Question

An electron microscope is designed to resolve objects as small as 135 pm, about the
size of a gold atom. What energy electrons must be used in this microscope?

I've seen people use the size of the object as the wavelength, I want to know why ? and some poeple use E=hc/lamda and others use E=h^2/2m(lamda)^2, why? help would be much appreciated.

Answer 1

We use it due to wave nature of electron

Wave Nature of Electron

As a young student at the University of Paris, Louis DeBroglie had been impacted by relativity and the photoelectric effect, both of which had been introduced in his lifetime. The photoelectric effect pointed to the particle properties of light, which had been considered to be a wave phenomenon. He wondered if electons and other "particles" might exhibit wave properties. The application of these two new ideas to light pointed to an interesting possibility:

E=h^2/2m(lamda)^2=