Calculate the energy of one mole of photons of radiation whose frequency is $5 \times 10^{14} \ Hz$.

The energy $(E)$ of one photon is given by the expression: $E = h \nu$.
Given:
$h = 6.626 \times 10^{-34} \ J \ s$
$\nu = 5 \times 10^{14} \ s^{-1}$
Energy of one photon:
$E = (6.626 \times 10^{-34} \ J \ s) \times (5 \times 10^{14} \ s^{-1}) = 3.313 \times 10^{-19} \ J$.
Energy of one mole of photons:
$E_{mole} = (3.313 \times 10^{-19} \ J) \times (6.022 \times 10^{23} \ mol^{-1}) = 199508.26 \ J \ mol^{-1} \approx 199.51 \ kJ \ mol^{-1}$.