Question

An electron, initially at rest, is accelerated through a potential difference of 1000 Volts and acquires a DeBroglie wavelength of λ. By approximately how much voltage should a proton be accelerated to acquire the same DeBroglie wavelength?

Answer 1

the equation for DeBroglie wavelength is \[\lambda = h / mv\] so you need \[\lambda _{proton}=\lambda _{electron}\] The electron gets the energy from the potential difference \[E = qV=1/2mv\] solving for velocity \[v = \sqrt{2qV/m}\] plug that into the equation for the DeBroglie wavelength \[\lambda = h / (m \sqrt{2qV/m})\] set that equal to the equation for the protons wavelength \[h / (m _{proton} \sqrt{2qV _{proton}/m _{proton}}) = h / (m _{electron} \sqrt{2qV _{electron}/m _{electron}})\] plug in all the numbers and then solve for the voltage the proton must pass through

Answer 2

thanks!!