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Computing DeBroglie Wavelengths

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.
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,
use the
**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.

(If
, 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
giving
.

So, for example, compute the wavelength of a 100 eV electron.
This is non-relativistic since 100 eV « 510000 eV.
So
eV or 10000 eV.

Jim Branson
2013-04-22