The energy of a single photon of frequency f is equal to
[tex]E=hf[/tex]
where h is the Planck constant. Using the relationship between frequency f and wavelength [tex]\lambda[/tex]:
[tex]f= \frac{c}{\lambda} [/tex]
where c is the speed of light, we can rewrite the energy of the photon as
[tex]E=h \frac{c}{\lambda} [/tex]
The photons in the problem have wavelength [tex]\lambda=739 nm=739 \cdot 10^{-9}m[/tex], so their energy is
[tex]E=h \frac{c}{\lambda}=(6.6\cdot 10^{-34}Js) \frac{3\cdot 10^8 m/s}{739 \cdot 10^{-9}m}=2.7\cdot 10^{-19}J[/tex]
However, this is the energy of a single photon. In the problem we have 1 mol of photon, and 1 mol corresponds to
[tex]N_A = 6.023 \cdot 10^{23}[/tex] photons (Avogadro number)
so, to find the total energy of 1 mol of photon, we should multiply the energy of a single photon by the number of photons:
[tex]E_t = N_A E = (6.023 \cdot 10^{23})(2.7 \cdot 10^{-19}J)=1.63 \cdot 10^5 J[/tex]
