4. (5 points) There can often be confusion about when to use the wavelengths of light and the various formulae for light versus the de Broglie wavelength for matter and the formula that connects the wavelength of matter to kinetic energy or momentum. (a) Write down in one column all the expressions for light that you can think of (connecting Alight and c and v and connecting photon energy to h, c, v, ), and in a second column write all the expressions for matter (connecting matter to momentum and kinetic energy). Discuss briefly when to use each column and why. (b) Calculate the de Broglie wavelength in nm for an electron accelerated from rest through a potential energy change of 1000 V. (c) Suppose we want to construct an electron microscope to resolve features of approximately 100 nm. What minimum kinetic energy of electrons (in eV) would be necessary? The number you calculate will probably seem small. However, in practice, accelerating voltages of 20 keV or more are used routinely in a real electron microscope. How can this be understood? Use the internet to find some answers about how electron microscopes work and are constructed to discuss your answer.