To develop this problem it is necessary to apply the concepts related to electromagnetic energy and Broglie's hypothesis.
By definition we know that the electrical energy of a proton can be expressed as
E = qV
Where,
q = Charge of proton
V = Voltage
Replacing with our values
E = qV
[tex]E = (1.6*10^{-19})(220) \rightarrow[/tex] It is necessary to add the two potentials
[tex]E = 4.224*10^{-17}J[/tex]
From Broglie's hypothesis we know that the wavelength is given by
[tex]\lambda = \frac{h}{P}[/tex]
Where,
h = Planck's constant
p = Momentum
The momentum of a particle can be expressed in terms of energy, that is,
[tex]P = \sqrt{E*2m}[/tex]
Where,
m = mass
E = Energy (potential or kinetic)
Therefore replacing this value at lambda,
[tex]\lambda = \frac{h}{\sqrt{E*2m}}[/tex]
[tex]\lambda = \frac{6.625*10^{-34}}{\sqrt{(4.224*10^{-17})*2(1.67*10^{-27})}}[/tex]
[tex]\lambda = 1.763*10^{-12}m[/tex]
