What speed must an electron have if its momentum is to be the same as that of an x-ray photon with a wavelength of 0.20 nm?

The momentum of a photon is given by the following relationship:

where
h is the Planck constant
is the photon wavelength

For the photon in our problem, , so its momentum is


The electron must have the same momentum of this photon, and its momentum is given by (in the non-relativistic approximation)

where
m is the electron mass
v is its speed

Re-arranging this formula, we can calculate the electron speed:


And this velocity is quite small compared to the speed of light (), so the non-relativistic approximation that we used for the electron's momentum is valid.

10 is the . . .