We usually quote the energy of a particle in terms of its
kinetic energy in electron Volts, eV (or Million electron Volts, MeV).
The reason for this is that particles are usually accelerated to some energy by
an electric field.
If I let an electron (or proton...) be accelerated through a 100 Volt potential difference,
it will have a kinetic energy of 100eV.
Computing DeBroglie Wavelengths
The whole problem of computing a deBroglie wavelength is to convert from kinetic energy to momentum.
If you always want to be correct without any need for thinking,
relativistically correct formula for the kinetic energy
and solve it for
then use this handy formula to get the answer.
I remember that
allowing me to keep the whole calculation in eV.
I also know the masses of the particles.
, make sure the precision of your calculator sufficient
or use the non-relativistic method below.)
If you know that the particle is super-relativistic, so that
then just use
and life is easy.
If you know that the particle is highly non-relativistic,
, then you can use
So, for example, compute the wavelength of a 100 eV electron.
This is non-relativistic since 100 eV « 510000 eV.
eV or 10000 eV.