$($a$)$ An electron is accelerated through a potential difference of $55$ kV $.$ After striking a target nucleus of a certain material, a photon of wavelength $0\mathrm{.}51{10}^{-10}m$ is liberated.

$($i$)$ Compute the energy of the electron after the interaction?

$[3$ Marks$]$

$($ii$)$ What is the maximum photon frequency that this accelerated electron is capable of generating in the material?

$[3$ Marks$]$

$($b$)$ Explain the phrase "Wave particle duality".

$[3$ Marks$]$