planks constant, and c = speed of light.
The frequency and wavelength are simply related by the speed of light, so they're just different ways of measuring the same thing: [math]\nu = c/\lambda[/math] And the energy of the photon is just: [math]E = h\nu = hc/\lambda[/math] The condition for a photon to be wave-like is that it is delocalized (spread out) in space. Under those conditions, the wavelength corresponds to the spacing between the peaks of amplitude of the wave.