The energy gained by the proton will be
E=qoV=p22mp ...... ( 1 )
where qo is the charge on the proton, V is the p.d applied, p is the momentum of the proton and mp is the mass of the proton.
The momentum p of the proton is given by de Broglie's equation as
p=hλ
Therefore, for an electron to have the same λ, it must have the same momentum.
∴ Ee=p22me
Using p from equation 1,
⟹ Ee=mpqoVme
⟹ Ee=qoV(mpme)=qo(1838V)
Therefore, an electron must be accelerated through a p.d of 1838V volt in order to achieve a wavelength λ.