In this problem:

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> According to a model based on the electromagnetic theory of light, the electron absorbs all the energy that is incident on the surface within a distance of $5.0\times 10^{-11}\ \mathrm{m}$ from the electron. The intensity of light incident on the surface is $1.6\ \mathrm{W\ m^{-2}}$. The energy required to remove an electron from the surface is $1.8\ \mathrm{eV}$.
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> (a) Calculate, on the basis of this model, that the time taken for the electron to gain sufficient energy to leave the surface is $23\ \mathrm{s}$. (The area of a circle of radius $R$ is $\pi R^2$.)
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> (b) Experimental observation indicates that electrons are emitted from the surface in less than $10^{-9}\ \mathrm{s}$. Explain how this observation is consistent with the particle theory of light.
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The answer to the first part is trivial, however, my main problem lies in the second part. Although I've studied this concept several times I tend to forget it. And I believe that this is because, I've not really understood. As far as I can recall, if we assume that light behaves as a wave, then there will be a longer time lag. But why?