In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals $P$, $Q$ and $R$ are $E_P, E_Q$ and $E_R$, respectively, and they are related by $E_P=2 E_Q=2 E_R$. In this experiment, the same source of monochromatic light is used for metals P and Q while a different source of monochromatic light is used for the metal $R$. The work functions for metals $P$, Q and R are $4.0 \mathrm{eV}, 4.5 \mathrm{eV}$ and 5.5 eV , respectively. The energy of the incident photon used for metal R, in eV, is $\_\_\_\_$ .