A metal having a work function of $2\mathrm{.}5$ eV is illuminated with white light that has a continuous wavelength band from $400$ nm to $700$ nm $.$ For which one of the following ranges of the wavelength band in this white light are photoelectrons NOT produced? $,c=3\mathrm{.}00{10}^8\frac{m}{s},1eV=1\mathrm{.}60{10}^{-19}J)$

A$)500$ nm to $700$ nm