Question

An electron is accelerated from rest through a difference of potential V.
a) Show that the de Broglie wavelength, in unit of angstrom Å (10-10 m), for a non-
relativistic electron accelerated through a small potential difference is:
λ ＝12.27/(v)^1/2

b) Calculate λ if the electron is accelerated through 50 V.
c) Find the de Broglie wavelength for a relativistic electron that is accelerated from rest
through a large difference potential difference at a modern particle collider.
d) Show that
( λ non-relativistics − λ relativistics)/ λ relativistics = 2.21 ≈ 2.2
for electrons with
total energy of 10 MeV. In other words, that the percent error between the non-
relativistic and the relativistic de Broglie wavelength is about 220% for 10 MeV
electrons.

Answer 1