Suppose you need to image the structure of a virus with a BIO diameter of \(50 \mathrm{~nm}\). For a sharp image, the wavelength of the probing wave must be \(5.0 \mathrm{~nm}\) or less. We have seen that, for imaging such small objects, this short wavelength is obtained by using an electron beam in an electron microscope. Why don't we simply use short-wavelength electromagnetic waves? There's a problem with this approach: As the wavelength gets shorter, the energy of a photon of light gets greater and could damage or destroy the object being studied. Let's compare the energy of a photon and an electron that can provide the same resolution.

a. For light of wavelength \(5.0 \mathrm{~nm}\), what is the energy (in \(\mathrm{eV}\) ) of a single photon? In what part of the electromagnetic spectrum is this?

b. For an electron with a de Broglie wavelength of \(5.0 \mathrm{~nm}\), what is the kinetic energy (in \(\mathrm{eV}\) )?