By what potential difference must a a proton and b an electr

By what potential difference must (a) a proton and (b) an electron be accelerated to have a wavelength of = 5.0 x 10^-12 m? You should have two numbers one representing the proton and the second representing the electron. Comment on these numbers paying attention to the feasibility of using protons instead of electrons for diffraction experiments.

Solution

Energy of wave with wavelength lambda.

Energy = h c / lambda

a) for proton.

Energy = (6.626 x 10^-34 x 3 x 10^8) / (5 x 10^-12) = 3.9756 x 10^-14 J

and energy = q deltaV

3.9756 x 10^-14 = 1.6 x 10^-19 x deltaV

deltaV = 248475 volt

b) electrons also have same lambda hence same energy .

and q is also same in magnitude hence same potential diff.

so deltaV = - 248475 Volt