- To "see" spatial details of a size $d$, you need a probe (light, for example) whose wavelength satisfies $\lambda \lesssim d$. What energy of photons do you need to "see" spatial details of (a) atomic size $\left(d \sim 10^{-10} \mathrm{~m}\right)$, (b) nuclear size $\left(d \sim 10^{-14} \mathrm{~m}\right),(\mathbf{c})$ the distribution of "sub-elementary" constituents inside a proton (distances of order $10^{-17} \mathrm{~m}$, say). [Your answer to part (a) may surprise you, since it suggests that energies of order keV's are needed to probe an atom, whereas we know that we can learn about atomic energy levels with photons of a few $\mathrm{eV}$. However, the latter tell us about energy levels, but not about spatial details. It remains true that to learn about spatial details one needs keV's.]