The remote control of a TV emits infra-red light of wavelength $900\mathrm{nm}$. The TV detector is made of a semiconductor whose band gap is $x \mathrm{eV}$. The detector is shielded by a semiconductor optical filter whose band gap is $y \mathrm{eV}$. From the four options below, select the best option for the TV to function.

Given below are two statements:

Statement $\mathrm{I}:$ Two photons having equal linear momenta have equal wavelengths.

Statement $\mathrm{II}:$ If the wavelength of the photon is decreased, then the momentum and energy of a photon will also decrease.

In the light of the above statements, choose the correct answer from the options given below.