It is stated in the text that special relativity must be used to calculate the de Broglie wavelength of electrons in an electron microscope. Let us discover how much of an effect relativity has. Consider an electron accelerated through a potential difference of \(1.00 \times 10^{5} \mathrm{~V}\).

a. Using the Newtonian (nonrelativistic) expressions for kinetic energy and momentum, what is the electron's de Broglie wavelength?

b. The de Broglie wavelength is \(\lambda=h / p\), but the momentum of a relativistic particle is not \(m v\). Using the relativistic expressions for kinetic energy and momentum, what is the electron's de Broglie wavelength?