a) When a beam of electrons is directed through an accelerating electrostatic field (two parallel plates with a potential difference of V volts), the potential energy gained by each electron (E = eV (e times V)), can be equated to its kinetic energy as follows:

eV = 1/2 m_e v²

Use this relation to derive an equation for the wavelength of an electron accelerated through an electrostatic field.

b) Calculate the wavelength of an electron when it is accelerated by 1.00 x 10³ V. Could this electron be used to image a crystal structure? Explain.