Through how many volts of potential difference must an electron be accelerated to achieve a wavelength of 0.57 nm ?

We must use two formulas of energy first how energy is related to wavelength:

Such that , c is the speed of light in a vacuum and h is Plank's constant.

And the second equation is how energy relates to voltage:

Such that q is the charge of the particle (in this case the electron) and V is voltage.  By substituting the second equation into the first we have:

We know that:

And so:

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.