Quantum - potential difference problem.

[Physics103]

question:

A certain proton needs to have a lamba of 0.0055 x 10^-9m. What potential difference must this proton be accelerated to achieve this wavelength?

what i know:

im assuming that what we need to find in this question is the amount of kinetic enegry needed to achieve such a lambda.

E = hv / y y will represent lambda
i also know that
Ek = eV <--- potential difference
and that
Ek = 1/2mv^2

so eV = 1/2mv^2
and v is = E x lambda / h

so

eV = 1/2m (eV x lamba / h) ^2

am i on the right track here or am i completely lost??

 

[Astronuc]

It depends on whether or not the proton is relativistic.

You are looking for the potential which will impart a kinetic energy to a proton such the wavelength is as given.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html#c3

You might try the relativistic and non-relativistic formulae to see the difference.

 

[Physics103]

hmmm, will do.

thanks for the help